2022

[1]Tao Meng

1]School of Computer and Information Engineering, Central South University of
Forestry and Technology, Changsha, 410082, Hunan, China 2]Department of
Computer Science, State University of New York, New Paltz, New York 12561, USA

# A Multi-view Mask Contrastive Learning Graph Convolutional Neural Network
for Age Estimation

Yiping Zhang<EMAIL_ADDRESS>Yuntao Shou<EMAIL_ADDRESS><EMAIL_ADDRESS>Wei Ai<EMAIL_ADDRESS>Keqin Li<EMAIL_ADDRESS>[  [

###### Abstract

The age estimation task aims to use facial features to predict the age of
people and is widely used in public security, marketing, identification, and
other fields. However, the features are mainly concentrated in facial
keypoints, and existing CNN and Transformer-based methods have inflexibility
and redundancy for modeling complex irregular structures. Therefore, this
paper proposes a Multi-view Mask Contrastive Learning Graph Convolutional
Neural Network (MMCL-GCN) for age estimation. Specifically, the overall
structure of the MMCL-GCN network contains a feature extraction stage and an
age estimation stage. In the feature extraction stage, we introduce a graph
structure to construct face images as input and then design a Multi-view Mask
Contrastive Learning (MMCL) mechanism to learn complex structural and semantic
information about face images. The learning mechanism employs an asymmetric
siamese network architecture, which utilizes an online encoder-decoder
structure to reconstruct the missing information from the original graph and
utilizes the target encoder to learn latent representations for contrastive
learning. Furthermore, to promote the two learning mechanisms better
compatible and complementary, we adopt two augmentation strategies and
optimize the joint losses. In the age estimation stage, we design a Multi-
layer Extreme Learning Machine (ML-IELM) with identity mapping to fully use
the features extracted by the online encoder. Then, a classifier and a
regressor were constructed based on ML-IELM, which were used to identify the
age grouping interval and accurately estimate the final age. Extensive
experiments show that MMCL-GCN can effectively reduce the error of age
estimation on benchmark datasets such as Adience, MORPH-II, and LAP-2016.

###### keywords:

age estimation; graph neural network; contrastive learning; extreme learning
machine

##  1 Introduction

Age estimation plays a significant role in human-computer interaction and
computer vision, with promising applications in face retrieval, social media,
market analysis, human-computer interaction, and security monitoring [67, 47,
46, 68, 38, 51]. However, various intrinsic factors such as gender and race
and extrinsic factors such as facial expressions, facial decoration, dressing,
body postures, and background environmental factors make age estimation
complex and challenging [1, 43, 48, 49, 53, 2].

In the past few years, there has been a flurry of research in this area, with
various approaches emerging [9, 18, 37, 52, 55, 50, 56]. Typically,
traditional age estimation approaches could be categorized into five different
types: classification methods, regression methods, label distribution, ranking
methods, and hybrid methods [1, 20, 54, 3, 39]. Traditional methods are mainly
based on handcrafted models that employ image processing filtering techniques
for feature extraction and machine learning algorithms, such as decision trees
and support vector machines. However, these techniques are insufficient to
cope with the complexity of real-world environments and practical
applications, as they cannot effectively deal with facial images that exhibit
variations in scale, rotation, and lighting [18, 42, 4].

To address the challenges posed by these complex environments, current age
estimation methods leverage convolutional neural networks (CNNs) to recognize
challenging facial images and achieve robust age estimation [36, 43, 23]. Li
_et al._ [36] proposed using local regressors to delineate age data regions,
gated network simulations to construct regression forests to provide
continuous age weights, and regression-weighted combinations to obtain
estimated ages. Rothe _et al._ [43] proposed age prediction based on the
expectation values of convolutional networks for classification while building
an IMDB-WIKI face dataset as a pre-training dataset. Gürpinar _et al._ [23]
proposed a two-stage system for estimating with a face detector based on a
deformable partial CNN model, and a kernel extreme learning machine is used
for classification. Zhang _et al._ [69] presented C3AE leveraging a multi-
scale feature stitching approach to compensate for the small model fitting
problem through two levels of serial supervision.

In addition, with the great fire of the Transformer in the vision field, Xue
_et al._ [66] proposed TransFER to learn different relation-aware local
representations of facial expression features based on the transformer. Wan
_et al._ [60] proposed a novel spatial FAT for Face Attribute Transformer
(FAT) and its variants to achieve high-quality makeup migration. FAT can model
the deep semantic correspondence and interaction between source and reference
faces and accurately estimate and convey face attributes. Moreover, Xia _et
al._[62] proposed the Sparse Local Patch Transformer (SLPT) method to learn
the intrinsic relationship between key feature points, which can better
capture facial information, and its effect exceeds the previous CNN model.

Nevertheless, although CNNs and Transformers have achieved good results in
many fields, they process images, text, and other data using the traditional
Euclidean space, i.e., structured data for representation, which is inflexible
and redundant for image data with complex structural semantics. Especially for
human faces, the main information is concentrated around the key points of the
human faces, including the mouth, eyebrows, eyes, nose, etc. As shown in Fig.
1, the emergence of Graph Neural Networks (GNNs) [25] provides an effective
method for complex structural semantic feature extraction. In order to
minimize the excessive proliferation of nodes, ViG (Vision gnn) draws on ViT’s
concept of segmentation to divide the image into smaller patches, a division
that introduces complex dependencies between nodes and their nearest neighbors
to construct an adaptive graph. Compared with CNNs and Transformers, utilizing
GNNs [70] can overcome the limitations of limited receptive fields and regular
locations, thus effectively capturing long-range contextual information in
non-Euclidean spaces. Therefore, we believe that GNNs can better deal with the
key features of faces and their connections.

Figure 1: The illustration of CNN, Transformer, and GNN on image
representation. a) CNN uses convolution operators to extract features on
images with grid structure. b) Transformer uses the attention mechanism to
extract features on images with sequence structure. c) GNN uses the
information aggregation mechanism to extract features on images with graph
structure. The graph structure encompass sequences and grids as varied
instances capturing long-range contextual information. Therefore, GNN extracts
image features with more flexibility and little redundancy.

To better implement vision tasks, using GNN alone is not enough to realize its
potential [28, 29, 70]. For example, when faced with limited face datasets, we
may need to combine self-supervised learning (SSL). There are two families of
self-supervised approaches: contrastive SSL and generative SSL. Contrastive
learning (CL) is the dominant self-supervised learning paradigm in the pre-
training stage by employing simple discriminations to extract features, which
bring the distance between positive samples closer and pushes the distance
between negative samples further. Relying on robust data augmentation, MoCo
[26] and SimCLR [10] are two iconic contrastive learning methods that use a
siamse network structure to maximize the consistency of learned
representations between similar samples. Corresponding to contrastive
learning, masked image modeling (MIM) as generative SSL, enlightened by the
idea of masked language modeling (MLM) in NLP [16], randomly masks several
image patches and then reconstructs the masked image patches in an
autoencoding manner. BeiT [6] used a pre-trained discrete variational
autoencoder (dVAE) for image token sorting. MAE [27] proposed an asymmetric
encoder-decoder framework that reconstructs the original pixels from the
underlying representation. Moreover, at the graph level [28], Variational
graph auto-encoders (VGAE) predicted the edge of loss, embedding propagation
(EP) proposed to restore the vertex features, and GPT-GNN proposed an
autoregressive architecture for iteratively performing node and edge
reconstruction. However, contrastive learning and masked image modeling both
have deficiencies and limitations. Masked image modeling optimizes local
features to achieve the reconstruction goal but lacks semantic information
about the learned features. In contrast, contrastive learning learns latent
discriminability through relationships between different images, leading to
more semantically meaningful representations. Therefore, considering the
merits and defects of both methods, we integrate the two methods better to
extract different distinctive features for the input image.

Motivated by the analysis above, we propose a Multi-view Mask Contrastive
Learning Graph Convolutional Neural Network (MMCL-GCN) for age estimation.
MMCL-GCN is a hybrid structure. First, a graph convolutional neural network
(GCN) is designed to extract image features, and then a classifier and
regressor based on an extreme learning machine (ELM) are designed to estimate
age. Specifically, the overall structure of the MMCL-GCN network contains a
feature extraction stage and an age estimation stage. In the feature
extraction stage, we introduce a graph structure to construct face images as
input and then design a multi-view mask contrastive learning mechanism to
learn complex structural and semantic information about face images. The
learning mechanism employs an asymmetric siamese network architecture, which
utilizes an online encoder-decoder structure to reconstruct the missing
information from the original graph and utilizes the target encoder to learn
latent representations for contrastive learning. Furthermore, to promote the
two learning mechanisms better compatible and complementary, we adopt the
primary node masking strategy for the online encoder, the secondary edge
dropping strategy for the target encoder and optimize the joint losses. Both
encoder and decoder can use GNN as the backbone network, which can be GCN
[33], GIN [58], or GAT [64]. In the age estimation stage, to fully use the
image features extracted by the online encoder, we choose the extreme learning
machine instead of the traditional softmax method for the classification and
regression tasks of age estimation. Technically, to deal with high-dimensional
features more effectively and avoid model degradation, we design a multi-layer
extreme learning machine (ML-IELM) with identity mapping. Then, a classifier
and a regressor were constructed based on ML-IELM, which were used to identify
the age grouping interval and accurately estimate the final age. Our
contributions to this paper are summarized as follows:

  * •

A novel image feature extraction method with a Multi-view Mask Contrastive
Learning framework, i.e., MMCL, is proposed. MMCL can effectively fuse
contrastive learning and mask image reconstruction to learn latent
discriminative features and high-level local features of images.

  * •

A multi-layer extreme learning machine with identity mapping (ML-IELM) is
designed, and constructing classifiers and regressors based on ML-IELM can
effectively reduce the age estimation error.

  * •

Finally, extensive experiments on three popular benchmark datasets, MORPH-II,
LAP-2016 and Adience, show that MMCL-GCN outperforms existing comparison
algorithms in terms of mean absolute error and normal score
($\epsilon$-error).

##  2 Related Work

In this section, the self-supervised methods are first introduced, including
masked image autoencoders and contrastive learning. Then we briefly describe
the frontier research of graph neural networks. Finally, we retrospect several
related works in age estimation, especially those deep learning-based methods.

###  2.1 Contrastive Learning

Contrastive learning has received significant attention in various self-
supervised and unsupervised paradigms [10, 26, 34]. It entails learning
feature representations from unlabeled data and using them in downstream
tasks. In the learning process, it constructs positive and negative instances
such that positive instances are closer together in the projection space, and
negative instances are pushed away.

Contrastive Multi-view Coding (CMC) [34], an early adopter of multi-view
contrastive learning, demonstrated the flexibility of contrastive learning and
the feasibility of multi-view multimodality. After that, MoCo [26] and SimCLR
[10] are two important foundational works that push the boundaries of
contrastive learning. MoCo is very similar to Inst Disc in that it utilizes a
queue instead of a memory bank to store negative samples, allowing it to take
more negative examples from contrastive learning. Moreover, MoCo replaced the
constraint term in the loss with a momentum encoder, thus achieving a better
result with a momentum update encoder. In SimCLR, the authors pointed out that
strong data augmentation is crucial for contrastive learning, and they also
made use of a negative sample during the training period. Most importantly,
they suggested using a non-linear projection head and maximizing the protocols
expressed in the plan. BYOL drew on the core principles of MoCo and SimCLR and
introduced an online encoder after the projection head to predict the output
of the momentum encoder. Furthermore, SimSiam [11] proposed the simple Siamese
networks by replacing momentum updates through stop-gradient techniques. Based
on siamese networks [11] and extensions of MoCo and BYOL, MoCo-v3 [12] and
DINO [8] leveraged visual transformers (ViT) as the backbone of their models
with better success.

Although contrastive learning has achieved good performance in the self-
supervised domain of images, it focuses on learning global discriminative
features and lacks the attention of local information.

###  2.2 Masked Image Encoding

Mask coding is a standard method for generative self-supervised learning for
pre-training, which aims to reconstruct the missing information of the
original data, and was originally widely used in the field of natural language
processing (NLP) [16, 6].

In NLP, Masked Language Modelling (MLM) [16] has shown great versatility in a
variety of downstream tasks. BEiT [6] is pioneering work in transferring the
BERT form of pre-training to the field of vision and introducing the task
concept of MIM pre-training. Aligned with the success of ViT [17], masked
modeling extends to visual tasks with great potential. MAE (Masked
Autoencoders) [27] proposed an alternative ViT backbone network that uses
random masks to process the input image blocks, and direct reconstruction of
masked image blocks for training. SimMIM [63] proposes a simple mask learning
framework, MaskFeat, which achieves SOTA results. In MaskFeat [61], the
reconstruction target changed from the original pixel values to the low-level
local features (HOG) descriptors, which no longer relied on large datasets and
improved pre-training efficiency.

Although masked image modeling has achieved good performance, autoencoders
encourage preserving information in the latent representation rather than
modeling the relationship between different images for contrastive learning.
Several current works have proposed methods that use a similar siamese
structure assembling two components [5, 30]. This motivates us to further
investigate combining contrastive learning and masking image modeling at the
graph level to develop an enhanced pre-training model that learns different
data features in a complementary manner.

###  2.3 Graph Neural Networks

Graph neural networks (GNNs) [25] have become an increasingly popular method
for studying graph-structured data. GNNs achieve state-of-the-art performance
in various tasks such as node classification, link prediction, and graph
classification by aggregating information iteratively through neighboring
nodes and updating the node representations [64].

Early GNNs mainly focused on how to aggregate node information in a graph
structure. Micheli _et al._ [40] proposed an early formation of spatially
based graph convolutional networks through structurally compound non-recursive
layers. Bruna _et al._ [7] first proposed graph-based convolution on spectral
graph theory. Hamilton _et al._ [24] proposed GraphSAGE for efficient
computation and generalization capabilities by means of parameter sharing.
Casanova _et al._ [58] developed the graph attention network (GAT), which
computed the hidden representation of each node and followed a strategy of
self-attentive clustering of neighbors. Liu _et al._ [57] proposed the
Generative Interaction Network (GIN) to learn the iterative message-passing
procedures on graphs. Jiang _et al._ [31] proposed local graph elastic
convolutional networks (GeCNs) for sparse graph data representation learning.

Moreover, as self-supervised methods have made a splash in computer vision,
graph neural networks have also begun to explore these methods. Petar _et al._
[59] proposed DGI (Deep Graph Infomax) using contrastive learning on graph-
structured data. Hou _et al._ [28] proposed GraphMAE utilizing masked graph
autoencoders, which could outperform graph contrastive learning models. Shahid
_et al._ [44] proposed VA-GNN utilizing an unsupervised reposition approach
and jointly designed a VA neural network to achieve skeleton-based recognition
of human actions. Xu _et al._ [65] proposed Topology-aware CNN (Ta-CNN), which
implement the topology modeling power of GCNs using a CNN. Ju _et al._ [32]
introduced PARETOGNN achieving self-supervised by manifold pretext tasks
observing multiple philosophies.

With the continuous promotion of the application range of GNNs, Kai Han _et
al._ [25] recently proposed the GNN-based visual task processing architecture
ViG and achieved state-of-the-art performance in target detection. Since ViG
can process image data without being limited by the location of features and
can capture potentially complex structural relationships between features,
more and more researchers use ViG as the backbone network for visual tasks.
For example, Yu Zhang _et al._ [70] proposed a GCG-Net network for geographic
image classification in combination with a grouping optimization strategy.
Junjun Huang _et al._ [29] proposed an MGNN network for real-time polyp
detection using a masking strategy.

The above methods are well-explored for applying GNNs to processing vision
tasks. This paper explores a new direction of graph representation learning
for vision tasks, combining generative SSL and contrastive SSL to achieve more
powerful vision performance.

###  2.4 Age Estimation

In computer vision, advances in deep learning and countless studies have
achieved better results in age estimation [1]. These studies can be
categorized as single or hybrid structure-based approaches [19].

In a single-structure-based age estimation study, Chen [9] proposed a ranking-
CNN for age prediction that has a range of basic networks trained with regular
labels. Hassncer _et al._ [35] proposed a shallow CNN structure containing
three convolutional layers and two fully designed layers to learn feature
representations. Rothe _et al._ [43] estimate appearance age based on VGG-16
and the DEX (deep expectation of apparent age), the framework is pre-trained
on ImageNet, and the regression task is defined as a classification task with
softmax expectation refinement.

Furthermore, fusing several techniques has become popular in age estimation
due to hybrid architectures’ complementary advantages. Duan _et al._ [19]
proposed an ensemble structure called CNN2ELM, which consists of a three-layer
model, including feature extraction, feature fusion, and age prediction.
First, they trained three networks corresponding to attributes such as age,
gender, and race to extract and fuse different features from images of the
same person. Then, based on the extreme learning machine, they constructed an
age interval classifier and a specific age regressor for final age prediction.
Then Li _et al._ [36] proposed BridgeNet for age estimation, consisting of two
components: a gated network and a local regressor which could learn together
in an end-to-end manner.

However, the above age estimation methods are all based on CNNs, which can
only model the grid structure of images. In addition, single-layer extreme
learning machines cannot handle high-dimensional data well. In this paper, we
study age estimation based on hybrid structures, exploring the combination of
GNN and ELM models to enhance age estimation performance and achieve as
compact as possible while being more robust.

##  3 METHODOLOGY

This section details the proposed approach of multi-view mask contrastive
learning (MMCL) for image feature extraction and multi-layer extreme learning
machine with identity mapping (ML-IELM) for age estimation. The overall
framework is shown in Fig. 2.

Figure 2: The overall framework of MMCL-GCN contains two stages: feature
extraction stage and age estimation stage. In the feature extraction stage, we
introduce a graph structure to construct face images as input and then design
a Multi-view Mask Contrastive Learning (MMCL) mechanism to learn complex
structural and semantic information about face images. MMCL utilizes an online
encoder-decoder structure to reconstruct the masked patches from the original
graph and a target encoder for contrastive learning. Moreover, it adopts the
graph augmentation strategies and optimizes the joint losses to promote better
compatible and complementary.

In the age estimation stage, to achieve robust age estimation, we use a multi-
layer ELM classifier and regressor with identity mapping for preliminary age
grouping and final age prediction, respectively.

###  3.1 Overview

The complete process of MMCL-GCN consists of two stages: the feature
extraction stage and the age estimation stage. Before giving a specific
design, we encountered and answered the following questions.

Q1: _How to better exploit the potential of graph neural networks in vision
tasks?_

Q2: _Is it feasible to combine contrastive learning and masked image modeling
and how to design an effective combination?_

Q3: _How to design architecture for more accurate and robust age prediction?_

In the feature extraction stage, we introduce constructing images via graph
structures as input and design multi-view mask contrastive learning (MMCL) to
learn complex structural semantics for vision tasks. Q1: Our learning
mechanism is an effective combination of contrastive learning, which can learn
more discriminative global features, and mask reconstruction, which can learn
important local features for restoration. Q2: Moreover, MMCL utilizes an
online encoder-decoder structure to reconstruct the masked information from
the original graph and a target encoder for contrastive learning. After MMCL
optimizes a reconstruction loss and a contrastive objective, we obtain a
robust and efficient online encoder for graph-level feature extraction. In the
age estimation stage, we use the facial features extracted by the online
encoder for age estimation. Q3: To achieve more accurate and robust age
estimation, we designed a multi-layer extreme learning machine (ML-IELM) with
identity mapping. Then we utilized an ML-IELM classifier for preliminary age
grouping and an ML-IELM regressor for final age prediction.

###  3.2 Framework of MMCL

Multi-view mask contrastive learning mainly consists of graph construction and
graph feature extraction. Below we describe these two components in detail.

Graph Construction: For an input 2D image $I$, whose resolution is
$\left(H,W\right)$ and the channel is $C$, $I\in\mathbb{R}^{H\times W\times
C}$ is converted and tokenized to $N$ patches, where $P^{2}$ is the resolution
of each image patch, and the resulting number of patches is $N=HW/P^{2}$. Then
all patches are embedded into $M$ feature dimension, the feature vector
$X=\left\\{x_{i=1}^{n}\right\\}\in\mathbb{R}^{N\times M}$. Moreover, we obtain
a graph $\mathcal{G}\left(V,E\right)$ where V denotes all the nodes, $E$
denotes all the edges, $D$ denotes the degree matrix and the connectivity of
the nodes is computed by the adjacent matrix $A=\mathbb{R}^{n\times n}$ ($n$
is the number of nodes). Specifically, let the feature node $v_{i}$ has $K$
nearest neighbors $\Bbbk\left(v_{i}\right)$ and indicate the edge from node
$i$ to node $j$ by $e_{ij}$.

Graph Feature Extraction: After constructing a graph based on image features,
we investigate the methods to extract graph features through GNNs. When
transforms the image patches as graph node feature vectors, GNNs process them
for efficient information exchange between image blocks, and compute the
feature distances to determine the nearest neighbor. This graph representation
learning has significant advantages in that it not only extracts richer
information through a larger receptive field but also overcomes the deficiency
of neural networks in processing images through a regular grid, which
facilitates the detection of irregular and complex defects.

A common expression for a graph convolutional neural network (GCN) is:

$\displaystyle
H^{l+1}=\sigma\left(\tilde{D}^{-\frac{1}{2}}\tilde{A}\tilde{D}^{-\frac{1}{2}}H^{l}\varTheta^{l}\right)$
(1)

where $\tilde{A}=A+I$, $I$ is the unit matrix,
$\tilde{D}=\sum_{j}{\tilde{A}_{ij}}$ is the degree matrix, $H^{0}$ of the
input layer is $X$, $H^{l}$ is the embedding of the graph nodes in the $l$-th
layer, $\varTheta^{l}$ is the trainable weight and is the activation function.

GCNs basically follows a strategy of aggregating information about its
neighbors, i.e., by aggregating the representations of neighboring nodes and
then updating the representation of the current node. The structural
information of the $k$-th neighborhood could be captured after $k$ iterations,
and a $k$-layer graph neural network generalization can be expressed as:

$\displaystyle
a_{v}^{(k)}=AG{G^{(k)}}\left({\left\\{{h_{{v^{\prime}}}^{(k-1)}:{v^{\prime}}\in\Bbbk(v)}\right\\}}\right)$
(2)

$\displaystyle
h_{v}^{\left(k\right)}=COM^{\left(k\right)}\left(h_{v}^{\left(k-1\right)},a_{v}^{k}\right)$
(3)

where $a_{v}^{\left(k\right)}$ is the feature embedding of aggregated neighbor
nodes, $h_{v}^{\left(k\right)}$ is the $k$-th layer embedding of the vertex,
$\Bbbk\left(v_{i}\right)$ denotes a set of vertices adjacent to $v_{i}$, and
$AGG^{\left(k\right)}\left(\cdot\right)$ and
$COM^{\left(k\right)}\left(\cdot\right)$ are the aggregation function and
activation function of the GNN layer. In different cases, it is necessary to
choose different $AGG\left(\cdot\right)$ function and $COM\left(\cdot\right)$
function. In GCN, average pooling is used instead of maximum pooling, and the
$AGG\left(\cdot\right)$ function and $COM\left(\cdot\right)$ function is
defined as:

$\begin{split}h_{v}^{(k)}=ReLU\left({W\cdot
MEAN\left({\left\\{{h_{{v^{\prime}}}^{(k-1)}:{v^{\prime}}\in{\Bbbk
k}(v)}\right\\}}\right)}\right)\end{split}$ (4)

After $k-$layer propagation, the output embedding of $\mathcal{G}$ is
summarized at the layer by $READOUT\left(\cdot\right)$ function. Finally, the
node features are aggregated to obtain graph-level features $h_{\mathcal{G}}$
and adopt a multi-layer perceptron (MLP) for downstream task:

$\displaystyle h_{\mathcal{G}}=READOUT\left(\left\\{h_{v}^{(k)}\mid
v\epsilon\mathcal{G}\right\\}\right)$ (5) $\displaystyle
z_{\mathcal{G}}=MLP\left(h_{\mathcal{G}}\right)$ (6)

Multi-view Mask Contrastive Learning: In particular, our architecture adopts
an asymmetric siamese network that has an online encoder, an online decoder,
and a target encoder. The online encoder-decoder learns local latent features
by reconstructing the masked information, and the target encoder provides the
online encoder contrastive supervision to learn the strong instance
discriminability.

Let $\mathcal{F}_{o}\left(\cdot\right)$ as the online encoder,
$\mathcal{F}_{t}\left(\cdot\right)$ as the target encoder,
$\mathcal{H}_{o}\left(\cdot\right)$ as the online decoder, the parameters of
$\mathcal{F}_{o}\left(\cdot\right)$ as $\varTheta_{o}$ and
$\mathcal{F}_{t}\left(\cdot\right)$ as $\varTheta_{t}$. The encoder maps the
feature vector $X=\left\\{x_{i=1}^{n}\right\\}$ to embedding feature
$H=\left\\{h_{i=1}^{n}\right\\}$. Generally, reconstruct the input image as:

$\displaystyle
H=\mathcal{F}\left(A,X\right)=\sigma\left(\tilde{D}^{-\frac{1}{2}}\tilde{A}\tilde{D}^{-\frac{1}{2}}H^{l}\varTheta^{l}\right)$
(7) $\displaystyle\mathcal{G}^{\prime}=\mathcal{H}\left(A,H\right)$ (8)

The type of online encoder and target encoder are the same expressive GNNs
while the online decoder is a shallow GNN. In the optimization process, to
slow down the parameter changes of the target network, different from the
online encoder updates parameters $\varTheta_{o}$ by back propagation, the
target encoder updates parameters $\varTheta_{t}$ by exponential moving
average [26]:

$\displaystyle\varTheta_{t}\leftarrow
m\varTheta_{t}+\left(1-m\right)\varTheta_{o}$ (9)

where $m\in\left[0,1\right)$ is the momentum hyperparameter and we set to
0.999. The momentum update rule propagates the update gradually from
$\varTheta_{t}$ to $\varTheta_{o}$ , so that $\varTheta_{o}$ evolves smoothly
and consistently.

Figure 3: The examples of our major graph augmentation methods, including Edge
Dropping,and Node Masking.

Further, as shown in Fig. 3, to augment our samples, we apply a primary node
masking strategy with a mask matrix $\left[M_{0}\right]$ for the online
encoder. Node masking refers to the random masking features of some nodes on a
given graph, either completely masking the feature vector or masking several
parts of the feature vector, which can be formally defined as:

$\displaystyle t_{i}\left(X\right)=M_{0}\otimes X$ (10)

where $\left[M_{0}\right]$ is the mask matrix.

Then the online decoder through $\mathcal{H}_{o}\left(\cdot\right)$ maps the
embedding feature $H$ back to the feature vector $X^{\prime}$. As graphs, the
amount of information reconstructed by the decoder is comparatively more
insufficient than the multi-dimensional node features. Regular decoder or
simple multi-layer perceptron (MLP) decoding expression ability is low, so we
choose more expressive GNN as our decoder.

Additionally, for the target decoder, to better learn neighborhood
information, we employ a secondary edge dropping strategy. Edge dropping is
one of the most commonly used topology enhancement methods, which focuses on
perturbing the graph adjacency matrix by randomly dropping some edges:

$\displaystyle t_{i}\left(A\right)=M_{1}\otimes A$ (11)

where $M_{1}$ is the drop matrix.

After that, we take the generated latent representation from the online
encoder and target encoder to contrastive learning, where the online decoder
is used to conduct the reconstruction tasks. Through multiple rounds of
training and optimization of joint losses, contrastive learning can learn
potential discriminability by relationships between different images, and
masked image modeling can obtain high-level local features by reconstructing
masked blocks. After possessing robust feature representation learning
capability, only the online encoder is utilized for downstream age estimation.

###  3.3 Training Objective

Reconstruction loss: Corroborating the findings of [28], MSE (mean square
error) loss may not be enough for feature reconstruction while existing graph
autoencoders (GAEs) have adopted MSE as their reconstruction criteria. Based
on it, we employ the scaled cosine error (SCE) for our autoencoders computing
reconstruction loss, which is formulated as follows:

$\displaystyle\mathcal{L}_{rc}=\frac{1}{\lvert\tilde{V}\lvert}\sum\left(1-\frac{x_{i}^{T}x_{i}^{\prime}}{\left\|x_{i}\right\|\cdot\left\|x_{i}^{\prime}\right\|}\right)^{\gamma},\gamma\geqslant
1$ (12)

where $\tilde{V}$ denotes the masked subset nodes of $V$, $x_{i}$ is the
primitive image features, $x_{i}^{\prime}$ is the reconstructed output. The
scaling factor $\gamma$ is a hyper-parameter adjustable among different
datasets and the loss is averaged over all masked nodes.

Figure 4: The illustration of training objective. MMGL adopts an asymmetric
siamese network, utilizes graph augmentation methods and minimizes the joint
losses to promote organic combination of the two mechanisms.

Contrastive loss: In order to simulate the performance of real-life images
under the influence of lighting, angle and other factors, we perform data
augmentation by changing the grayscale and shifting the original image.
Through data augmentation while preserving the content to form a positive
sample, we generate two views ${I_{i}}$, $I_{i}^{+}\in\mathbb{R}^{H\times
W\times C}$ of each image and respectively provide them to the online encoder
and target encoder. And we store the other images in a batch as the negative
samples for contrastive objective. Moreover, after encoding, we used the MLP
projection head $\mathcal{P}\left(\cdot\right):\mathbb{R}^{N\times
M}\mapsto\mathbb{R}^{N\times M}$ to project the graph representation into the
space where the contrastive loss is computed.

Our contrastive objective is based on the augmentation of the original image,
following RELIC [14], introducing an invariance objective, which ensures that
a data point and its positives and negatives are invariant in the expansion of
that data point. To optimize the invariance, we define the Kullback-Leibler
divergence between the probabilities of two augmented data views as the
invariance loss, which is formulated as:

$\displaystyle
KL\left(P\left(\mathcal{G}_{i}\right)\left\|P\left(\mathcal{G}_{i}^{+}\right)\right.\right)=sg\left[\mathbb{E}_{P\left(\mathcal{G}_{i},\mathcal{G}_{i}^{+}\right)}\log
P\left(\mathcal{G}_{i},\mathcal{G}_{i}^{+}\right)\right]$ (13)
$\displaystyle-\mathbb{E}_{P_{\left(\mathcal{G}_{i},\mathcal{G}_{i}^{+}\right)}}\log
P\left(\mathcal{G}_{i},\mathcal{G}_{i}^{+}\right)$

where $P$ is the data probability distribution, $KL\left(\cdot\right)$ is the
Kullback-Leibler (KL) divergence, $\mathcal{G}_{i}^{+}$ is the augmented
sample of $\mathcal{G}_{i}$ , and $sg\left(\cdot\right)$ denotes the stop
gradient, which can avoid degenerate solutions during optimization.

In addition to this, we managed to combine the usual contrastive loss InfoNCE
[26] and modify it to fit the graph level shown as:

$\displaystyle\mathcal{L}_{cl}=-\alpha\log\frac{\exp\left(\mathcal{G}_{i}\cdot\mathcal{G}_{i}^{+}/\tau\right)}{\sum{{}_{j=0}^{K}\exp\left(\mathcal{G}_{i}\cdot\mathcal{G}_{j}/\tau\right)}}$
(14) $\displaystyle+\eta
KL\left(P\left(\mathcal{G}_{i}\right)\left\|P\right.\left(\mathcal{G}_{i}^{+}\right)\right)$

where $K$ is the batch size, $\tau$ is the temperature constant,
$\mathcal{G}_{i}^{+}$ is the positive sample obtained by data augmentation of
$\mathcal{G}_{i}$ and $\mathcal{G}_{j}$ is the negative sample of
$\mathcal{G}_{i}$ originating from different images in the queue. The relative
importance of the contrastive loss and invariance loss is weighted by the
$\eta$ scalar.

Overall, Fig. 4 explicitly shows the training architecture. The training
objective is a weighted loss function by combining reconstruction loss
$\mathcal{L}_{rc}$ and contrastive loss $\mathcal{L}_{cl}$ defined as:

$\displaystyle\mathcal{L}_{MC}=\mu\mathcal{L}_{rc}+\left(1-\mu\right)\mathcal{L}_{cl}$
(15)

The entire inference process of the MMCL pseudocode is contained in Algorithm
1.

Algorithm 1 Multi-view Mask Contrastive Learning (MMCL).
---
Input: images $\mathcal{I}=\left\\{I_{1},I_{2},...,I_{n}\right\\}$, mask
matrix $M_{0}$,drop
matrix $M_{1}$ and hyper-parameters $m$, $\gamma$, $\eta$, $\mu$;
Output: The Online Encoder with parameters $\varTheta_{o}$.
1: for epoch=$1,\ldots,K$ do
2: for sampled minibatch ${{\cal G}_{i}}$, $i$=$1,\ldots,N$ do
3: data augmentation,
$t\left(\mathcal{G}_{i}^{+}\right)\sim\tau\left(\mathcal{G}_{i}\right)$.
// primary node masking.
4: $\mathcal{G}_{i}\sim t_{i}\left(X\right)=M_{0}\otimes X$.
// secondary edge dropping.
5: $\mathcal{G}_{i}^{+}\sim t_{i}\left(A\right)=M_{1}\otimes A$.
// graph encoder.
6: online encoder, $H_{i}=\mathcal{F}_{o}\left(A,t_{i}\left(X\right)\right)$.
7: target encoder,
$H_{i}^{+}=\mathcal{F}_{t}\left(t_{i}\left(A\right),X\right)$.
// graph decoder.
8: target decoder, ${{\cal G}_{i}}^{\prime}={{\cal
H}_{o}}\left({A,{H_{i}}}\right)$.
// parameter update.
9: calculate loss ${L_{rc}}$ by using Eq. (12).
10: calculate loss ${{\cal L}_{cl}}$ by using Eq. (14).
11: calculate loss ${{\cal L}_{MC}}$ by using Eq. (15).
12: update parameters $\varTheta_{o}$ by using Eq. (9).
13: end for
14: end for
15: Return the online encoder network.

###  3.4 Age Estimation

In the age estimation stage, we do supervised training to evaluate the
representations from the online encoder. Our age estimation framework consists
of three components: feature extraction, age grouping, and final prediction.

Feature Extraction: For the feature extraction model, we first pre-train the
model in an unsupervised manner. We then use the corresponding attribute
labels to train and fine-tune the feature extraction model. For age
estimation, we then combine the features extracted by the fine-tuning network
into a feature matrix to train the ELM model.

The classical extreme learning machine (ELM) is a single implicit layer
feedforward neural network with high efficiency, high correctness, and strong
generalization performance, which the output equation of the $i$-th hidden
layer node is:

$\displaystyle h_{i}\left(x\right)=G\left(a_{i},b_{i},x\right)$ (16)

where $a_{i}$ denotes the $i$-th hidden node weight vectors, $b_{i}$ denotes
the $i$-th hidden node weight biases, and $G\left(a_{i},b_{i},x\right)$
denotes a nonlinear piecewise continuous function.

The output is weighted and summed according to whether the task is a
classification or a regression, single or multi-classification, which is
formulated as:

$\displaystyle
f\left(x\right)=\sum_{i=1}^{L}{\beta_{i}G\left(a_{i},b_{i},x\right)=\beta H}$
(17)

where $\beta$ denotes the output weights’ vector, and $H$ denotes the output
matrix of the hidden layer.

That learning goal to minimize the loss function can be written as follows:

$\displaystyle\min:\lambda\left\|f\left(x\right)-T\right\|_{\mu}^{\sigma_{1}}+\left\|\beta\right\|_{\nu}^{\sigma_{2}}$
(18)

where $\sigma_{1}>0$, $\sigma_{2}>0$, and $\mu$, $\nu$ = 0, $\frac{1}{2}$, 1,
···, $+\infty$. $\lambda$ is the parameter that weighs between these two, $T$
is the training data target matrix.

However, there are some shortcomings in classical ELMs, which have limited
learning ability for high-dimensional complex data features and are prone to
overfitting based on empirical risk minimization. Multilayer ELM stacks
multiple ELM into a multilayer ELM autoencoder (ML-ELM), which is suitable for
data dimensionality reduction, image noise reduction, and representation of
high-dimensional complex abstract features. The dimensionality reduction of
features helps improve classification accuracy and reduce the error rate.
Further, this paper adopts ML-IELM (multilayer ELM based on identity mapping)
so that the output neurons can not only obtain the re-coding of data through
the nodes of the last hidden layer but also obtain the data information
directly from the input neurons through the constant mapping, which increases
the richness and comprehensiveness of the data obtained by the output neurons
of the network, and thus achieves the purpose of improving the generalization
and accuracy of the network. The structure of multi-layer extreme learning
machine with identity mapping is shown in Fig. 5.

Figure 5: The illustration of multilayer ELM based on identity mapping.

The mathematical model of ML-IELM is:

$\displaystyle{\cal F}\left(x\right)={\cal
F}\left\\{{{W^{oi}}X+\left({{W^{oh}}\hat{H}}\right)+C}\right\\}$ (19)

where ${{W^{oi}}}$ denotes the weight matrix between the output neuron and the
input neuron, ${{W^{oh}}}$ denotes the matrix of weights between the last
implicit layer and the output layer, ${\cal F}\left(.\right)$ denotes the
identity mapping function, $X$ indicates the input data, ${\hat{H}}$ denotes
the output matrix of the last hidden layer and $C$ denotes the bias term.

The goal of the ML-IELM network is to compute the optimal weight matrix from
the hidden node to the output node so that the network output at that weight
value minimizes the error between the output and the desired output value. The
optimization model of the network is defined as:

$\displaystyle\begin{array}[]{l}\min:\lambda\left\|{{\cal
F}\left(x\right)-T}\right\|_{\mu}^{{\sigma_{1}}}+\left\|\beta\right\|_{\nu}^{{\sigma_{2}}}\\\
=\lambda\left\|{{\cal
F}\left({{W^{oi}}{W^{oh}}C}\right)\left[{\begin{array}[]{*{20}{c}}X\\\
{\hat{H}}\\\
I\end{array}}\right]-T}\right\|_{\mu}^{{\sigma_{1}}}+\left\|\beta\right\|_{\nu}^{{\sigma_{2}}}\end{array}$
(20)

where $\sigma_{1}>0$, $\sigma_{2}>0$, and $\mu$, $\nu$ = 0, $\frac{1}{2}$, 1,
···, $+\infty$. $\lambda$ is the parameter that weighs between these two, $T$
is the training data target matrix and $I$ is the unit matrix.

Age Grouping: First, we use ML-IELM to train the classifier, classify faces
into different age groups, and reduce the task difficulty of subsequent
regressors. During training, we obtain the average weights and biases of the
hidden layers of the ELM classifier model.

Final Prediction: After using ML-IELM classifiers to divide the age groups
into smaller groups, we utilize the smaller age groups with accurate age
labels to train the ML-IELM regressor. During training, we obtain the average
weights and biases of the hidden layer of the ELM regressor. Then we make a
final age prediction via the trained ML-IELM regressor.

##  4 Experiments

In this section, we present experimental details and demonstrate the
effectiveness of the proposed representation learning model MMCL-GCN. The
feature extraction module MMCL (Multi-View Mask Contrastive Learning) in the
MMCL-GCN model can be trained unsupervised. Therefore, we first pre-train MMCL
on ImageNet-1K [15] dataset in a self-supervised manner, where all frames are
extracted. We then further train the MMCL-GCN model on the IMDB-WIKI [43]
dataset in a supervised manner to evaluate the learned representation for age
estimation. After that, we conduct experiments in the popular age estimation
datasets and compare them with the baselines. Taking into account the
characteristics of different datasets, we employ varied criteria to better
accurately assess the model capabilities. The proposed architecture is trained
on an NVIDIA Tesla V100 and implemented with the publicly available Caffe
codes. We resize the original images to 256× 256 pixels, and then select a 224
× 224 crop from the center or the four corners from the entire processed
image. Moreover, we leverage different dropout measures to reduce the risk of
overfitting. In the end, we perform ablation studies on each component to
investigate the individual functions in our framework.

###  4.1 Dataset

Experiments are carried out on a number of age estimation benchmark datasets:
IMDB-WIKI, Morph II [42], Adience Benchmark [21], LAP-2016 Dataset [22]. Our
feature extraction module MMCL is pretrained on ImageNet-1K and IMDB-WIKI
following previous work, and evaluated on the Adience Benchmark, Morph II and
LAP-2016 datasets.

IMDB-WIKI: This dataset is one of the largest age datasets available. The
sources include 20,000 individuals from IMDB (a celebrity website) and
Wikipedia with 460723 and 62328 images, respectively, because it contains more
noise, e.g., multiple faces in one image. Therefore, we only use it for pre-
training and fine-tuning.

MORPH-II: The dataset is the most popular age estimation dataset available,
containing 55,134 images of 13,000 people’s faces, with photos collected by
people aged 16-77 years, with an average age of 33 years. In addition to age,
other attributes about the person was recorded, such as race and gender.
Referring to a widely used evaluation protocol [18], the dataset was randomly
divided into two non-overlapping parts, the training dataset (80$\%$) and the
test dataset (20$\%$).

Adience Benchmark: The dataset consists of 26,580 images of 2,284 people,
divided into eight intervals using interval annotation. The images were taken
in real scenes and are heavily influenced by noise, pose and lighting,
implying a solution to the problem of age and gender detection in the real
life. Both the raw data and corrected faces are available on the website.

LAP-2016 Dataset: The LAP (Look At People) competition was held in 2016 and
consisted of 7,591 images, with each sample labeled with mean $\mu$ and
standard deviation $\sigma$. The LAP-2016 dataset was relatively distributed
across ages 20-40, with fewer datasets in the 0-15 and 65-100 intervals, so we
pre-trained the network on the ImageNet-1K and IMDB-WIKI dataset and then just
fine-tuned the aging network. The dataset is divided into 4,113 training
images, which 1,500 for validation and 1978 for testing.

###  4.2 Unsupervised Training

Following the standard architecture, we use ViG-S [25] as the encoders and a
2-layer shallow GCN as the decoder. We utilize ImageNet-1K for pre-training
with unsupervised manner and each sample generate a view by data augmentation
such as greyscaling and shifting. Although the cotrastive objective requires a
sufficient number of negative examples, we do not need large batches by
default using queue and therefore set the batch size to 1,024. For large
datasets, we use cumulative gradients to simulate large batch sizes. By
default, we pre-trained the model for 1,600 epochs with 50 warm-up epochs. The
learning rate is 1.5e$-$4 with 0.01 weight decay. The mask ratio is set to
0.50 and drop ratio is set to 0.20 by default.

We compare the representation learning performance of MMCL with the computer
vision baselines. For contrastive SSL, MoCo [26] utilized a queue instead of a
memory bank to store negative samples and replaces the constraint term in the
loss with a momentum encoder for better results. SimCLR [10] used more data
augmentation, larger batchsize and a nonlinear projection header to maximize
the agreement expressed in the plan. For generative SSL, MAE [27] employed
random mask to process the input image blocks and reconstructed the masked
image patches for training. CAE [13] introduced latent context regressor to
predict the hidden representation of masked patches based on the hidden
representation of visible patches and then decoded and reconstructed it.

Figure 6: The pre-training performance of MMCL with state-of-the-art methods
in terms of top-1 accuracy on ImageNet-1K.

Then we evaluate our graph representation learning pre-trained model using
top-1 accuracy on ImageNet-1K classification. As shown in Fig. 6, our MMCL
significantly improves the representation learning between masked image
modeling and contrastive learning, which outperforms the state-of-the-art. We
achieve 86.2$\%$ with ViG-S not only outperform the contrastive methods such
as MoCo, but also competitive with the SOTA methods such as MAE (83.6$\%$) and
CAE (83.9$\%$).

###  4.3 Supervised Training

Pre-training: In supervised training, we first load the pre-trained weight and
train the entire model on IMDB-WIKI with both images and the corresponding
labels. By default, the learning rate is 1.5e-3 with 0.01 weight decay.

Fine-tuning: For the age estimation tasks, we train the facial datasets to
obtain strong and robust feature extraction model. The networks are
initialized with the weights gained from training on the ImageNet and IMDB-
WIKI. Following the experiment settings in [19], we evaluate the proposed
method on Morph-II, LAP-2016 dateset and an unconstrained dataset Adience
Benchmark. For the networks, we set the base$\\_$lr as 0.01, momentum as 0.9,
and gamma as 0.1. The weight$\\_$decay is set as 0.0005. For ELM
classification and regression, $\beta$ is set as $\\{$ $10^{-5}$, $10^{-4}$, …
, $10^{2}$, $10^{3}$$\\}$ and $L$ is set as $\\{$1800,2000, … , 4000$\\}$.

Optimization: We use AdamW as the default optimizer for pre-training, fine-
tuning and age estimation, regarding age estimation, AdamW is still preferred,
but we also use stochastic gradient descent (SGD) and LARS. We use the linear
scaling rule: $lr=base\\_lr\times batch\\_size/256$ to set the learning rate.
We also adopted the cosine learning rate schedule with a warmup of 50 epochs.

###  4.4 Evaluation Criteria

MAE(Mean Absolute Error): The mean absolute value of the deviation of each
sample’s label from its corresponding estimate is a useful measure of the
accuracy of the ELM regressor. In general, the mean absolute error (MAE) for
age prediction can be calculated as follows:

$\displaystyle MAE=\frac{1}{N}\sum_{i=1}^{N}\lvert{x_{i}-y_{i}}\rvert$ (21)

where $x_{i}$ denotes the true label, $y_{i}$ is the predicted value, and $N$
represents the number of testing samples.

CS(Cumulative Score): The cumulative score is more appropriate when training
samples are available at essentially every age. The larger the cumulative
score, the better the age estimation performance, which is defined as:

$\displaystyle CS\left(L\right)=\left(n_{e}\leqslant L/N\right)\times 100\%$
(22)

where $n_{e}\leqslant L$ expresses the number of test images whose absolute
error $\epsilon$ of the age estimation is not larger than $L$ years.

Normal Score($\epsilon$-error): Calculate the proportion of samples that are
inaccurately predicted as a percentage of all samples. Owing to the LAP-2016
dataset was labelled through several annotators, the performance of age
estimation can be more accurately measured by taking into account the
following factors. The smaller the $\epsilon$-error, the better the
performance of the age estimation classifier. By fitting a normal distribution
with mean ${\mu}$ and standard deviation ${\sigma}$ of the annotations for
each sample, the $\epsilon$-score is calculated as follows:

$\displaystyle\epsilon=1-e^{-\frac{\left(x-\mu\right)^{2}}{2\sigma^{2}}}$ (23)

Therefore, $\epsilon\in\left(0,1\right)$, and 1 is worst case while 0 denotes
best case.

###  4.5 The State-of-the-Art Baselines Comparison

We compare our proposed architecture with various state-of-the-art estimation
baselines. We classify competing methods into bulky models and compact models
based on their model sizes. For bulky models, DEX [43] was pre-trained in
ImageNet based on VGG-16, defining the regression problem as a classification
problem with softmax expectation refine, which achieved improvement over
direct regression training. BridgeNet [36] divided the data space by a local
regressor to handle heterogeneous data, and utilized a gated network to learn
the continuous weights used by the local regressor. For compact models, SSR-
Net [67] adopted a coarse-to-fine strategy to adjust the predicted age stage
by stage dynamic range. C3AE [69] proposed a multi-scale feature stitching
approach to compensate for the small model fitting problem by two-level serial
supervision.

Age Estimation on the MORPH-II: Our method combines the MMCL with ML-IELM and
compares the performance of MORPH-II with the state-of-the-art baseline
methods. The robustness and effectiveness of MMCL-GCN are analyzed in terms of
the MAEs. Table 1 presents the detailed results, which list the backbone
networks and MAE.

Our method achieves the best performance among previous works. For bulky
models, DEX achieved good results attribute to the recalibration of face image
rotation and pre-training on IMDB-WIKI. BrigeNet jointly trained local
regressors and gated networks that could be easily integrated into end-to-end
models with any other deep neural networks. RANG and EGroupNet took into
account race, gender factors affecting age prediction. Good results have also
been obtained recently for some lightweight compact models. SSR-NET proposed
dynamic soft stagewise that can be panned and scaled, and C3AE is efficient
based on cascading contexts. However, the former is scalable but has more
redundant parameters, while the latter is compact but difficult to handle age
estimation in complex environments. Our model uses a medium-scale graph neural
network and two powerful ML-IELM with multi-factor feature extraction, which
is both robust, compact and scalable.

Table 1: Comparison with the state-of-the-art methods on Morph II. Method | Backbone | MAE | Model size
---|---|---|---
Ranking[9] | - | 2.96 | 2.2GB
DEX[43] | VGG-16 | 2.68 | 530MB
MV[41] | VGG-16 | 2.41 | 530MB
BrigeNet[36] | VGG-16 | 2.35 | 530MB
RANG[19] | CNN | 2.61 | -
EGroupNet[20] | - | 2.48 | -
DLDLF[45] | VGG-16 | 2.19 | 530MB
C3AE[69] | - | 2.78 | 0.25MB
SSR-NET[67] | - | 3.16 | 0.32MB
MMCL-GCN | ViG-S | 2.13 | 47.8MB

We were able to achieve such results attributed to: i) the strong feature
extraction capability in a smaller volume based on graph neural networks,
combined with contrastive learning and masked image modeling. ii) the
effective graph augmentation strategy and the excellent loss function designed
that enable the representation learning beyond convolutional neural networks.
iii) the integrated multiple attributes of race, gender and age, and the use
of classification before regression, which greatly improve the prediction
accuracy.

Age Estimation on the LAP-2016 Dataset: We further provide the results of the
MMCL-GCN evaluated on LAP-2016 dataset. The test error is employed for
evaluation owing to this dataset was labelled through several annotators, so
the performance of age estimation can be more accurately measured by this
criterion. Table 2 presents the final results. Our method achieves 0.2157
$\epsilon$-score outperform the state-of-the-art methods on LAP-2016 dataset.
This is probably attributed to the powerful feature extraction capability of
our graph representation learning model and the more accurate predictions
resulting from the ML-IELM classification and regression strategy.

Table 2: Comparison with the state-of-the-art methods on LAP-2016. The data in the table are mainly from [1]. Method | MAE |  $\epsilon-$error
---|---|---
4-fusion framework | - | 0.3738
RANG[19] | - | 0.3679
EGroupNet[20] | - | 0.3578
VGG+Revised Contrative Loss | - | 0.3679
AGEn | 3.82 | 0.3100
GNN+Mean-Varian Loss | - | 0.2867
AL | - | 0.2859
DLDL-V2 | 3.452 | 0.267
Children-specialized CNN | - | 0.2411
Soft-Ranking | - | 0.232
MMCL-GCN | - | 0.2157

Age Estimation on the Adience Benchmark: We use an unconstrained dataset to
vetisfy the performance of our model, and the average accuracy is more
suitable to evaluate it for which is more difficult to distinguish races
because the images were not manual filtered initially. Table 3 shows the age
estimation results on the Adience Benchmark. We obtained an average accuracy
of 0.7031, which shows that our model is competitive even in complex real-
world environments. This may be attributed to our strong representation
learning model and the benefit of pre-training on large datasets.

Figure 7: The examples of satisfactory estimation (a) and unsatisfactory
estimation (b) on Morph-II (left) and Adience benchmark(right). Despite the
mistakes of our model in some pictures, the deviations of unsatisfactory
predictions from the actual values are basically in the same age group
compared to other methods [19, 67], and we are also better in predicting faces
in the face of some complex environments.

Some samples of age prediction results are provided in Fig. 7, the images on
the left are from the Morph-II and the right are from the LAP-2016 dataset.
(a) shows the satisfactory predictions, illustrating the effectiveness of GNNs
for feature extraction and the reliability of our method. (b) Shows some
unsatisfactory predictions, possibly due to face misdetection, alignment
errors and complex environment.

Table 3: Comparison with the state-of-the-art methods on Adience Benchmark. Method |  Average Accuracy
---|---
DEX[43] |  0.64$\pm$0.042
Best from[20] |  0.5071$\pm$0.051
CNN+ELM[23] |  0.5127$\pm$0.0497
RANG[19] |  0.6649$\pm$0.0508
EGroupNet[20] |  0.6978$\pm$0.0713
MMCL-GCN |  0.7031$\pm$0.0419
Table 4: The ablation study of graph augmentation strategies. index | Node mask | Edge drop | Accuracy
---|---|---|---
1 | $\times$ | $\times$ | 84.5
2 | $\times$ | ✓ | 84.9
3 | ✓ | $\times$ | 85.1
4(MMCL-GCN) | ✓ | ✓ | 85.6

###  4.6 Ablation Studies

To analyze the effectiveness of the key components and methodological
strategies in the architecture and to validate the design we adopted at MMCL-
GCN, we perform a series of ablation experiments, and our performance is based
on the model with 800 pre-training epochs.

The Effects of graph augmentation strategies: We study the influence of the
graph augmentation strategy, and Table 4 shows the result of primary node
masking and secondary edge dropping strategies. The results manifest the
ability of using a graph augmentation strategy alone to achieve a 1$\%$ to
2$\%$ improvement, and a more significant improvement of 2$\%$ to 6$\%$ when
the two are used together. Because our structure is asymmetric, the organic
combination of contrastive learning and masked image modeling, using graph
augmentation strategies can maximize the advantages of both, obtaining both
local and global features. The primary node masking strategy is more helpful
to learn local potential information, and the the secondary edge dropping
strategy is more helpful to learn structural features for global capture, thus
making the representations better compatible and complementary.

The Effects of mask ratio and drop ratio: We further investigate the effect of
node mask ratio and edge drop ratio on representation learning. For most
cases, images have more redundant information and a higher mask ratio is more
helpful for the model to learn features. Fig. 8 (a) shows that in ImageNet-1K,
the optimal mask ratio is 0.5${\sim}$0.75. However, in the facial datasets,
too high a mask ratio degrades the performance. Further, due to the
specificity of our structure, contrastive learning prefers more complete
images for supervision, and too high mask ratio is detrimental to it.
Therefore, our solution adopts a compromise, where the optimal mask ratio is
0.25${\sim}$0.5 in the facial datasets. We default the mask ratio to 0. 5
which the efficiency gain compensates for the small performance loss.

Fig. 8 (b) shows the performance of different edge drop ratios. In most cases,
our model maintains good capability, keeping a low edge drop ratio of
0.15${\sim}$0.2 leads to a large improvement in model performance, while there
is a significant decrease in accuracy as the ratio increases. Probably, the
feature information of the graph is more sensitive to edges, and too high drop
ratio can seriously damage the graph structure. In our experiments, we set the
default drop ratio to 0.2.

Figure 8: The ablation study of mask ratio and drop ratio.

The Effects of contrastive and reconstruction losses: We compare our MMCL-GCN
loss function with baselines MAE and MoCo. Table 5 demonstrates that by
jointly training the optimized contrastive loss and reconstruction loss, we
end up with a smaller target loss. This motivates us that masked autoencoder
and contrastive learning are not only compatible training targets, they are
also complementary. By optimizing the loss function and joint training
optimization, we obtain a gain of 1${\%}{\sim}$2.5${\%}$.

Table 5: The ablation study of contrastive and reconstruction losses. Method | Contrastive loss | Reconstruction loss
---|---|---
MoCo | 8.714 | —
MAE | — | 0.1383
MMCL | 8.529$\left(\downarrow\right)$ | 0.1349$\left(\downarrow\right)$

The Effects of ML-IELM modules: Combining MMCL and ML-IELM is the key to
performing robust age estimation. The powerful and effective MMCL is used for
face feature extraction, and the trained ML-IELM is applied for age grouping
before regression to obtain the final age prediction results. In a series of
experiments based on the same parameter settings as the previous experiments,
we change the choice of classifiers and regressors while following the same
age prediction strategy.

We compare the simple three-layer MLP, the classical ELM, and the widely used
ML-ELM by applying the proposed ML-IELM to three facial datasets using MAE
(Mean Absolute Error) as the evaluation criterion. The comparison results in
Fig. 9 show that the ML-IELM proposed in this paper has a much lower age
prediction error and better generalization performance. Compared with MLP, ELM
network architecture is simpler and more efficient. Because ELM has limited
learning ability for high-dimensional complex data features and is prone to
overfitting based on empirical risk minimization, ML-IELM is further improved
and optimized based on ML-ELM, which results in a better overall performance.
Although the improved ML-IELM does not improve accuracy on the MORPH-II
dataset, it has more obvious improvement on the unrestricted dataset of
Aidence, i.e., it is reliable in the face of more complex and rich data
features.

Figure 9: The ablation study of ML-IELM modules.

##  5 Conclusion

This paper has proposed a Multi-view Mask Contrastive Learning Graph
Convolutional Neural Network for Age Estimation (MMCL-GCN). This method
includes two stages: the feature extraction stage and the age estimation
stage. At the graph level, MMCL-GCN leverages contrastive learning to fuse
masked image modeling for obtaining a robust and efficient feature extraction
model. We designed a multi-layer extreme learning machine (ML-IELM) with
identity mapping in the age estimation stage. We built classifiers and
regressors based on ML-IELM for age grouping and final prediction. Our
proposed method is evaluated on several prevailing age estimation databases,
MORPH-II, Adience Benchmark, and LAP-2016 dataset, in which the performances
equal or surpass the state-of-the-art baseline results. In future work, we
will do more research at the graph level of computer vision tasks and have
better breakthroughs in face recognition.

##  6 Acknowledgements

This work is supported by National Natural Science Foundation of China (Grant
No. 61802444); the Changsha Natural Science Foundation (Grant No. kq2202294),
the Research Foundation of Education Bureau of Hunan Province of China (Grant
No. 20B625, No. 18B196, No. 22B0275); the Research on Local Community
Structure Detection Algorithms in Complex Networks (Grant No. 2020YJ009).

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# Seeing measurements at OAUNI on 2016 and 2017 campaigns

A Pereyra1,2 J Tello2 and M Zevallos2 1 Geophysical Institute of Peru,
Astronomy Area, Badajoz 169, Ate, Lima, Perú  2 Faculty of Science, National
University of Enginnering, Av. Túpac Amaru 210, Lima, Perú<EMAIL_ADDRESS>
###### Abstract

We present seeing measurements at OAUNI site gathered on 2016 and 2017
campaigns using V and R broadband filters. In order to quantify the seeing we
used the full-width-at-half-maximum from stellar profiles on photometric
sequences during the observational windows of our supernovae program. A
typical median seeing of 1$.\\!\\!^{\prime\prime}$8 was found on 2016 and a
worst value of 2$.\\!\\!^{\prime\prime}$0 on 2017. The last one was probably
affected by anomalous conditions related to the 2017 extreme climatic
phenomena. The monthly first quartile analysis indicates that best seeing
conditions can be achieved at a level of 1$.\\!\\!^{\prime\prime}$5\. In
general, our results indicate a reasonable sky quality for the OAUNI site.

##  1 Introduction

Site testing is crucial to optimize the selection of a given site with
potential for astronomical observations. For this purpose is necessary a good
knowledge of local meteorological factors which alter the quality of the
astronomical images. In general, the level of atmospheric turbulence or
seeing, the rate of clear skies and the luminosity level for the background
sky are parameters to consider in this process.

In particular, the deformations of the front wave from celestial bodies
induced by changes on the atmospheric refraction index of turbulence layers
[1, 2] characterizes the seeing disk measured on the focal plane of the
optical system. As more atmospheric turbulence is present, the stellar
profiles show bigger seeing disks and vice versa. The seeing can be measured
in several ways, including direct measurements of the full-width-at-half-
maximum (fwhm) from stellar profiles or using special techniques as the
differential image motion monitor [3]. It can be demonstrated that the fwhm of
a long exposure stellar image measured at zenith angle (z) and a given
wavelength ($\lambda$) is proportional to sec(z)${}^{0.6}\times\lambda^{-0.2}$
where sec(z) is the airmass ($\chi$) [4]. In this computation the
approximation of a plane-parallel atmosphere is assumed which implies zenith
angles lower than 60∘ (or $\chi$ $<$ 2). These corrections have to be
considered when targets, observed to different line of sight and filters, are
used for comparative seeing studies. In particular, best seeing conditions are
expected at longer wavelengths.

This work presents a systematic study of the astronomical seeing as part of a
site testing program developed at the astronomical observatory of the National
University of Enginnering [5] (OAUNI in spanish) on 2016 and 2017. This
facility operates since 2015 at the Huancayo site of the Geophysical Institute
of Peru. Previous and sporadic seeing measurements were performed on this site
but with inconclusive results [6, 7, 8, 9].

##  2 Observations and Reductions

The observations were made using the 0.5m OAUNI telescope [5] during the 2016
and 2017 observational campaigns using the observational windows available in
the supernovae (SNe) photometry program (see for example, [10, 11]). We chosen
this program for our seeing statistics because consecutive measurements in V
(effective wavelength, $\lambda_{eff}$ = 551nm) and R ($\lambda_{eff}$ =
658nm) broadband filters are usual for a typical supernova target. This fact
lets a quasi simultaneous comparison of the seeing conditions in both bands.
In general, we observed during the dry season at the central peruvian Andes
covering mainly July and August months centered in new moon. As a detector was
used a front-illuminated CCD STXL-6303E of 3072$\times$2048 pixels2 and
9$\mu$m/pixel. At the f/8.2 Cassegrain focus the detector yields a plate scale
of 0.45$"$/pixel and a field-of-view (FOV) of 23${}^{\prime}\times$15′. All
the measurements were gathered with the detector cooled to -10 C to minimize
the dark current.

Table 1: Seeing measurements from supernovae fields observed during 2016$-$2017 campaigns. SN field |  Local time (UT$-$5) | filter | N | $\chi_{\rm{mean}}$ | seeing (”) |
---|---|---|---|---|---|---
| date | begin | end |  |  |  |  obsmean |  cormean |  cormedian |  cormode
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
PSNJ1410 | 2016/01/10 | 04:08 | 04:21 | V | 30 | 1.411 |  2.37 $\pm$ 0.18 |  1.92 $\pm$ 0.15 | 1.90 | 1.86
|  | 04:23 | 04:36 | R | 30 | 1.359 |  2.46 $\pm$ 0.21 |  2.05 $\pm$ 0.17 | 2.08 | 1.90
ASASSN16gq | 2016/07/10 | 20:49 | 21:16 | V | 60 | 1.248 |  2.01 $\pm$ 0.20 |  1.76 $\pm$ 0.18 | 1.75 | 1.69
|  | 21:21 | 21:35 | R | 30 | 1.342 |  1.91 $\pm$ 0.17 |  1.60 $\pm$ 0.14 | 1.62 | 1.62
ASASSN16gp | 2016/07/11 | 22:01 | 22:27 | V | 60 | 2.647 |  3.12 $\pm$ 0.28 |  1.74 $\pm$ 0.16 | 1.72 | 1.64
|  | 22:37 | 23:03 | R | 60 | 3.407 |  3.47 $\pm$ 0.40 |  1.66 $\pm$ 0.19 | 1.62 | 1.52
ASASSN16fp | 2016/07/13 | 03:58 | 04:11 | V | 30 | 1.483 |  2.08 $\pm$ 0.15 |  1.64 $\pm$ 0.13 | 1.62 | 1.55
|  | 04:13 | 04:26 | R | 30 | 1.571 |  2.05 $\pm$ 0.13 |  1.57 $\pm$ 0.10 | 1.57 | 1.57
ASASSN16hw | 2016/08/05 | 21:53 | 22:13 | V | 45 | 1.218 |  2.38 $\pm$ 0.22 |  2.12 $\pm$ 0.19 | 2.08 | 1.99
|  | 21:31 | 21:51 | R | 45 | 1.282 |  2.46 $\pm$ 0.29 |  2.12 $\pm$ 0.25 | 2.05 | 1.96
ASASSN16hz | 2016/08/09 | 04:33 | 04:53 | V | 45 | 1.407 |  2.06 $\pm$ 0.24 |  1.68 $\pm$ 0.21 | 1.69 | 1.72
|  | 04:11 | 04:32 | R | 45 | 1.295 |  1.92 $\pm$ 0.22 |  1.64 $\pm$ 0.19 | 1.62 | 1.65
ASASSN16jt | 2016/09/04 | 20:18 | 21:43 | V | 90 | 1.285 |  2.32 $\pm$ 0.24 |  2.00 $\pm$ 0.18 | 1.96 | 1.91
|  | 20:40 | 22:04 | R | 90 | 1.247 |  2.21 $\pm$ 0.18 |  1.94 $\pm$ 0.16 | 1.93 | 1.89
SN2017erp | 2017/07/22 | 20:55 | 21:15 | V | 45 | 1.141 |  2.52 $\pm$ 0.20 |  2.33 $\pm$ 0.18 | 2.32 | 2.22
|  | 20:09 | 20:29 | R | 45 | 1.049 |  2.86 $\pm$ 0.17 |  2.78 $\pm$ 0.16 | 2.78 | 2.86
SN2017erp | 2017/07/23 | 20:25 | 20:44 | V | 45 | 1.081 |  2.83 $\pm$ 0.43 |  2.70 $\pm$ 0.42 | 2.59 | 2.36
|  | 20:03 | 20:22 | R | 45 | 1.045 |  2.84 $\pm$ 0.29 |  2.76 $\pm$ 0.28 | 2.73 | 2.72
SN2017erp | 2017/07/24 | 20:34 | 21:38 | V | 90 | 1.175 |  2.86 $\pm$ 0.27 |  2.60 $\pm$ 0.26 | 2.61 | 2.62
|  | 20:13 | 21:15 | R | 90 | 1.119 |  2.68 $\pm$ 0.19 |  2.51 $\pm$ 0.19 | 2.50 | 2.51
SN2017erp | 2017/07/25 | 22:54 | 23:59 | V | 90 | 2.536 |  2.50 $\pm$ 0.37 |  1.44 $\pm$ 0.14 | 1.43 | 1.55
|  | 22:32 | 23:37 | R | 90 | 2.136 |  2.25 $\pm$ 0.22 |  1.44 $\pm$ 0.11 | 1.45 | 1.51
SN2017erp | 2017/07/26 | 20:01 | 20:28 | V | 60 | 1.066 |  2.00 $\pm$ 0.19 |  1.92 $\pm$ 0.18 | 1.92 | 1.91
|  | 19:38 | 19:58 | R | 45 | 1.031 |  2.03 $\pm$ 0.40 |  1.99 $\pm$ 0.39 | 1.91 | 1.73
SN2017erp | 2017/07/27 | 19:50 | 20:10 | V | 45 | 1.050 |  1.98 $\pm$ 0.36 |  1.92 $\pm$ 0.35 | 1.82 | 1.70
|  | 19:29 | 19:49 | R | 45 | 1.024 |  2.10 $\pm$ 0.31 |  2.07 $\pm$ 0.30 | 2.07 | 2.08
SN2017erp | 2017/07/28 | 20:07 | 20:27 | V | 45 | 1.085 |  2.00 $\pm$ 0.17 |  1.90 $\pm$ 0.16 | 1.91 | 1.90
|  | 19:46 | 20:06 | R | 45 | 1.049 |  2.03 $\pm$ 0.18 |  1.97 $\pm$ 0.18 | 1.97 | 1.96
SN2017erp | 2017/07/29 | 19:54 | 20:14 | V | 45 | 1.068 |  1.86 $\pm$ 0.22 |  1.79 $\pm$ 0.21 | 1.78 | 1.59
|  | 19:32 | 19:52 | R | 45 | 1.037 |  2.01 $\pm$ 0.22 |  1.97 $\pm$ 0.21 | 1.99 | 1.97
SN2017erp | 2017/08/20 | 19:49 | 20:09 | V | 45 | 1.315 |  2.29 $\pm$ 0.22 |  1.95 $\pm$ 0.17 | 1.94 | 1.78
|  | 19:26 | 19:46 | R | 45 | 1.221 |  1.80 $\pm$ 0.18 |  1.60 $\pm$ 0.15 | 1.63 | 1.64
SN2017erp | 2017/08/21 | 19:58 | 20:35 | V | 80 | 1.436 |  2.22 $\pm$ 0.26 |  1.79 $\pm$ 0.20 | 1.77 | 1.71
|  | 19:27 | 19:56 | R | 60 | 1.259 |  2.15 $\pm$ 0.26 |  1.87 $\pm$ 0.24 | 1.86 | 1.87
SN2017erp | 2017/08/22 | 20:56 | 21:24 | V | 60 | 1.995 |  2.53 $\pm$ 0.15 |  1.68 $\pm$ 0.10 | 1.67 | 1.62
|  | 20:27 | 20:54 | R | 60 | 1.655 |  2.49 $\pm$ 0.28 |  1.85 $\pm$ 0.21 | 1.83 | 1.70
|  |  |  |  |  |  |  |  |  |

All the images were reduced using IRAF [12] with typical calibration
corrections of dark current and flatfield. Special IRAF routines were used to
align the sequences of images along with standard routines as xregister and
imalign. In order to compute the seeing we measured automatically the fwhm of
stellar profiles in a particular supernova sequence in each filter and date.
Typical images sequence consisted of series between 30 and 90 individual
frames always with a integration time of twenty seconds (by frame). Special
care was taken with frames affected by tracking problems or by occasional
vibration of gust of wind. In these cases, the frames were exclude on the
following analysis. The mean fwhm for the same three brightest stars in each
sequence was computed using the IRAF routine imexamine. Comparison with
similar routines as daoedit [13] and psfmeasure [14, 15] resulted in similar
values.

The observation log from the supernovae program during the 2016 and 2017
campaigns is shown in Table 1. The SN field used for the seeing computation is
indicated in Col. (1). During the 2016 campaign were observed seven SN targets
in different nights (one by night). On 2017 one target was observed in eleven
nights. The local observation date is shown in Col. (2) along with the
interval time of the observational windows (Cols. 3$-$4). The last ones are
typically between thirteen and forty minutes. The used filter is indicated in
Col. (5) with the number of measurements in a given observation sequence in
Col (6). The mean airmass during the sequence is shown in Col. (7). Finally,
Cols. 8$-$11 indicate the mean seeing without airmass correction (obsmean)
with its 1-sigma dispersion, the proper value with the correction applied
(cormean) along with the median (cormedian) and the mode (cormode) values,
respectively.

The total number of individual seeing measurements showed in this work is
about two thousand and must be taken with care in the sense that this sample
represents an aleatory survey of the local seeing for the OAUNI site. In
general, a typical good observation night includes eight or nine continuous
hours and we are sampling short observational windows with no more than 1.5
hours by night (including both filters). Nevertheless, we believe that the
measurements presented here are representative and useful to analyze the
monthly and interannual seeing feature for this site.

Figure 1:  Good seeing measurements on 2016/07/13 (left) and 2017/08/20
(right). (a,b) Histograms with airmass correction in V (blue) and R (red)
filters. (c,d) Seeing time evolution. Average seeing (solid line) and its
1-sigma dispersion (dotted lines) are indicated for each filter. (e,f) Airmass
during the observational window. Figure 2:  Bad seeing measurements on
2016/08/05 (left) and 2017/07/24 (right). As Fig. 1. Figure 3:  (a) Full
seeing time evolution with airmass correction between 2016$-$2017\. Individual
measurements in V (blue) and R (red) filters. (b) Monthly seeing analysis for
the full sample showing minimum, first quartile, median, third quartile and
maximum in each case. (c,d,e) Histograms for 2016, 2017 and full sample.
(f,g,h) Interannual seeing analysis.

##  3 Analysis

As indicated in §1, the fwhm airmass correction applies for $\chi$ $<$ 2\. At
least in two cases (2016/07/11 and 2017/07/25 nights) the mean airmasses (see
Table 1) are higher than this limit. In general, higher airmasses
underestimated the seeing values. In order to avoid this situation, the
following analysis considers only seeing values under this limit resulting in
about five hundred measurements filtered of the full sample.

Figures 1 and 2 show examples of good and bad seeing nights, respectively. The
observational windows in Fig. 1-left for 2016/07/13 night indicate better
seeing conditions with a median as low as 1$.\\!\\!^{\prime\prime}$62 and
1$.\\!\\!^{\prime\prime}$57 for V and R bands, respectively (see Table 1). The
sampled time interval was of 30 min with $\chi$ $<$ 1.6 observing to the West.
In general, lower seeing values in R than V are expected under normal
conditions (§1). The same pattern is observed on 2017/08/20 night (Fig.
1-right) with a median seeing of 1$.\\!\\!^{\prime\prime}$63 in R band but the
seeing being worst in V (1$.\\!\\!^{\prime\prime}$94). In this case, the
monitoring was of $\sim$45 min with $\chi$ $<$ 1.4 also looking to the West.
Considering the mean values of these nights, typical 1-sigma dispersion lower
than $\sim$0$.\\!\\!^{\prime\prime}$15 is indication of a stable observational
window. On the other hand, the 2016/08/05 night in Fig. 2-left show bad seeing
conditions in a 42 min observational window with typical median seeing of
2$.\\!\\!^{\prime\prime}$1 in both filters and with a little bit larger
1-sigma dispersion ($\sim$0$.\\!\\!^{\prime\prime}$22). In this case, the
observations were made with $\chi$ $<$ 1.3 on the East hemisphere. Worst
seeing conditions were found on 2017/07/24 night (Fig. 2-right). Two
alternative sequences in both filters were acquired during a 90 min
observational window with a higher median seeing ($>$
2$.\\!\\!^{\prime\prime}$5) and 1-sigma dispersion ($\sim$
0$.\\!\\!^{\prime\prime}$23). In this night the West hemisphere was monitored
with $\chi$ $<$ 1.2. Considering the last two cases, a 1-sigma dispersion of
0$.\\!\\!^{\prime\prime}$22 can still characterize stable conditions, even for
nights with bad seeing. It is interesting because the photometry for several
science programs requires primarily a stable atmosphere even although the
intrinsic seeing is not the best. Finally, 83% of the analyzed nights on 2016
shown median seeing values following the expected wavelength dependence, i.e.
better and smaller seeing in R filter as compared with the V values.
Nevertheless, on 2017 this pattern only is seen in 30% of the nights and it
seems indicate an anomalous trend.

Table 2:  Monthly seeing analysis. year | N | filter | seeing (”)
---|---|---|---
|  |  | mean |  Q1 | median |  Q3 | mode
2016/01 | 30 | V |  1.92 $\pm$ 0.15 | 1.81 | 1.90 | 2.03 | 1.75
| 30 | R |  2.05 $\pm$ 0.17 | 1.91 | 2.05 | 2.17 | 2.10
2016/07 | 90 | V |  1.70 $\pm$ 0.17 | 1.58 | 1.69 | 1.80 | 1.58
| 59 | R |  1.58 $\pm$ 0.12 | 1.51 | 1.58 | 1.66 | 1.53
2016/08 | 90 | V |  1.90 $\pm$ 0.29 | 1.68 | 1.95 | 2.10 | 1.68
| 88 | R |  1.88 $\pm$ 0.32 | 1.62 | 1.92 | 2.05 | 1.98
2016/09 | 77 | V |  1.94 $\pm$ 0.18 | 1.84 | 1.93 | 2.02 | 1.86
| 90 | R |  1.94 $\pm$ 0.16 | 1.84 | 1.92 | 2.05 | 1.83
2017/07 | 323 | V |  2.23 $\pm$ 0.45 | 1.87 | 2.21 | 2.54 | 2.20
| 346 | R |  2.27 $\pm$ 0.46 | 1.92 | 2.30 | 2.66 | 2.68
2017/08 | 126 | V |  1.82 $\pm$ 0.19 | 1.69 | 1.78 | 1.93 | 1.72
| 146 | R |  1.79 $\pm$ 0.23 | 1.64 | 1.77 | 1.92 | 1.68
|  |  |  |  |  |  |
Table 3:  Annual analysis for seeing . year | N | filter | seeing (”)
---|---|---|---
|  |  | mean |  Q1 | median |  Q3 | mode
2016 | 287 | V |  1.85 $\pm$ 0.24 | 1.68 | 1.84 | 2.01 | 1.79
| 267 | R |  1.85 $\pm$ 0.27 | 1.63 | 1.86 | 2.04 | 2.04
2017 | 449 | V |  2.11 $\pm$ 0.43 | 1.77 | 2.04 | 2.40 | 1.72
| 492 | R |  2.13 $\pm$ 0.46 | 1.74 | 2.06 | 2.54 | 1.92
2016-17 | 736 | V |  2.01 $\pm$ 0.39 | 1.74 | 1.92 | 2.21 | 1.86
| 759 | R |  2.03 $\pm$ 0.43 | 1.69 | 1.96 | 2.27 | 1.87
|  |  |  |  |  |  |

In order to help the interannual seeing comparison and/or detect any seasonal
pattern, Fig. 3 shows all the measurements collected on 2016 and 2017
campaigns in both filters. The full seeing evolution considering the
individual mesurements is indicated in Fig. 3a and the monthly analysis
showing the basic statistics is shown in Fig. 3b and Table 2. As we can see,
2016 was sampled in four months (January, July, August and September) and 2017
only in two (July and August). Nevertheless, the number of measurements on
2016 (554) was a little bit higher than the half ones on 2017 (941).
Therefore, our sample let to compare the months of July and August in both
years. In general, the best seeing conditions are obtained on 2016 July with a
median of 1$.\\!\\!^{\prime\prime}$6 and 1$.\\!\\!^{\prime\prime}$7 on R and V
band, respectively. On the other hand, 2017 July presented the worst seeing
values as compared with the rest of months, with a median seeing above of
2$.\\!\\!^{\prime\prime}$2\. Interestingly, 2016 August and 2017 August show
similar mean values (1$.\\!\\!^{\prime\prime}$9 and
1$.\\!\\!^{\prime\prime}$8, respectively) in both filters. Considering the dry
season at the central peruvian Andes (between May and August), the best seeing
conditions are expected to happen on July. In this sense our results for 2017
seems to indicate an anomalous year which could be affected by the extreme
climatic event Niño Costero just ended on 2017 May. This is reinforced by the
fact that the clear sky rate measured in our site by ground-based weather
radar [16] drops from 84% in 2016 July to 77% on 2017 July and. The poor
seeing wavelength dependence on 2017 appointed above also corroborates this
finding. However, the normal conditions on 2016 seem to indicate that good
seeing can be achieved at a level of 1$.\\!\\!^{\prime\prime}$5 if we
considering the first quartile founded on July of that year. For the sake of
completeness, we noted that the occasional open nights at the beginning (2016
September) and in the middle (2016 January) of a typical rainy season on our
site shown moderate seeing values
($\sim$1$.\\!\\!^{\prime\prime}$9$-$2$.\\!\\!^{\prime\prime}$0).

Finally, the interannual seeing comparison is shown in Figs. 3c$-$e with
histograms for 2016, 2017 and both years, respectively. The statistics
analysis is indicated in Figs. 3f$-$g and Table 3. The V and R mean values are
similar in all cases considering their typical dispersion. The 2016 sample is
characterized by a median seeing of 1$.\\!\\!^{\prime\prime}$84 and
1$.\\!\\!^{\prime\prime}$86 at V and R bands, respectively. On the other hand,
the 2017 sample shows a worst seeing with a median of
2$.\\!\\!^{\prime\prime}$04 on V and 2$.\\!\\!^{\prime\prime}$06 on R and
reflecting the irregular conditions of 2017 July. The full sample considering
the measurements combined by the two years has a median seeing of
1$.\\!\\!^{\prime\prime}$92 and 1$.\\!\\!^{\prime\prime}$96 for V and R bands,
respectively. The statistics shown here indicate that our site has a
reasonable sky quality for astronomical observations. As comparison, the best
sites in the world with astronomical facilities have median seeing values
lower than 1$.\\!\\!^{\prime\prime}$0 [17].

##  4 Conclusions

This work shows seeing measurements obtained at OAUNI site during 2016 and
2017 observational campaigns. This is part of an ongoing site testing program
at the central peruvian Andes. The full-width-at-half-maximum of stellar
profiles were measured directly on astronomical images of our supernovae
scientific program yielding around one thousand and a half useful individual
measurements. The seeing of a total of eighteen nights was evaluated in two
filters during both campaigns. The comparative monthly analysis indicates
better observational conditions for optical astronomical during the dry season
on the site. This was particularly true on 2016 with a typical median seeing
of 1$.\\!\\!^{\prime\prime}$8\. On the other hand, 2017 shown to be an
anomalous year with a worst median seeing of 2$.\\!\\!^{\prime\prime}$0 and
far for showing a typical seeing wavelength dependence. The extreme climate
phenomena of the first semester on that year can explain this particular
feature. In general, the best seeing conditions considering both years were
present on 2016 July with the best monthly quartile of
1$.\\!\\!^{\prime\prime}$5\. These findings suggest a reasonable sky quality
for optical astronomical observations at OAUNI site. In this sense, it is
appropriate to indicate that the seeing levels reported here do not prevent
the development of selected astronomical scientific programs [18, 19, 20] .

The author is grateful for the economic support from The World Academy of
Sciences (TWAS), Rectorate and the Instituto General de Investigación (IGI) at
UNI, and Concytec (Convenio 102-2015 Fondecyt). Special thanks to the Huancayo
Observatory staff for the logistic support.

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