# Morpho-Photometric Classification of KiDS DR5 Sources Based on Neural
Networks: A Comprehensive Star-Quasar-Galaxy Catalog

Hai-Cheng Feng Yunnan Observatories, Chinese Academy of Sciences, Kunming
650216, Yunnan, People’s Republic of China  Key Laboratory for the Structure
and Evolution of Celestial Objects, Chinese Academy of Sciences, Kunming
650216, Yunnan, People’s Republic of China  Center for Astronomical Mega-
Science, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District,
Beijing 100012, People’s Republic of China  Key Laboratory of Radio Astronomy
and Technology, Chinese Academy of Sciences, 20A Datun Road, Chaoyang
District, Beijing 100101, People’s Republic of China  Rui Li Institude for
Astrophysics, School of Physics, Zhengzhou University, Zhengzhou, 450001,
People’s Republic of China  Nicola R. Napolitano School of Physics and
Astronomy, Sun Yat-sen University, Zhuhai Campus, 2 Daxue Road, Xiangzhou
District, Zhuhai, People’s Republic of China  CSST Science Center for
Guangdong-Hong Kong-Macau Great Bay Area, Zhuhai, 519082, People’s Republic of
China  INAF – Osservatorio Astronomico di Capodimonte, Salita Moiariello 16,
80131 - Napoli, Italy  Sha-Sha Li Yunnan Observatories, Chinese Academy of
Sciences, Kunming 650216, Yunnan, People’s Republic of China  Key Laboratory
for the Structure and Evolution of Celestial Objects, Chinese Academy of
Sciences, Kunming 650216, Yunnan, People’s Republic of China  Center for
Astronomical Mega-Science, Chinese Academy of Sciences, 20A Datun Road,
Chaoyang District, Beijing 100012, People’s Republic of China  Key Laboratory
of Radio Astronomy and Technology, Chinese Academy of Sciences, 20A Datun
Road, Chaoyang District, Beijing 100101, People’s Republic of China  J. M. Bai
Yunnan Observatories, Chinese Academy of Sciences, Kunming 650216, Yunnan,
People’s Republic of China  Key Laboratory for the Structure and Evolution of
Celestial Objects, Chinese Academy of Sciences, Kunming 650216, Yunnan,
People’s Republic of China  Center for Astronomical Mega-Science, Chinese
Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing 100012,
People’s Republic of China  Key Laboratory of Radio Astronomy and Technology,
Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing
100101, People’s Republic of China  Ran Li  University of Chinese Academy of
Sciences, Beijing 100049, People’s Republic of China  National Astronomical
Observatories, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District,
Beijing 100012, People’s Republic of China  H. T. Liu Yunnan Observatories,
Chinese Academy of Sciences, Kunming 650216, Yunnan, People’s Republic of
China  Key Laboratory for the Structure and Evolution of Celestial Objects,
Chinese Academy of Sciences, Kunming 650216, Yunnan, People’s Republic of
China  Center for Astronomical Mega-Science, Chinese Academy of Sciences, 20A
Datun Road, Chaoyang District, Beijing 100012, People’s Republic of China
Kai-Xing Lu Yunnan Observatories, Chinese Academy of Sciences, Kunming 650216,
Yunnan, People’s Republic of China  Key Laboratory for the Structure and
Evolution of Celestial Objects, Chinese Academy of Sciences, Kunming 650216,
Yunnan, People’s Republic of China  Center for Astronomical Mega-Science,
Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing
100012, People’s Republic of China  Mario Radovich  INAF - Osservatorio
Astronomico di Padova, via dell’Osservatorio 5, 35122 Padova, Italy  Huan-Yuan
Shan  Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai
200030, People’s Republic of China  Jian-Guo Wang Yunnan Observatories,
Chinese Academy of Sciences, Kunming 650216, Yunnan, People’s Republic of
China  Key Laboratory for the Structure and Evolution of Celestial Objects,
Chinese Academy of Sciences, Kunming 650216, Yunnan, People’s Republic of
China  Center for Astronomical Mega-Science, Chinese Academy of Sciences, 20A
Datun Road, Chaoyang District, Beijing 100012, People’s Republic of China
Wen-Zhe Xi  Yunnan Observatories, Chinese Academy of Sciences, Kunming 650216,
Yunnan, People’s Republic of China  University of Chinese Academy of Sciences,
Beijing 100049, People’s Republic of China  Ling-Hua Xie  School of Physics
and Astronomy, Sun Yat-sen University, Zhuhai Campus, 2 Daxue Road, Xiangzhou
District, Zhuhai, People’s Republic of China  Yang-Wei Zhang  South-Western
Institute for Astronomy Research, Yunnan University, Kunming 650500, People’s
Republic of China

###### Abstract

We present a novel multimodal neural network for classifying astronomical
sources in multiband ground-based observations, from optical to near infrared,
to separate sources in stars, galaxies and quasars. Our approach combines a
convolutional neural network branch for learning morphological features from
$r$-band images with an artificial neural network branch for extracting
spectral energy distribution (SED) information. Specifically, we have used
9-band optical ($ugri$) and NIR ($ZYHJK_{s}$) data from the Kilo-Degree Survey
(KiDS) Data Release 5. The two branches of the network are concatenated and
feed into fully-connected layers for final classification. We train the
network on a spectroscopically confirmed sample from the Sloan Digital Sky
Survey cross-matched with KiDS. The trained model achieves 98.76% overall
accuracy on an independent testing dataset, with F1 scores exceeding 95% for
each class. Raising the output probability threshold, we obtain higher purity
at the cost of a lower completeness. We have also validated the network using
external catalogs cross-matched with KiDS, correctly classifying 99.74% of a
pure star sample selected from Gaia parallaxes and proper motions, and 99.74%
of an external galaxy sample from the Galaxy and Mass Assembly survey,
adjusted for low-redshift contamination. We apply the trained network to
27,334,751 KiDS DR5 sources with $r\leqslant 23$ mag to generate a new
classification catalog. This multimodal neural network successfully leverages
both morphological and SED information to enable efficient and robust
classification of stars, quasars, and galaxies in large photometric surveys.

Neural networks(1933), Classification(1907), Surveys(1671), Catalogs(205), A
stars(5), Quasars(1319), Galaxies(573)

##  1 Introduction

Stars, galaxies, and quasars are the three main categories of astronomical
objects in most large scale surveys, enabling advances in our understanding of
cosmic structure, evolution, and fundamental physics. Stars, the most
observable entities in the universe, are the basic building blocks of
galaxies. Systematic observations and cataloging of stars not only yield a
wealth of information about stellar evolution and the synthesis of heavy
elements, but also aid in mapping the structure and dynamics of the Milky Way
(Helmi, 2020; Zhang et al., 2023). Galaxies, large assemblies of stars, gas,
dust, and dark matter bound by gravity, serve as fundamental components of
large-scale structure. A comprehensive census and analysis of galaxies can
reveal the underlying distribution of dark matter and provide a platform for
testing cosmological models that describe the origin and evolution of the
Universe (Bond et al., 1996; Behroozi et al., 2013). Quasars, also known as
quasi-stellar objects (QSOs), represent extremely luminous galactic nuclei
fueled by matter accretion onto supermassive black holes. They serve as
invaluable tools for probing the formation and evolution of supermassive black
holes, and understanding their connection to their host galaxies (Schmidt,
1963; Salpeter, 1964; Kormendy & Ho, 2013). Accurate classification of these
diverse celestial objects stands as an indispensable prerequisite for
conducting detailed follow-up studies and science analyses.

Over the course of several decades, extensive efforts have been devoted to
develop various approaches for separating stars, QSOs, and galaxies.
Spectroscopic observations are among the most reliable methods, primarily due
to the unique physical properties of these three types of astronomical objects
(e.g., Baldwin et al., 1981; Feng et al., 2021; Verro et al., 2022). The
emergence of spectroscopic survey projects, such as the Sloan Digital Sky
Survey (SDSS; York et al., 2000), the Large Sky Area Multi-Object Fiber
Spectroscopic Telescope (LAMOST; Cui et al., 2012), and the Dark Energy
Spectroscopic Instrument (DESI; DESI Collaboration et al., 2016), has enabled
the collection of spectra for millions of targets. This has, in turn, led to
the proposal of some automatic spectral classification methods, including the
Baldwin-Phillips-Terlevich (BPT) diagnostic scheme (Baldwin et al., 1981) and
template matching (Bolton et al., 2012). However, most spectroscopic surveys
employ multi-object fiber spectrographs, which are limited to observing
hundreds to thousands of targets concurrently, necessitating exposure times of
several thousand seconds. This requires a significant amount of telescope time
to obtain large statistical samples, but results in relatively shallow data
for each target. As a result, target pre-selection is often implemented in
these surveys, which can introduce bias in sample statistics and increase the
likelihood of missing peculiar celestial populations.

As alternative to spectroscopy, multi-band imaging can effectively trace the
impact of different radiative process in the spectral energy distributions
(SEDs) of astronomical sources. In this case, source classification can be
performed via color-color diagnostic (Richards et al., 2002; Peters et al.,
2015) or SED fitting (Ilbert et al., 2009; Salvato et al., 2009). The
photometric approach has the advantage to collect all targets under a limited
brightness in the field of view, effectively eliminating any selection bias.
In contrast to spectroscopic observation, photometry requires shorter exposure
times, often just a few minutes, to reach deeper limiting magnitudes.
Furthermore, image data can provide morphological details that are not
accessible from spectra, which contains rich physical information. Indeed, the
first attempt to perform object classifications, the primary methods were
visual inspection of images or analysis of morphological parameters (e.g.,
Hubble, 1926; MacGillivray et al., 1976; Yee, 1991; Scranton et al., 2002;
Kelvin et al., 2014; López-Sanjuan et al., 2019). This technique proved to be
effective in differentiating between stars (point sources) and galaxies
(extended structures), and even enabled the identification of certain QSOs
with notable host galaxies (Guo et al., 2022).

Ongoing wide-field imaging surveys provide continuous streams of multi-band
photometric data, enabling the potential for obtaining complete samples of
various celestial object. Current projects like the Hyper Suprime-Cam Subaru
Strategic Program (HSC-SSP; Aihara et al., 2018), Dark Energy Survey (DES; The
Dark Energy Survey Collaboration, 2005), and Kilo Degree Square Survey (KiDS;
de Jong et al., 2015) are amassing observations spanning hundreds of millions
of targets. Upcoming programs, like the China Space Station Telescope (CSST;
Gong et al., 2019), Large Synoptic Survey Telescope (LSST; Ivezić et al.,
2019), and the Euclid mission (Laureijs et al., 2011), will dramatically
escalate data volumes into billions or more. The wealth of data sets
underscores the urgent need for rapid and efficient classification algorithms.

SED-based classification methods typically require a broad wavelength
coverage. Depending on the classes one wants to classify these might include
other bands like X-rays, infrared or radio. However, most survey projects
operate within relatively narrow wavelength ranges. For instance, HSC and DES
focus on optical bands, the Two Micron All Sky Survey (2MASS; Skrutskie et
al., 2006) on near-infrared (NIR) bands, and the Wide-Field Infrared Survey
Explorer (WISE; Wright et al., 2010) on mid-infrared bands. Classifying on the
basis of photometric data points with short wavelength intervals may be
affected by degeneracy (Buchs et al., 2019). One approach to address this is
to combine multiple survey data (e.g., Ilbert et al., 2009; Fotopoulou et al.,
2016; Khramtsov et al., 2021; Salvato et al., 2022; Yang & Shen, 2023), but
this approach can only be applied to targets with overlapping regions and is
limited to the depth of the shallowest survey. Traditional morphology-based
classification demands high-quality data where low-surface brightness galaxies
may be missed. Additionally, classifications suffer intrinsic degeneracies
like compact galaxies and high-redshift QSOs confused as point sources.
Combining the SED of celestial objects with their morphological features holds
promise in mitigating degeneracies during the classification process and fully
exploring the scientific potential of survey data (Sevilla-Noarbe et al.,
2018; Khramtsov et al., 2019).

Machine learning (ML) technology, with its outstanding speed and accuracy, has
been widely applied in the field of astronomical big data processing (e.g.,
Dieleman et al., 2015; Bai et al., 2019; Logan & Fotopoulou, 2020; Szklenár et
al., 2020; Chen, 2021; Zhou et al., 2021; Dubois et al., 2022; Li et al.,
2022; Xie et al., 2023). Unlike traditional methods relying on physical
modeling, ML can directly learn and mine the intrinsic features of celestial
objects from vast observational data, sometimes even making new discoveries
beyond existing theories. Currently, many ML algorithms have been successfully
utilized in astronomical classification tasks. Techniques like Random Forests,
extreme gradient boosting (XGBoost), support vector machines (SVM), and
artificial neural networks (ANN) are commonly used for analyzing catalogs of
photometric or morphological parameters, while convolutional neural networks
(CNN) can directly extract information from images or spectra (Cabayol et al.,
2019; Li et al., 2019; Tadaki et al., 2020; Nakazono et al., 2021; Chaini et
al., 2023). Although some studies have attempted to feed both SED and
morphological information into ML models (Fadely et al., 2012; Khramtsov et
al., 2019), most studies still adopt parameterized morphological parameters
obtained through traditional methods, which can be affected by noise.

Motivated by the potential to enhance classification performance, we construct
a multimodal neural network that combines the flexibility of ANN and CNN to
simultaneously extract SED and image features, respectively. We have applied
this network to the KiDS DR5 dataset to generate a new Star-QSO-Galaxy
catalog. In Section 2, we provide a brief introduction to the data from each
survey. Section 3 presents the methodology, detailing the construction and
training of the multimodal neural network. The findings are discussed in
Section 4, followed by the concluding remarks in Section 5.

Figure 1: The distributions of $r$-band magnitude (left panel) and $u-g$ color
(right panel) for KiDS and SDSS datasets. In both panels, the black histograms
represent the overlapping sources between KiDS and SDSS, the orange histograms
depict the data from the KiDS survey, while the blue, red, and green
histograms denote stars, QSOs, and galaxies identified by SDSS spectroscopy,
respectively.

##  2 Data

The aim of this paper is to provide a Galaxy-QSO-Star catalog for KiDS public
Data Release 5 (DR5). Ground-truth labels required for supervised ML come from
SDSS DR17. Additionally, we adopt Gaia (Gaia Collaboration et al., 2016) DR3
and Galaxy and Mass Assembly (GAMA; Driver et al., 2011) DR4 to further test
the performance of classification algorithm to Galactic (stars) and
extragalactic (QSOs and galaxies) objects, respectively.

###  2.1 KiDS

KiDS is a $ugri$-band wide-field imaging survey with the OmegaCAM camera
mounted at the VLT Survey Telescope (Capaccioli & Schipani, 2011; Capaccioli
et al., 2012). The complete observations cover $\sim$1350 deg2 in the Galactic
North and South. 1006 deg2 of them have been released under DR4 (Kuijken et
al., 2019), while the remaining DR5 is internal data. Thanks to the excellent
observing conditions, the $r$-band limiting magnitude is $\sim$25 (5$\sigma$
in 2 square arcsec) with typical seeing of $\sim$0.7$\farcs$ In addition,
VISTA Kilo-degree Infrared Galaxy (VIKING; Edge et al., 2013) is KiDS partner
survey carried out with the VISTA telescope which can complement its near-
infrared data in $ZYHJK_{s}$-band. Therefore, we can obtain a total of 9-band
optical-NIR data to separate QSOs from stars and galaxies.

For each object, KiDS DR5 provides its 9-band Gaussian Aperture and PSF (GAaP;
Kuijken et al., 2015) magnitudes, and then 8 adjacent band colors (e.g.,
$u-g$, $g-r$, etc.) can be derived. The GAaP technique is specifically
designed to improve color measurement accuracy by homogenizing the PSF across
different filters. This is especially important for galaxies and some nearby
QSOs. To avoid any confusion introduced by the unreliable measurements, we
only adopt the 65,909,027 objects which have all 9-band measurements. Figure 1
shows the distribution of their $r$-band GAaP magnitude and corresponding
$u-g$ color. Considering that supervised machine learning algorithms are
limited by the feature space coverage of training samples (see Figure 1), we
further select the 27,334,751 objects with $r\leqslant$ 23 mag as inference
data (see Section 4). In principle, the reliability of the magnitude
measurement should be characterized by the error or the signal-to-noise ratio
(S/N), but this can be ignored for bright sources.

###  2.2 SDSS

DR17 is the final annual release of SDSS-IV (Abdurro’uf et al., 2022) which
has cumulated 5,801,200 spectroscopically identified objects in specObj-
dr17111https://data.sdss.org/datamodel/files/SPECTRO_REDUX/specObj.html data
base. We apply TOPCAT tool (Taylor, 2005) to cross-match SDSS sample with
KiDS, and 177,843 objects are obtained within a matching radius of 1 arcsec.
To ensure the reliability of SDSS identification, we only select the confident
spectroscopic classification measurements depending on the ZWARNING flag
(ZWARNING = 0; Bolton et al., 2012), which yield 167,009 objects. The final
cross-matched sample includes 31,306 stars, 19,608 QSOs, and 116,095 galaxies.
We then randomly split a subset of 127,009 as the training dataset to train
the multimodal neural network model described in Section 3, while the
remaining 40,000 sources are equally divided into validation and testing
datasets. Note that the inference data are deeper than the labeled sample (see
Figure 1), thus it is necessary to test the performance of our algorithm.

###  2.3 Gaia

Gaia is an European Space Agency’s all-sky space-astrometry mission launched
on 19 December 2013. Its primary science goal is to study the structure and
dynamics of the Galaxy through high precision astrometry, which can help us to
isolate a clean sample of star with significant parallax or proper motion.
There are 1,811,709,771 sources brighter than $G$ = 21 (corresponding to
$r\approx$ 20) in the Gaia DR3 catalog (Gaia Collaboration et al., 2021,
2022), and 4,840,178 of them can be matched to KiDS within 1 arcsec through
the CDS Upload X-Match Window of TOPCAT. Then, the most confident stars are
selected by the significance of parallax and proper motion. We required that a
star in the sample should satisfy either of the following criteria (see also
in Yang & Shen, 2023):

$\frac{|\varpi|}{\sigma_{\varpi}}\geqslant 5,$ (1)

or

$\frac{\mu^{2}_{\alpha}+\mu^{2}_{\delta}}{\sqrt{\mu^{2}_{\alpha}\sigma^{2}_{\mu_{\alpha}}+\mu^{2}_{\delta}\sigma^{2}_{\mu_{\delta}}}}\geqslant
5,$ (2)

where $\varpi$, $\sigma_{\varpi}$, $\mu_{\alpha}$, $\sigma_{\mu_{\alpha}}$,
$\mu_{\delta}$, and $\sigma_{\mu_{\delta}}$ are parallax, parallax error,
proper motion in RA, proper motion error in RA, proper motion in DEC, and
proper motion error in DEC, respectively. This selection step results in a
sample of 3,444,939. The final Gaia star dataset contains 3,422,113 sources
after removing 22,826 SDSS objects.

###  2.4 GAMA

GAMA is a spectroscopic survey carried out on the 3.9-m Anglo-Australian
Telescope which is designed to study the formation and evolution of cosmology
and galaxy. The final data release of GAMA, DR4 (Driver et al., 2022),
contains reliable redshift measurements (NQ $>$ 2) for 330,542 sources. Most
of them are galaxies, while some stars and QSOs can be distinguished by
redshift (e.g., the objects with redshifts $z\sim 0$ and $z>1$ are most likely
to be stars and QSOs, respectively). We cross-matched KiDS with GAMA using a
radius of 1 arcsec, yielding a sample of 279,404. However, 48,902 of them are
duplicated with SDSS observations which may cause bias in the test results. To
maintain an independent GAMA sample, we removed these objects, leaving a total
of 230,502 sources.

##  3 Method

We employed two standard models, ANN and CNN, both of which are categories of
deep learning and significant branches of ML (Smith & Geach, 2023). These
models are designed based on the concept of emulating the operations of
biological neural networks, which in turn allow for the efficient processing
and analysis of complex data. ANN (McCulloch et al., 1943), also referred to
as Multi-Layer Perceptron (MLP), comprises multiple interconnected layers of
artificial neurons that mimic the connections and synaptic processing of
biological brains. Each neuron learns weighting and bias parameters to capture
nonlinear relationships within inputs, thus enabling accurate prediction and
classification. CNN (Lecun et al., 1998), on the other hand, is a specialized
neural network architecture that is particularly effective in image and signal
processing tasks. By employing components such as convolutional layers,
pooling layers, and fully connected layers, CNN is capable of extracting
spatial and morphological features from input data. It accomplishes this
through weight sharing and local perception mechanisms. As a result, CNN
exhibits superior performance in tasks like image classification and object
detection, where its ability to analyze complex visual information is
particularly advantageous.

Figure 2: Schematic of the multimodal neural network architecture, consisting
of 18,257,155 neurons. Each blue or purple rectangle represents a layer, and
each light pink rectangle represents two identical ResNet blocks. The SED
branch inputs photometry from 9 KiDS bands and 8 adjacent band colors, and the
image branch processes a $41\times 41$ pixels $r$-band image. The output layer
provides classification probabilities for stars, quasars, or galaxies.

###  3.1 Neural network architecture

As illustrated in Figure 2, our multimodal neural network integrates two
simultaneous branches tailored for feature extraction from SED and image data.
These branches aim to capture different attributes of the data: the ANN is
tasked with analyzing complex nonlinear patterns in multi-band photometric
information, while the CNN focuses on extracting spatial structures and
morphological features from astronomical images. The high-level features
extracted from both data streams are combined to form a complementary feature
vector that feeds into the final classification layers, thereby improving the
overall accuracy of our model.

The ANN branch begins with an input layer, where it receives photometric
information spanning nine bands along with eight colors derived from adjacent
bands. Following this are four fully connected layers, each harboring 512
neurons. These dense layers are dedicated to capturing the complex non-linear
relationships embedded within the SED data. The output from the final dense
layer is subsequently flattened into a one-dimensional vector containing 8704
elements.

In parallel, the CNN branch operates on a $41\times 41$ pixels (8′ $\times$
8′) $r$-band image input, initiating the feature extraction with a $5\times 5$
convolutional layer comprising 32 channels. This layer is primarily
responsible for capturing basic visual features from the image data. This is
followed by an average pooling layer, which halves the size of the feature
maps while preserving the most critical information. To facilitate deeper
learning and more robust feature detection, we incorporate five ResNet (He et
al., 2015) basic blocks in succession. These blocks are arranged to address
the vanishing or exploding gradient issues by implementing shortcut
connections after every two convolutional layers. Each basic block is
comprised of four convolutional layers with $3\times 3$ kernels, with the
number of filters doubling at each subsequent block—beginning with 32 and
incrementing through 64, 128, 256, to 512. The final average pooling layer
further compresses the feature dimensions by half, then passing it to a
flattening layer that forms another one-dimensional 512-feature vector.

The feature vectors from the ANN and CNN—8704 and 512 dimensions,
respectively—are concatenated to form a comprehensive 9216-dimensional vector
that incorporates both the photometric and morphological characteristics of
the astronomical sources. This integrated vector is then refined through a
series of dense layers with a descending number of neurons (512, 256, 128, and
64), progressively reducing the dimensionality of the feature space and
concentrating on the most salient features. Culminating the network is a final
dense layer with three neurons, corresponding to the categories of stars,
galaxies, and QSOs. This output layer employs a softmax activation function to
produce a probabilistic distribution over the three classes, facilitating the
determination of the most likely category for each astronomical source.

Throughout the network, each hidden layer applies the ReLU activation function
to ensure non-linearity and prevent gradient saturation, which is vital for
maintaining gradient flow during the training process. We adopted the
categorical cross-entropy as our loss function and utilized the Adam optimizer
to refine the training of our model.

Figure 3: Evaluation metrics for classification of stars, quasars, and
galaxies at different output probability thresholds. The panels display
F1-score (top left), $\rm Frac_{thre}$ (top right), Precision (bottom left),
and Recall (bottom right), with blue, red, and green lines representing the
metrics for stars, quasars, and galaxies, respectively. Figure 4: Confusion
matrix for the internal testing dataset. Each panel has predicted categories
(star, quasar, galaxy) on the vertical axis and true categories from SDSS on
the horizontal axis. The top panel shows the number of targets predicted in
each category, while the bottom panel shows these numbers normalized as
percentages.

###  3.2 Evaluation metrics

In ML, several standard metrics are commonly employed to assess classification
performance, including Accuracy, Precision, Recall, and F1-score. These
metrics are defined in the following manner:

${\rm Accuracy=\frac{TP+TN}{TP+TN+FP+FN}},$ (3)

${\rm Precision=\frac{TP}{TP+FP}},$ (4) ${\rm Recall=\frac{TP}{TP+FN}},$ (5)
${\rm F1-score=2\times\frac{Precision\times Recall}{Precision+Recall}},$ (6)

where TP (True Positives) is the number of positive samples correctly
classified; TN (True Negatives) is the number of negative samples correctly
classified; FP (False Positives) is the number of negative samples
misclassified as positive; FN (False Negatives) is the number of positive
samples misclassified as negative.

Accuracy, as shown in Equation 3, reflects the proportion of all correctly
classified samples and provides a direct metric for evaluating overall model
performance. However, this indicator may be ineffective in the case of
imbalanced datasets. Consequently, it is primarily utilized to search for the
optimal model on the validation dataset, rather than to evaluate the detailed
performance of each class.

Precision, also known as Purity in astronomy, quantifies the fraction of true
positives among the predicted positives. Recall represents the proportion of
all positive samples that are successfully identified by the model, equivalent
to Completeness in astronomy. It is important to note that ML practitioners
often enhance classification confidence by setting a threshold for output
probabilities, potentially excluding data below the threshold. When
calculating Recall, some studies count these below-threshold samples as FN,
while others completely ignore them. In scenarios where they are included,
Recall still aligns with Completeness, otherwise, Recall needs to be adjusted
by multiplying the fraction of samples above the threshold ($\rm
Frac_{thre}$). Therefore, in our analysis of the testing dataset, we compute
$\rm Frac_{thre}$ for different thresholds. The F1-score, the harmonic average
of Precision and Recall, is particularly valuable as it provides a balanced
measure of classification performance, reflecting the overall efficacy of the
model across each category of sources. This metric was instrumental in
evaluating the ability of our multimodal neural network to classify
astronomical sources. Figure 3 displays the distribution of these evaluation
metrics across different output probability thresholds, with corresponding
values tabulated in Table 1.

Additionally, the confusion matrix is a powerful tool for evaluating
classification problems, offering a visual representation of the relationship
between model predictions for each class and the actual ground-truth
categories. Figure 4 illustrates the results at an output probability
threshold of 0.995, where each column represents the number of predictions for
the corresponding class, and each row represents the ground-truth classes. To
render the classification precision of each category more discernible, we have
normalized the confusion matrix and displayed it in a percentage format.

Table 1: Classification Performance at Different Thresholds.

Threshold | Class | Precision | Recall | F1-score | $\rm Frac_{thre}$ | Completeness
---|---|---|---|---|---|---
|  | (%) | (%) | (%) | (%) | (%)
$p\geqslant$ pmax | Star | 98.65 | 98.62 | 98.63 | 100.00 | 98.62
| QSO | 96.71 | 94.53 | 95.61 | 100.00 | 94.53
| Galaxy | 99.09 | 99.44 | 99.26 | 100.00 | 99.44
$p\geqslant$ 0.5 | Star | 98.65 | 98.62 | 98.63 | 100.00 | 98.62
| QSO | 96.76 | 94.53 | 95.63 | 100.00 | 94.53
| Galaxy | 99.09 | 99.44 | 99.27 | 99.98 | 99.42
$p\geqslant$ 0.8 | Star | 98.91 | 99.16 | 99.03 | 98.48 | 97.65
| QSO | 98.19 | 96.30 | 97.24 | 95.64 | 92.10
| Galaxy | 99.44 | 99.66 | 99.55 | 99.18 | 98.85
$p\geqslant$ 0.9 | Star | 99.06 | 99.32 | 99.19 | 97.10 | 96.44
| QSO | 98.79 | 97.08 | 97.93 | 92.93 | 90.22
| Galaxy | 99.58 | 99.76 | 99.67 | 98.23 | 98.00
$p\geqslant$ 0.99 | Star | 99.70 | 99.66 | 99.68 | 82.38 | 82.10
| QSO | 99.45 | 98.69 | 99.07 | 84.29 | 83.19
| Galaxy | 99.82 | 99.94 | 99.88 | 85.74 | 85.69
$p\geqslant$ 0.995 | Star | 99.77 | 99.77 | 99.77 | 72.32 | 72.15
| QSO | 99.66 | 99.09 | 99.37 | 80.66 | 79.93
| Galaxy | 99.87 | 99.95 | 99.91 | 78.19 | 78.15
$p\geqslant$ 0.999 | Star | 99.79 | 99.79 | 99.79 | 39.23 | 39.14
| QSO | 99.73 | 99.66 | 99.69 | 67.34 | 67.11
| Galaxy | 99.96 | 99.97 | 99.97 | 52.74 | 52.73

Note. — Evaluation metrics including Precision, Recall, F1-score, $\rm
Frac_{thre}$, and Completeness at different output probability thresholds for
stars, quasars, and galaxies.

###  3.3 Implementation

Our neural network model is implemented and trained using
Keras222https://keras.io, a high-level open-source API that provides a user-
friendly interface built on top of the TensorFlow333https://www.tensorflow.org
framework. For the training and testing process, we utilized a GPU-accelerated
computer equipped with NVIDIA GeForce RTX 3080 laptop GPU to enhance
computational efficiency.

During the training phase, the hyperparameters such as batch size and
regularization factor were determined through repeated experiments. We found
that setting the batch size and regularization factor to 128 and 0.001,
respectively, was sufficient to achieve good performance on the testing
dataset (containing 20,000 samples). To rapidly and accurately pinpoint the
optimal model, we employed a tiered learning rate strategy, conducting
training at learning rates of 1e-3, 1e-4, and 1e-5, across 30 epochs for each
rate. Each epoch took approximately 34 seconds, with a total training time of
$\sim$51 minutes. We then selected the best model based on the minimum loss
and maximum accuracy on the validation dataset. This model achieved nearly
identical performance on the testing dataset, and we arbitrarily chose the
model with the lowest loss to make predictions on the full dataset.

Figure 5: Same as Figure 4 but for confusion matrices at different output
probability thresholds, showing how the predictive performance changes with
the adjustment of the threshold.

##  4 Results and Discussion

We assessed the overall classification capability and applicability of the
proposed multimodal neural network by examining its performance on an
independent internal testing dataset. Furthermore, two external datasets were
utilized to validate the robustness and generalization ability of the model
beyond the training sample space. Finally, we applied the trained network to
the full KiDS DR5 dataset and generated a new Star-QSO-Galaxy catalog for
objects brighter than 23 mag in $r$-band.

###  4.1 Performance on Testing Datasets

####  4.1.1 Internal Testing Dataset

Although the validation dataset was not directly involved in model training,
its role in model selection may inadvertently lead to overfitting, thereby
increasing the risk of information leakage. To address this concern and
objectively assess the performance of our model, we randomly selected 20,000
spectroscopically confirmed sources from the SDSS-KiDS cross-matched sample to
compose an independent testing dataset. The sample was exclusively for final
testing, without participating in the training or validation stages. This
ensures an unbiased assessment, mitigating the potential for the model to
overfit to any particular subset of the data.

On this isolated testing dataset, our multimodal neural network achieved an
overall accuracy of 98.76%, closely aligning with the 98.69% accuracy observed
in the validation dataset. Such consistency indicates that our model
generalizes well from the validation phase to unseen new data, which is
crucial for practical applications. We then conducted more detailed
performance assessments on each class of sources, including Precision, Recall,
and F1-score. The results are presented in Figure 3 and Table 1.

The classification metrics revealed that galaxies exhibited the best
performance with all three metrics exceeding 99%. This success is largely
attributed to the enormous galaxy sample size used during training. This was
followed by the stars, with all metrics also exceeding 98.6%, reflecting
robust identification of these two types of celestial objects. QSOs achieved
slightly lower Precision and Recall at 96.71% and 94.53% respectively, likely
due to the relatively smaller training sample size, as well as the potential
for misclassification of some low-redshift active galactic nuclei as galaxies
due to contamination from their host galaxies. This latter point is evidenced
by the confusion matrix depicted in Figure 4, where the majority of
misclassified QSOs were grouped with galaxies. Despite this, a robust F1-score
of 95.6% demonstrates that the model is still reliable in terms of QSO
classification.

In machine learning paradigms, our model assigns a probability vector to each
target for classification, with each value representing the likelihood of a
predefined class (such as Stars, QSOs, or Galaxies in our definition). The sum
of these probabilities is 1, and typically, a higher probability (p) for a
target being classified into a certain class indicates greater confidence,
which implies higher Purity (Precision). Therefore, we can set a threshold for
$p$, retaining only those samples that exceed this threshold as the final
result, thereby enhancing the sample Purity. It is important to note that this
strategy, while beneficial for sample Purity, may decrease the Completeness of
the sample. For example, a higher threshold may exclude objects with
insufficient classification confidence, potentially leading to the absence of
some actual category members in the final catalog.

To balance Purity and Completeness in various astronomical applications, we
tested the performance of our multimodal neural network at different
thresholds. Figure 3 shows the variations in evaluation metrics as a function
of the threshold, with some detailed values listed in Table 1. As expected, an
increase in the threshold can improve Precision, Recall, and the F1-score,
whereas $\rm Frac_{thre}$ and the derived Completeness ($\rm
Frac_{thre}\times$ Recall, as shown in Table 1) exhibit a declining trend. We
also examined the confusion matrix at different thresholds (Figure 5), and the
results showed a clear decrement in misclassification rates with threshold
increments. This trend suggests that raising the threshold for $p$ indeed
amplifies the Purity of the sample but at the cost of Completeness.

An analysis of Figures 3 and 5 reveals that the choice of probability
threshold significantly impacts the classification of QSOs, in contrast to a
minor effect on the classification of Galaxies. This is primarily because the
model already achieves excellent performance in predicting Galaxies, leaving
limited scope for further refinement. Intriguingly, we found that when the
threshold is fixed at 0.9, the Completeness for all categories can be
maintained above 90%, and the Purity exceeds 98%. As the threshold is further
increased to 0.99, Purity can reach above 99%, while Completeness still
maintains a level of 82%. Beyond this point, Completeness quickly declines
despite a marginal gain in Purity. Hence, setting the probability threshold
between 0.9 to 0.99 appears to offer an effective balance between Purity and
Completeness.

Figure 6: Redshift distribution for the GAMA testing dataset. The black solid
line shows the distribution for all targets, while the blue dotted line, red
dashed line, and green solid line represent the distributions for targets
predicted as stars, quasars, and galaxies by the multimodal neural network,
respectively. Figure 7: $gri$ color-composited images of some misclassified
targets. The vertical axis represents the spectral classification labels from
SDSS, and the horizontal axis represents the predictions made by the
multimodal neural network. Figure 8: Color-color diagrams ($g-r$ vs. $r-i$)
for KiDS and SDSS datasets. From top to bottom, the panels represent stars,
QSOs, and galaxies. The red shaded regions indicate the cross-matched data
between SDSS and KiDS, while the blue contours represent all KiDS data
brighter than 23 mag.

####  4.1.2 External Testing Datasets

Considering the issue of pre-selected sources in the SDSS dataset, there is
potential for our neural network model to overfit to this data. To
comprehensively evaluate the generalization capability of the model in
practical applications, it is necessary to validate it on external datasets.
Currently, most publicly released spectroscopic survey data have limited
overlap with KiDS, which constrains the availability of extensive testing
samples. We primarily utilize Gaia and GAMA as external data sources to verify
the generalization performance of our model on stellar and galaxy (including
QSO) classification, respectively.

Most targets in the Gaia database do not have corresponding spectroscopic
observations, but its high-precision astrometric measurements enable us to
filter out a pure stellar sample. This sample is considered unbiased in terms
of stellar radiation and can effectively avoid potential selection effects.
Through cross-matching with KiDS, we obtained over 3.4 million independent
testing samples (see Section 2.3). None of these data were involved in model
tuning or evaluation. The test results showed that as high as 99.74% of the
targets were correctly predicted as stars, even exceeding the performance on
the internal testing dataset. This discrepancy is mainly attributed to the
contamination present in SDSS spectroscopic classifications (see Section 4.2),
indicating that our algorithm actually has superior performance in star
classification.

For extragalactic objects, we adopted the abundant spectroscopic redshift
galaxy sample from GAMA for testing. Over 230k of these targets that overlap
with KiDS but not with SDSS. The prediction results revealed that only 97.70%
of the targets were categorized as galaxies, with the remaining 1.21%
classified as stars and 1.11% as quasars, which did not appear to meet
expectations. However, upon further examination of the redshift distribution
of these targets (see Figure 6), we found that the majority of those predicted
as stars had redshifts around 0, confirming that they indeed reside within the
Milky Way. After removing these low-redshift (arbitrarily chosen $z<$ 0.04)
targets, the fraction of categorized as galaxies increased to 98.72%, while
stars and quasars accounted for 0.26% and 1.02%, respectively. Figure 6 also
shows that targets with redshifts greater than 0.8 were almost all classified
as QSOs. Given the depth of the GAMA survey, it is unlikely to observe such
high-redshift galaxies, so these classification results should be reasonable.
If QSO classification is also regarded as correct, we can conclude that the
classification Precision for extragalactic objects reached 99.74%.

In this test, we did not impose any restrictions on the threshold of $p$, but
the model still demonstrated excellent performance for both Galactic and
extragalactic targets, further confirming the stability and reliability of our
algorithm across different datasets. This establishes a solid foundation for
future applications to more extensive samples and other survey data.

###  4.2 Limitations and Challenges

In addition to the choice of ML algorithms, data quality fundamentally
determines the upper limit of model performance. Clean data allows the model
to focus on learning the underlying patterns that are consistent with the
real-world problems during the training process, thereby enhancing its
stability and interpretability. Conversely, dirty data may mislead the
learning process of model parameters and evaluation results, increasing the
risk of overfitting. Indeed, there are some misclassified targets in the SDSS
spectral data (Bolton et al., 2012; Lyke et al., 2020). However, since the
proportion of these misclassifications is relatively low (about only a few
percent), the model still performs impressively well on the testing dataset.
This can also be attributed to the strong noise-resistant capability of DNNs,
as well as the use of techniques such as regularization and batch training
during the training process. Through random inspection of misclassified
samples, we found that some SDSS labels themselves were erroneous, and our
multimodal neural network model was even able to effectively correct these
errors, especially for galaxies misclassified as stars by SDSS (as shown in
Figure 7).

The performance of the model is also influenced by the data volume. A larger
dataset can provide richer and more detailed feature representations, which
helps the model learn complex patterns and effectively mitigate noise and
outlier. This, in turn, enhances its accuracy and generalization ability. In
our training, the number of quasar samples was significantly less than that of
stars and galaxies, which somewhat limited the recognition capabilities of the
model for these targets. This indicates that although our method has
demonstrated impressive classification performance, there is still room for
further improvement as spectral data continues to accumulate in the future.

Due to the inherent extrapolation uncertainty of ML models, their
applicability typically depends on the coverage of the feature space by the
known data. In our study, the SDSS spectroscopic depth in the $r$-band is
approximately 22 mag, which is $\sim$2 mag brighter than KiDS, and there are
also differences in the color distribution between them (see Figure 1).
Therefore, it is necessary to filter the prediction data to ensure the
reliability of the final results. This requires understanding the specific
feature space boundaries of the model, which is a challenge for neural network
models. We primarily compared the brightness and color distributions of the
two databases—historically the most commonly used features—and found that the
most significant difference was in brightness. By limiting our focus to
targets with $r$-band magnitudes brighter than 23, we found that the color
distribution of most KiDS data aligned with SDSS (e.g., 99.96% of $u-g$ colors
were within the range of -1 to 4). This phenomenon may be related to the
requirements in the data preprocessing stage, where all bands must have
reliable photometric detection values, thus excluding some extremely red and
blue targets. The color consistency increases our confidence in the prediction
results for brighter sources, but also introduces limitations for the model in
identifying targets with extreme color properties.

To determine the applicable brightness range of the model, we conducted the
following tests. First, we selected two equal-sized samples based on their
$r$-band magnitudes, with brightness ranges of $16.5\leq r<18.5$ mag and
$18.5\leq r<20.5$ mag, respectively. By comparing the model performance of
these two brightness groups, we found that their classification abilities were
basically equivalent. Even when extrapolating the testing data by 1 mag toward
the faint end, the performance evaluation metrics did not show a significant
decline for either model. Subsequently, we further tested the model using
three different brightness thresholds ($r<19$ mag, $r<20$ mag, and $r<21$
mag), confirming that all three results could essentially extrapolate by 1 mag
under these conditions. These two tests help us infer that our multimodal
neural network can effectively handle targets with magnitudes up to $\sim$23
mag.

While there may be other feature restrictions besides brightness, the testing
results from the Gaia and GAMA surveys suggest that their impact is not
substantial. These two datasets, apart from the targets being relatively
bright ($r<$ 20 mag), may have different feature distributions compared to
SDSS, but our model still performs very well on them, indicating that within
the permissible brightness range, the model can be well generalized to new
data.

Furthermore, some intrinsic issues with KiDS data could also affect the
accuracy of the final predictions. For instance, the presence of obvious
companions or saturation around some targets (as shown in Figure 7) may impact
the measurement of target flux or the extraction of morphological features,
potentially leading to misclassification. Systematically addressing these
issues requires comprehensive cleaning and preprocessing of predictive data,
which is beyond the scope of this study.

Table 2: Column Descriptions of the KiDS DR5 Galaxy-QSO-Star Catalog

No. | Column Name | Description | Units | Datatype
---|---|---|---|---
1 | Name | KiDS unique source identifier from ASTROband table | - | string
2 | RA | J2000 Right Ascension | degree | double
3 | DEC | J2000 Declination | degree | double
4 | $r$ | KiDS $r$-band GAaP magnitude | mag | double
5 | class | classification: STAR/QSO/GALAXY | - | string
6 | $p_{\rm max}$ | Maximum output probability | - | double

Note. — Description of columns in the KiDS DR5 Galaxy-QSO-Star Catalog. The
table lists the properties stored for each object, including identifiers,
coordinates, magnitudes, classification results, and probabilities.

###  4.3 Application to KiDS DR5

We apply the trained multimodal neural network model to the entire KiDS DR5
dataset to predict the categories of target sources. Our goal is to compile a
new Star-QSO-Galaxy catalog covering an area of approximately 1350 deg2.
According to our prior testing outcomes, we only classify targets with an
$r$-band magnitude less than 23. To facilitate diverse research interests, we
provide the $r$-band magnitude and the associated maximum output probability
($p_{\rm max}$) for each target, with detailed information listed in Table 2.

This value-added catalog contains a total of 27,334,751 targets, of which
6,427,859 are identified as stars, 3,304,636 as quasars, and 17,602,220 as
galaxies. Notably, 13,068,232 targets fall within the $22<r\leqslant 23$ mag
range in the $r$-band, which are extrapolated results, accounting for nearly
half ($\sim$47.81%) of the total number of targets. This portion of the data
exceeds the brightness range directly trained by our model, yet the model has
demonstrated acceptable accuracy and stability within this magnitude range in
previous tests. Therefore, we decide to include these extrapolated results in
the final catalog.

To validate the effectiveness of our final classification results, we compared
the $g-r$ vs. $r-i$ color-color distributions of stars, QSOs, and galaxies in
our KiDS catalog with those in the SDSS dataset. As shown in Figure 8, the
results exhibit a general agreement between the two datasets, suggesting that
our model successfully captures the overall color properties of different
sources. Furthermore, we examined the size-magnitude diagram for each class of
sourcesfor each class of sources, which is a commonly used method to
differentiate between stars and galaxies (e.g., Zuntz et al., 2018). Here, we
adopt the half-light radius ($R_{1/2}$) to represent size, and the magnitude
is in the $r$-band. The results are shown in Figure 9. It is evident that
stars are primarily located at the bright end, with sizes typically consistent
with the PSF, reflecting their point-source nature. In contrast, galaxies are
predominantly found at the fainter end and exhibit significantly larger sizes
compared to stars, indicative of their more extended structures. Quasars are
primarily distributed between the star and galaxy populations in the size-
magnitude space. This distribution aligns well with known observational
characteristics and supports our classification results.

Figure 10 presents the $r$-band magnitude distribution for each category,
revealing a dominance of stars at the brighter end ($r<20$ mag), while the
number of quasars and galaxies increases rapidly towards the faint end, which
aligns with empirical expectations. Moreover, the distribution of $p_{\rm
max}$ (Figure 10) indicates exceedingly high classification confidence for the
majority of targets. Over 85% of the catalog entries have a $p_{\rm
max}\geqslant 0.9$, and remarkably, for targets with $r\leqslant 22$ mag, this
proportion exceeds 91%. This means that even under relatively stringent
selection criteria, we can still obtain about 13 million high-confidence
classification results.

Figure 9: The $r$ vs. $R_{1/2}$ for objects in our catalog. The contours
represent the density distribution of stars (blue), QSOs (red), and galaxies
(green). The dashed line (black) at $0.41^{\prime\prime}$ indicates the
$R_{1/2}$ corresponding to the average KiDS $r$-band seeing of
$0.7^{\prime\prime}$, assuming a Gaussian PSF where $R_{1/2}\approx
0.5887\times\mathrm{FWHM}$. Figure 10: Distribution of $r$-band magnitude (top
panel) and maximum output probability (bottom panel) for each type of object
in the value-added catalog. Each panel plots the distribution for targets
predicted as stars (blue dotted line), quasars (red dashed line), and galaxies
(green solid line). Figure 11: Examples of spectra, SEDs, and images for
different categories. The left panels show the SDSS spectra (black solid line)
and the SEDs from KiDS nine bands (red points). The right panels show color-
composited images from KiDS $gri$-bands.

###  4.4 Model Interpretation

Neural network models are often regarded as “black boxes” with internal
decision-making processes that are opaque to humans. This opacity makes it
difficult to directly analyze the intrinsic connections between celestial
object classification and their physical properties. Here, we attempt to use
empirical knowledge to explain the features that the model may have learned
during the its training, aiming to better understand the physical mechanisms
behind its excellent performance.

The proposed multimodal neural network extracts information from two input
branches: SED and image. As shown in Figure 11, different types of celestial
objects inherently exhibit distinct SED and morphological characteristics. The
SED primarily reflects the differences in internal radiation mechanisms and
the distances (redshifts) of the objects. Stars, for instance, typically
exhibit SEDs that can be approximated by blackbody radiation, with peak
positions mainly determined by their effective temperatures. On the other
hand, the spectrum of quasars in the ultraviolet to optical bands is dominated
by the “big blue bump”, a feature produced by high-temperature radiation from
the accretion disk, while the near-infrared is predominantly emission from hot
dust (Sanders et al., 1989; Elvis et al., 1994). The multi-wavelength
luminosity of galaxies is more complex, as it involves the combined effects of
stellar populations and dust (Conroy, 2013). The nine-band photometric data
provided by KiDS spans a broader wavelength coverage than SDSS spectra,
potentially yielding additional physical information. For example, the SED
peak of M-type stars is located in the near-infrared band (see Figure 11), and
as the redshift increases, the contribution of the “big blue bump” in quasars
becomes more pronounced in the optical-near-infrared bands. This prior
knowledge suggests that the model may achieve classification by learning the
relative brightness across multiple bands.

For the imaging side, it can provide rich details of the morphology of
celestial objects. These morphological features not only contain information
about the physical nature of objects but might also refine flux measurements,
as the shapes of different objects can affect the results of GAaP
measurements. To test the impact of images on classification, we separately
used MLP to classify the SED (see Appendix), and found that the performance
was significantly inferior to the multimodal neural network. This demonstrates
that incorporating morphological information can indeed significantly improve
classification efficacy. To further confirm which information directly aids
classification, we normalized all images and found that there was a negligible
effect on model performance. This implies that during the classification
process, the model primarily relies on the physical morphological features
rather than simply re-measuring the flux from the images. This is consistent
with the human inferential strategies, where we prefer to use the physical
properties of morphology itself rather than mere flux correction when
classifying. For example, extended galaxies are easily distinguishable from
stellar point sources, and the size can be used to estimate the distance of
the galaxy (see also Figure 9). For high-redshift quasars and compact
galaxies, they may appear more like stars in images, but we can at least rule
out the possibility of them being low-redshift extragalactic objects.

In summary, the multimodal neural network can extract luminosity information
from photometric data and morphological features from image data, and mapping
both to a high-dimensional feature space via a nonlinear function. Within this
space, various categories are effectively separated, thus achieving the
purpose of classification. The accuracy and efficiency of this method hold
promise for widespread application in next-generation multi-color survey
projects such as LSST, WFST (Wang et al., 2023), and Mephisto (Han et al.,
2022). Future space survey projects (e.g., CSST and Euclid) will provide
unprecedented high-resolution images and slitless spectral data, which will
further refine our model and enhance the precision of astronomical
classification. Moreover, the anticipated wealth of spectral data from future
spectroscopic surveys will enable our model to extend its performance to
fainter magnitudes.

##  5 Conclusion

In this work, we have developed a multimodal neural network architecture that
effectively combines morphological information from images and multi-band
photometry for the classification of stars, quasars, and galaxies in the KiDS
DR5 survey. By training on SDSS spectroscopic labels and testing on both
internal and external datasets, we demonstrate the model’s high accuracy,
robustness, and ability to generalize to new data. Our key findings are:

  1. 1.

On the internal SDSS testing dataset, the model achieves an overall accuracy
of 98.76%, with per-class F1 scores of 98.63%, 95.61%, and 99.26% for stars,
QSOs, and galaxies respectively. Raising the output probability threshold can
boost purity at the cost of completeness.

  2. 2.

The model correctly classifies 99.74% of a pure Gaia star sample, higher than
the performance on the SDSS testing dataset, indicating potential mislabeling
in SDSS that the network helps correct. It also correctly classifies 99.74% of
GAMA galaxies after accounting for low-redshift contaminants.

  3. 3.

We apply the model to classify over 27 million KiDS DR5 sources down to $r=23$
mag. Over 85% of the resulting catalog has a maximum probability $\geqslant$
0.9, indicating high classification confidence.

  4. 4.

The model’s strong performance stems from its ability to extract both
morphological and SED features. Normalizing images has little effect, showing
the network relies on physical morphological information rather than just flux
correction. Compared to an SED-only MLP, the multimodal network achieves
significantly better performance.

This work presents a novel and effective approach for classifying astronomical
sources by leveraging deep learning to combine imaging and photometric data.
The resulting catalog will enable a wide range of galaxy evolution, large-
scale structure, and cosmology studies with KiDS DR5. Future work will extend
the technique to a wider range of surveys and wavelengths, and explore its
potential for identifying unusual objects. Integrating multimodal information
with deep learning offers a promising tool for maximizing the scientific
return from the next generation of large-scale astronomical surveys.

This work is supported by National Key R&D Program of China (No.
2021YFA1600404), the National Natural Science Foundation of China (NSFC grants
No. 12303022, 12203096, 12203050, 12373018, 11991051, and 12203041), Yunnan
Fundamental Research Projects (grants NO. 202301AT070358 and 202301AT070339),
Yunnan Postdoctoral Research Foundation Funding Project, Special Research
Assistant Funding Project of Chinese Academy of Sciences, and the science
research grants from the China Manned Space Project with No. CMS-
CSST-2021-A06, NRN acknowledges financial support from the NSFC, Research Fund
for Excellent International Scholars (grant No. 12150710511), and from the
research grant from China Manned Space Project n. CMS-CSST-2021-A01.

This research made use of the cross-match service provided by CDS, Strasbourg.
Based on data products from observations made with ESO Telescopes at the La
Silla Paranal Observatory under programme IDs 177.A-3016, 177.A-3017 and
177.A-3018, and on data products produced by Target/OmegaCEN, INAF-OACN, INAF-
OAPD and the KiDS production team, on behalf of the KiDS consortium. OmegaCEN
and the KiDS production team acknowledge support by NOVA and NWO-M grants.
Members of INAF-OAPD and INAF-OACN also acknowledge the support from the
Department of Physics & Astronomy of the University of Padova, and of the
Department of Physics of Univ. Federico II (Naples). Funding for the Sloan
Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the
U.S. Department of Energy Office of Science, and the Participating
Institutions. SDSS-IV acknowledges support and resources from the Center for
High Performance Computing at the University of Utah. The SDSS website is
www.sdss4.org. SDSS-IV is managed by the Astrophysical Research Consortium for
the Participating Institutions of the SDSS Collaboration including the
Brazilian Participation Group, the Carnegie Institution for Science, Carnegie
Mellon University, Center for Astrophysics — Harvard & Smithsonian, the
Chilean Participation Group, the French Participation Group, Instituto de
Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the
Physics and Mathematics of the Universe (IPMU) / University of Tokyo, the
Korean Participation Group, Lawrence Berkeley National Laboratory, Leibniz
Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie
(MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-
Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical
Observatories of China, New Mexico State University, New York University,
University of Notre Dame, Observatário Nacional / MCTI, The Ohio State
University, Pennsylvania State University, Shanghai Astronomical Observatory,
United Kingdom Participation Group, Universidad Nacional Autónoma de México,
University of Arizona, University of Colorado Boulder, University of Oxford,
University of Portsmouth, University of Utah, University of Virginia,
University of Washington, University of Wisconsin, Vanderbilt University, and
Yale University. This work has made use of data from the European Space Agency
(ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia
Data Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. GAMA is a joint European-
Australasian project based around a spectroscopic campaign using the Anglo-
Australian Telescope. The GAMA input catalogue is based on data taken from the
Sloan Digital Sky Survey and the UKIRT Infrared Deep Sky Survey. Complementary
imaging of the GAMA regions is being obtained by a number of independent
survey programmes including GALEX MIS, VST KiDS, VISTA VIKING, WISE, Herschel-
ATLAS, GMRT and ASKAP providing UV to radio coverage. GAMA is funded by the
STFC (UK), the ARC (Australia), the AAO, and the participating institutions.
The GAMA website is https://www.gama-survey.org/.

Figure 12: The same as Figure 3, but showing evaluation metrics for
classification using only the MLP branch.

##  Appendix A Performance of MLP

To assess the contribution of morphological information in our multimodal
neural network, we conducted an independent performance evaluation of the MLP
branch. In this test, the MLP branch used only the SED features from the KiDS
dataset, which include photometry from 9-bands and 8 adjacent band colors,
without integrating the morphological features processed by the CNN branch.
The MLP was trained and evaluated using the same training and testing datasets
as the full multimodal network. Figure 12 shows the evaluation metrics for the
MLP at different output probability thresholds, analogous to Figure 3 for the
full multimodal network.

The MLP achieves an overall accuracy of 97.15% on the testing dataset, with F1
scores of 96.13%, 89.90%, and 98.49% for stars, quasars, and galaxies at the
default threshold. While still good, these metrics are noticeably lower than
the performance of the multimodal network, especially for quasars. The MLP
maintains high purity for galaxies and stars as the threshold is raised, but
suffers a faster drop in completeness compared to the multimodal network. For
quasars, the MLP fails to achieve both high purity and high completeness at
any threshold, whereas the multimodal network can reach 99% purity with 83%
completeness at $p\geqslant 0.99$.

These results demonstrate that the morphological information extracted by the
CNN branch contributes significantly to the high performance of the multimodal
network, especially when dealing with objects that are difficult to
distinguish morphologically. In this way, the multimodal neural network
effectively leverages complementary information from different data sources to
achieve high-accuracy classification of stars, quasars, and galaxies.

## References

  * Abdurro’uf et al. (2022) Abdurro’uf, Accetta, K., Aerts, C., et al. 2022, ApJS, 259, 35. doi:10.3847/1538-4365/ac4414
  * Aihara et al. (2018) Aihara, H., Arimoto, N., Armstrong, R., et al. 2018, PASJ, 70, S4. doi:10.1093/pasj/psx066
  * Bai et al. (2019) Bai, Y., Liu, J., Wang, S., et al. 2019, AJ, 157, 9. doi:10.3847/1538-3881/aaf009
  * Baldwin et al. (1981) Baldwin, J. A., Phillips, M. M., & Terlevich, R. 1981, PASP, 93, 5. doi:10.1086/130766
  * Behroozi et al. (2013) Behroozi, P. S., Wechsler, R. H., & Conroy, C. 2013, ApJ, 770, 57. doi:10.1088/0004-637X/770/1/57
  * Bolton et al. (2012) Bolton, A. S., Schlegel, D. J., Aubourg, É., et al. 2012, AJ, 144, 144. doi:10.1088/0004-6256/144/5/144
  * Bond et al. (1996) Bond, J. R., Kofman, L., & Pogosyan, D. 1996, Nature, 380, 603. doi:10.1038/380603a0
  * Buchs et al. (2019) Buchs, R., Davis, C., Gruen, D., et al. 2019, MNRAS, 489, 820. doi:10.1093/mnras/stz2162
  * Cabayol et al. (2019) Cabayol, L., Sevilla-Noarbe, I., Fernández, E., et al. 2019, MNRAS, 483, 529. doi:10.1093/mnras/sty3129
  * Capaccioli & Schipani (2011) Capaccioli, M. & Schipani, P. 2011, The Messenger, 146, 2
  * Capaccioli et al. (2012) Capaccioli, M., Schipani, P., de Paris, G., et al. 2012, Science from the Next Generation Imaging and Spectroscopic Surveys, 1
  * Chaini et al. (2023) Chaini, S., Bagul, A., Deshpande, A., et al. 2023, MNRAS, 518, 3123. doi:10.1093/mnras/stac3336
  * Conroy (2013) Conroy, C. 2013, ARA&A, 51, 393. doi:10.1146/annurev-astro-082812-141017
  * Chen (2021) Chen, Y. C. 2021, ApJS, 256, 34. doi:10.3847/1538-4365/ac13aa
  * Cui et al. (2012) Cui, X.-Q., Zhao, Y.-H., Chu, Y.-Q., et al. 2012, Research in Astronomy and Astrophysics, 12, 1197. doi:10.1088/1674-4527/12/9/003
  * de Jong et al. (2015) de Jong, J. T. A., Verdoes Kleijn, G. A., Boxhoorn, D. R., et al. 2015, A&A, 582, A62. doi:10.1051/0004-6361/201526601
  * The Dark Energy Survey Collaboration (2005) The Dark Energy Survey Collaboration 2005, astro-ph/0510346. doi:10.48550/arXiv.astro-ph/0510346
  * DESI Collaboration et al. (2016) DESI Collaboration, Aghamousa, A., Aguilar, J., et al. 2016, arXiv:1611.00036. doi:10.48550/arXiv.1611.00036
  * Dieleman et al. (2015) Dieleman, S., Willett, K. W., & Dambre, J. 2015, MNRAS, 450, 1441. doi:10.1093/mnras/stv632
  * Driver et al. (2011) Driver, S. P., Hill, D. T., Kelvin, L. S., et al. 2011, MNRAS, 413, 971. doi:10.1111/j.1365-2966.2010.18188.x
  * Driver et al. (2022) Driver, S. P., Bellstedt, S., Robotham, A. S. G., et al. 2022, MNRAS, 513, 439. doi:10.1093/mnras/stac472
  * Dubois et al. (2022) Dubois, J., Fraix-Burnet, D., Moultaka, J., et al. 2022, A&A, 663, A21. doi:10.1051/0004-6361/202141729
  * Edge et al. (2013) Edge, A., Sutherland, W., Kuijken, K., et al. 2013, The Messenger, 154, 32
  * Elvis et al. (1994) Elvis, M., Wilkes, B. J., McDowell, J. C., et al. 1994, ApJS, 95, 1. doi:10.1086/192093
  * Fadely et al. (2012) Fadely, R., Hogg, D. W., & Willman, B. 2012, ApJ, 760, 15. doi:10.1088/0004-637X/760/1/15
  * Feng et al. (2021) Feng, H.-C., Hu, C., Li, S.-S., et al. 2021, ApJ, 909, 18. doi:10.3847/1538-4357/abd851
  * Fotopoulou et al. (2016) Fotopoulou, S., Pacaud, F., Paltani, S., et al. 2016, A&A, 592, A5. doi:10.1051/0004-6361/201527402
  * Gaia Collaboration et al. (2016) Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1. doi:10.1051/0004-6361/201629272
  * Gaia Collaboration et al. (2021) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2021, A&A, 649, A1. doi:10.1051/0004-6361/202039657
  * Gaia Collaboration et al. (2022) Gaia Collaboration, Vallenari, A., Brown, A. G. A., et al. 2022, arXiv:2208.00211
  * Gong et al. (2019) Gong, Y., Liu, X., Cao, Y., et al. 2019, ApJ, 883, 203. doi:10.3847/1538-4357/ab391e
  * Guo et al. (2022) Guo, Z., Wu, J. F., & Sharon, C. E. 2022, arXiv:2212.07881. doi:10.48550/arXiv.2212.07881
  * Han et al. (2022) Han, Z., Yuan, X., Li, Z., et al. 2022, Proc. SPIE, 12188, 1218842. doi:10.1117/12.2637071
  * He et al. (2015) He, K., Zhang, X., Ren, S., et al. 2015, arXiv:1512.03385. doi:10.48550/arXiv.1512.03385
  * Helmi (2020) Helmi, A. 2020, ARA&A, 58, 205. doi:10.1146/annurev-astro-032620-021917
  * Hubble (1926) Hubble, E. P. 1926, ApJ, 64, 321. doi:10.1086/143018
  * Ilbert et al. (2009) Ilbert, O., Capak, P., Salvato, M., et al. 2009, ApJ, 690, 1236. doi:10.1088/0004-637X/690/2/1236
  * Ivezić et al. (2019) Ivezić, Ž., Kahn, S. M., Tyson, J. A., et al. 2019, ApJ, 873, 111. doi:10.3847/1538-4357/ab042c
  * Kelvin et al. (2014) Kelvin, L. S., Driver, S. P., Robotham, A. S. G., et al. 2014, MNRAS, 439, 1245. doi:10.1093/mnras/stt2391
  * Khramtsov et al. (2019) Khramtsov, V., Sergeyev, A., Spiniello, C., et al. 2019, A&A, 632, A56. doi:10.1051/0004-6361/201936006
  * Khramtsov et al. (2021) Khramtsov, V., Spiniello, C., Agnello, A., et al. 2021, A&A, 651, A69. doi:10.1051/0004-6361/202040131
  * Kormendy & Ho (2013) Kormendy, J. & Ho, L. C. 2013, ARA&A, 51, 511. doi:10.1146/annurev-astro-082708-101811
  * Kuijken et al. (2019) Kuijken, K., Heymans, C., Dvornik, A., et al. 2019, A&A, 625, A2. doi:10.1051/0004-6361/201834918
  * Kuijken et al. (2015) Kuijken, K., Heymans, C., Hildebrandt, H., et al. 2015, MNRAS, 454, 3500. doi:10.1093/mnras/stv2140
  * Laureijs et al. (2011) Laureijs, R., Amiaux, J., Arduini, S., et al. 2011, arXiv:1110.3193. doi:10.48550/arXiv.1110.3193
  * Lecun et al. (1998) Lecun, Y., Bottou, L., Bengio, Y., & Haffner, P. 1998, Proc. IEEE, 86, 2278. doi: 10.1109/5.726791.
  * Li et al. (2019) Li, R., Shu, Y., Su, J., et al. 2019, MNRAS, 482, 313. doi:10.1093/mnras/sty2708
  * Li et al. (2022) Li, R., Napolitano, N. R., Feng, H., et al. 2022, A&A, 666, A85. doi:10.1051/0004-6361/202244081
  * Logan & Fotopoulou (2020) Logan, C. H. A. & Fotopoulou, S. 2020, A&A, 633, A154. doi:10.1051/0004-6361/201936648
  * López-Sanjuan et al. (2019) López-Sanjuan, C., Vázquez Ramió, H., Varela, J., et al. 2019, A&A, 622, A177. doi:10.1051/0004-6361/201732480
  * Lyke et al. (2020) Lyke, B. W., Higley, A. N., McLane, J. N., et al. 2020, ApJS, 250, 8. doi:10.3847/1538-4365/aba623
  * MacGillivray et al. (1976) MacGillivray, H. T., Martin, R., Pratt, N. M., et al. 1976, MNRAS, 176, 265. doi:10.1093/mnras/176.2.265
  * McCulloch et al. (1943) McCulloch, W. S., Pitts W., 1943, Bull. Math. Biophys., 5, 115. doi:10.1007/BF02478259
  * Nakazono et al. (2021) Nakazono, L., Mendes de Oliveira, C., Hirata, N. S. T., et al. 2021, MNRAS, 507, 5847. doi:10.1093/mnras/stab1835
  * Peters et al. (2015) Peters, C. M., Richards, G. T., Myers, A. D., et al. 2015, ApJ, 811, 95. doi:10.1088/0004-637X/811/2/95
  * Richards et al. (2002) Richards, G. T., Fan, X., Newberg, H. J., et al. 2002, AJ, 123, 2945. doi:10.1086/340187
  * Salpeter (1964) Salpeter, E. E. 1964, ApJ, 140, 796. doi:10.1086/147973
  * Salvato et al. (2009) Salvato, M., Hasinger, G., Ilbert, O., et al. 2009, ApJ, 690, 1250. doi:10.1088/0004-637X/690/2/1250
  * Salvato et al. (2022) Salvato, M., Wolf, J., Dwelly, T., et al. 2022, A&A, 661, A3. doi:10.1051/0004-6361/202141631
  * Sanders et al. (1989) Sanders, D. B., Phinney, E. S., Neugebauer, G., et al. 1989, ApJ, 347, 29. doi:10.1086/168094
  * Schmidt (1963) Schmidt, M. 1963, Nature, 197, 1040. doi:10.1038/1971040a0
  * Scranton et al. (2002) Scranton, R., Johnston, D., Dodelson, S., et al. 2002, ApJ, 579, 48. doi:10.1086/342786
  * Sevilla-Noarbe et al. (2018) Sevilla-Noarbe, I., Hoyle, B., Marchã, M. J., et al. 2018, MNRAS, 481, 5451. doi:10.1093/mnras/sty2579
  * Skrutskie et al. (2006) Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163. doi:10.1086/498708
  * Smith & Geach (2023) Smith, M. J. & Geach, J. E. 2023, Royal Society Open Science, 10, 221454. doi:10.1098/rsos.221454
  * Szklenár et al. (2020) Szklenár, T., Bódi, A., Tarczay-Nehéz, D., et al. 2020, ApJ, 897, L12. doi:10.3847/2041-8213/ab9ca4
  * Tadaki et al. (2020) Tadaki, K.-. ichi ., Iye, M., Fukumoto, H., et al. 2020, MNRAS, 496, 4276. doi:10.1093/mnras/staa1880
  * Taylor (2005) Taylor, M. B. 2005, Astronomical Data Analysis Software and Systems XIV, 347, 29
  * Verro et al. (2022) Verro, K., Trager, S. C., Peletier, R. F., et al. 2022, A&A, 660, A34. doi:10.1051/0004-6361/202142388
  * Wang et al. (2023) Wang, T., Liu, G., Cai, Z., et al. 2023, Science China Physics, Mechanics, and Astronomy, 66, 109512. doi:10.1007/s11433-023-2197-5
  * Wright et al. (2010) Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868. doi:10.1088/0004-6256/140/6/1868
  * Xie et al. (2023) Xie, L., Napolitano, N. R., Guo, X., et al. 2023, Science China Physics, Mechanics, and Astronomy, 66, 129513. doi:10.1007/s11433-023-2173-8
  * Yang & Shen (2023) Yang, Q. & Shen, Y. 2023, ApJS, 264, 9. doi:10.3847/1538-4365/ac9ea8
  * Yee (1991) Yee, H. K. C. 1991, PASP, 103, 396. doi:10.1086/132834
  * York et al. (2000) York, D. G., Adelman, J., Anderson, J. E., et al. 2000, AJ, 120, 1579. doi:10.1086/301513
  * Zhang et al. (2023) Zhang, X., Green, G. M., & Rix, H.-W. 2023, MNRAS, 524, 1855. doi:10.1093/mnras/stad1941
  * Zhou et al. (2021) Zhou, X., Gong, Y., Meng, X.-M., et al. 2021, ApJ, 909, 53. doi:10.3847/1538-4357/abda3e
  * Zuntz et al. (2018) Zuntz, J., Sheldon, E., Samuroff, S., et al. 2018, MNRAS, 481, 1149. doi:10.1093/mnras/sty2219