Vol.0 (20xx) No.0, 000–000

11institutetext: School of Physical Science and Technology, Xinjiang
University, Urumqi 830046, China<EMAIL_ADDRESS>
22institutetext: Xinjiang Astronomical Observatory, Chinese Academy of
Sciences, 150 Science 1-Street, Urumqi, Xinjiang 830011, China;
<EMAIL_ADDRESS>
Received 2023 ****; accepted 2023 ****

# Identifying symbiotic stars with machine learning

Yongle Jia 11 Sufen Guo 1*1* Chunhua Zhu 11 Lin Li 11 Mei Ma 11 Guoliang Lü
221*1*

###### Abstract

Symbiotic stars are interacting binary systems, making them valuable for
studying various astronomical phenomena, such as stellar evolution, mass
transfer, and accretion processes. Despite recent progress in the discovery of
symbiotic stars, a significant discrepancy between the observed population of
symbiotic stars and the number predicted by theoretical models. To bridge this
gap, this study utilized machine learning techniques to efficiently identify
new symbiotic stars candidates. Three algorithms (XGBoost, LightGBM, and
Decision Tree) were applied to a dataset of 198 confirmed symbiotic stars and
the resulting model was then used to analyze data from the LAMOST survey,
leading to the identification of 11,709 potential symbiotic stars candidates.
Out of the these potential symbiotic stars candidates listed in the catalog,
15 have spectra available in the SDSS survey. Among these 15 candidates, two
candidates, namely V* V603 Ori and V* GN Tau, have been confirmed as symbiotic
stars. The remaining 11 candidates have been classified as accreting-only
symbiotic star candidates. The other two candidates, one of which has been
identified as a galaxy by both SDSS and LAMOST surveys, and the other
identified as a quasar by SDSS survey and as a galaxy by LAMOST survey.

###### keywords:

binaries: symbiotic — techniques: spectroscopic — binaries: spectroscopic —
methods: data analysis

##  1 Introduction

Symbiotic stars are a unique type of binary system, characterized by prolonged
interactions between the two stars (Lü et al. 2006, 2009, 2012; Han et al.
2020). These systems are composed of three components: a hot companion such as
a white dwarf, neutron star, or main sequence star with an accretion disk; a
cool companion, such as a red giant or asymptotic giant branch star; and an
ionized nebula formed from material lost by the cool companion (Kenyon et al.
1991; Munari et al. 2021). The spectrum of symbiotic stars is composed of
common features, including emission lines from the hot companion, absorption
lines from the cool companion, and the nebula’s material. In many symbiotic
stars, the cool companion loses mass through stellar wind or Roche-lobe
overflow, while the hot companion accretes enough material to produce the
symbiotic phenomenon (Mikołajewska 2007; Akras et al. 2021; Iłkiewicz et al.
2022). Symbiotic stars provide an excellent sample for studying the loss of
matter, acceleration mechanisms of stellar winds, and accretion of stellar
winds in late-type giants (Chen et al. 2017; Saladino et al. 2019). They are
also considered to be the precursors of $\rm I$a supernovae and important
sources of soft and hard X-rays (Munari & Renzini 1992).

Since symbiotic stars are unique astrophysical laboratories. Allen (1984)
provided a catalog of symbiotic stars, including 129 symbiotic stars and 15
symbiotic stars candidates. Kenyon (2009) summarized a catalog of symbiotic
stars, including 133 symbiotic stars and 20 symbiotic stars candidates.
Belczyński et al. (2000) provided a more detailed catalog of 188 symbiotic
stars and 30 symbiotic stars candidates. Akras et al. (2019a) provided a
catalog of 323 known symbiotic stars, 257 are Galactic and 66 extragalactic.
Akras (2023) obtained 814 symbiotic star candidates by GALEX UV and
2MASS/AllWISE IR photometry, and identified two symbiotic stars after spectral
analysis. Akras et al. (2019a) proposed a new subfamily of symbiotic stars for
the first time: the S+IR type.

The symbiotic stars are classified into four categories: S, D, D’, and S+IR
(Akras et al. 2019a). Akras et al. (2019a) used a blackbody radiation model to
fit the spectral energy map of symbiotic stars and found a number of S-type
symbiotic stars with an S-type SED profile and an infrared excess in the mid-
infrared regime. Akras et al. (2019a) named these symbiotic stars S+IR type.
Most of the symbiotic stars are S-type, and the SED profiles of S-type
symbiotic stars peak at 0.8 to 1.7 $\upmu$m with an average value of 1.07
$\upmu$m. Of course, a small percentage of S-type symbiotic stars with SED
diagrams peaking around 0.7 or 1.8 $\upmu$m. The temperature is between 3400
and 3800 K. Thirteen percent of the symbiotic stars are D-type, and the SED
diagram for D-type symbiotic stars peaks at 2 to 4 $\upmu$m with an average
value of 2.85 $\upmu$m. The number of D’-type symbiotic stars is relatively
small, with only 10 known symbiotic stars with G/K spectral type. The SED
diagram of D’-type symbiotic stars has two peaks between 2 and 10 $\upmu$m.
The SED diagram of S+IR-type symbiotic stars has a peak at 1.3 $\upmu$m. The
IR excess indicates the presence of a dusty shell around the symbiotic star
and a lower temperature than that of the D-type. It is most likely that there
is an accretion disk around the white dwarf (Akras et al. 2019a). Currently,
there is a lack of in-depth research on the spectral characteristics of S+IR-
type symbiotic stars. However, Gutierrez-Moreno & Moreno (1996); Pereira et
al. (1998); Mürset & Schmid (1999); Pereira et al. (2005); Kogure & Leung
(2007); Stoyanov et al. (2020) had conducted research on the spectral
characteristics of S-type, D-type and D’-type symbiotic stars. The latest list
of symbiotic stars was summarized by Merc et al. (2020), with 275 symbiotic
stars and 119 symbiotic stars candidates in the galaxy. Although the number of
observed symbiotic stars is increasing, the number of observed symbiotic stars
differs significantly from what was predicted. Lü et al. (2006) predicted that
the number of symbiotic stars with white dwarf(WD) accretors in the Galaxy may
range from about 1200 to 15000, and the model birth rate of symbiotic stars in
the Galaxy is from 0.035-0.131 yr-1. It is predicted that the number of
symbiotic stars in the galaxy should be from 3$\times$103 to 4$\times$105
(Allen 1984; Magrini et al. 2003; Lü et al. 2006). The number of known
symbiotic stars is very different from the predicted number, so we need to
discover more symbiotic stars to provide astronomers with data. Previously,
symbiotic stars were found by spectroscopic analysis. With the introduction of
various telescopes, astronomical data has grown exponentially, and the
previous methods of processing data are unsuitable for the current
requirements of processing large data. We need a new method to discover new
symbiotic stars from the huge amount of astronomical observation data.

Machine learning has become a well-established tool in the field of astronomy.
For instance, Gulati et al. (1998) and Singh et al. (1998) employed artificial
neural networks to classify stellar spectra, while Bu et al. (2014) applied
support vector machines to achieve a more detailed classification of stellar
spectra. Guo et al. (2018) utilized support vector machines to establish Wide-
field Infrared Survey Explorer (WISE) mid-infrared color criteria for the
selection of quasar candidates, resulting in the compilation of a catalog of
quasar candidates. Fu et al. (2021) employed the Extreme Gradient Boosting
(XGBoost) algorithm for machine learning to Pan-STARRSI (PSI) and AllWISE
photometry in order to classify quasars behind the Galactic plane (GPQ). This
led to the development of a reliable GPQ candidate catalog. Akras et al.
(2021) utilized machine learning methods to discover five new symbiotic stars
and proposed a novel method for their identification, thus rendering the
determination of symbiotic stars no longer dependent on spectroscopic analysis
alone. However, the method employed by Akras only distinguished symbiotic
stars from other objects containing $\rm H$ emission lines. It is likely that
other types of objects exist that have not been considered. Therefore, it is
imperative to develop a model that can be applied more broadly. In this study,
we expand upon this idea and propose a method that can be used to quickly
identify symbiotic stars among a large number of objects. We used the
aggregated coordinates of symbiotic stars that were cross-matched with AllWISE
and Two Micron All Sky Survey (2MASS) data for machine learning training, and
then applied the trained machine model to identify new symbiotic stars in
Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST). Through
the application of machine learning, we were able to identify a new set of
symbiotic stars candidates.

The paper is divided into several sections. in Section 2, we provide a
detailed description of the data sources utilized, including AllWISE, 2MASS,
LAMOST, and Sloan Digital Sky Survey (SDSS), and the composition of the
training data. In Section 3, we discuss the machine learning models selected
and the training process. In Section 4, we present our prediction results and
the spectral analysis of two newly-discovered symbiotic stars. Lastly, in
Section 5 we summarize our results.

##  2 Data

###  2.1 The AllWISE catalog

The WISE is a medium class explorer mission funded by NASA (Duval et al. 2004;
Wright et al. 2010; Liu et al. 2008). WISE uses a 40 cm telescope to image the
entire sky in four infrared bands W1, W2, W3, and W4 at 3.4, 4.6, 12, and 22
$\upmu$m and has already produced over a million images and hundreds of
millions of celestial bodies have been observed. The AllWISE catalog (Cutri et
al. 2021) extends the results of the Wide-field Infrared Survey Mission (Cutri
& et al. 2012). It combines data from the cryogenic and post-cryogenic periods
to provide the most comprehensive mid-infrared overview currently available.
The AllWISE Source Catalog contains accurate positions, motion measurements,
photometry and ancillary information for 747,634,026 objects (Cutri et al.
2013). The AllWISE survey has yielded better photometric sensitivity,
accuracy, and astrometric precision data than the WISE survey.

###  2.2 The 2MASS catalog

The 2MASS observes the sky in the near-infrared J (1.25 $\upmu$m ), H (1.65
$\upmu$m), and Ks (2.16 $\upmu$m) band separately, covering 99.998$\%$ of the
sky observed from both the northern 2MASS facility at Mt. Hopkins, AZ, and the
southern 2MASS facility at Cerro Tololo, Chile(Cutri et al. 2003; ). The
release data products include 4,121,439 Atlas Images in the three survey
bands, and Catalogs containing positional and photometric information for
470,992,970 Point sources and 1,647,599 Extended sources(Kleinmann 1992;
Kleinmann et al. 1994; Skrutskie et al. 2006).

###  2.3 The LAMOST catalog

The LAMOST is a new type of wide field of view and large aperture telescope
that is a special quasi-meridian reflecting Schmidt telescope located in
Xinglong Station of the National Astronomical Observatory, China (Cui et al.
2012; Zhao et al. 2012; Luo et al. 2015). LAMOST is an international leader in
the field of wide-field optical spectroscopy and astronomy. It observes
astronomical spectra in the northern sky. LAMOST began its first spectroscopic
survey in September 2012 and has released its tenth data release (LAMOST DR 10
v0), containing more than 11 million spectra of 10 million stars, 242,569
galaxies, and 76,167 quasars.

###  2.4 The SDSS catalog

The SDSS (Gunn et al. 1998; Finlator et al. 2000; York et al. 2000) is a wide-
field optical/infrared imaging and spectroscopy survey using a dedicated 2.5-m
wide-angle optical telescope at Apache Point Observatory. SDSS started in 1998
and has completed four phases: $\rm I$, $\rm II$, $\rm III$, $\rm IV$ and $\rm
V$. Currently, the SDSS 18th data (DR18) has been released (Almeida et al.
2023). SDSS provides images, spectra, and scientific catalogs. To date, more
than 6 million spectra have been observed by SDSS (Abdurro’uf et al. 2022).

###  2.5 Feature selection

The 2MASS J-H versus H-Ks color-color distribution diagrams have been widely
used to investigate the near-infrared properties of symbiotic stars, and to
differentiate between S-type, D-type, or other new candidates(Allen & Glass
1974; Rodríguez-Flores et al. 2014; Baella et al. 2013). Baella et al. (2016)
discovered that the W3-W4 color index from the WISE survey can differentiate
normal K giants from D-type symbiotic stars. Akras et al. (2019b) also
utilized the magnitudes from both 2MASS and WISE surveys to distinguish
symbiotic stars from other objects with strong H emission lines. Therefore, in
our study, we used magnitudes from seven bands (W1, W2, W3, W4, J, H, and Ks)
as the features for model training.

###  2.6 Data set composition

Currently, Merc et al. (2020) summarized the previously discovered and
confirmed symbiotic stars into a new symbiotic star catalog. As of September
2022, this catalog contains 275 Galactic and 200 extragalactic symbiotic
stars. This is by far the most comprehensive catalog of symbiotic stars. Since
a lot of observational data about stars in the Milky Way, we only use the
total of 275 Galactic symbiotic stars summarized in this catalog. We cross-
matched the aggregated 275 symbiotic stars with AllWISE at a radius of 10
arcsec due to the angular resolution of the WISE survey, which is 6.1′′,
6.4′′, 6.5′′ & 12.0′′ at 3.4, 4.6, 12 & 22 $\upmu$m (Wright et al. 2010). The
cross-match radius between the target source and the matched source is shown
in Figure 1. The sources in the catalog are cross-matched to their
corresponding sources in AllWISE, and 82.5$\%$ (227) of them are cross-matched
to sources in AllWISE with a radius less than 0.4 arcsec, only 3 sources were
found to have a radius greater than 10 arcsec. We believe that these 3 sources
do not have corresponding sources in AllWISE. We performed cross-matching
operations using TOPCAT (Taylor 2005). The AllWISE catalog has been cross-
matched with 2MASS with a matching radius of 3 arcsec (Cutri et al. 2013).
Therefore, when cross-matching a catalog with the AllWISE catalog, the
resulting match will include magnitude information from the 2MASS catalog. Two
symbiotic stars were missing some magnitude information, thus leaving a total
of 270 symbiotic stars available for training. We randomly divided the 270
symbiotic stars available for training into two parts. The first part
consisted of 198 symbiotic stars used as positive samples to compose the data
set with non-symbiotic stars. The second part consisted of 72 symbiotic stars
used separately to test the trained models.

We used the LAMOST DR9 V1.0 spectroscopic dataset, which comprises a vast
collection of 10,907,516 star spectra, 242,569 galaxy spectra, and 76,167
quasar spectra. To compose a training set, we employed a random selection
strategy to choose one spectrum from every 500 star spectra, one spectrum from
every 20 galaxy spectra, and one spectrum from every 3 quasar spectra. We
cross-matched the selected sources with AllWISE using a matching radius of 1
arcsec to ensure accurate matches. We removed spectra without 2MASS
magnitudes, resulting in a dataset of 12,348 star spectra, 9,014 galaxy
spectra, and 3,797 quasar spectra. Finally, we composed the dataset by using
these non-symbiotic stars as negative samples together with the 198 positive
samples.

Due to the significant difference in the number of symbiotic stars and non-
symbiotic stars in the training set, we randomly selected an additional 200
non-symbiotic stars from the non-symbiotic star samples in the training set as
additional training set samples. Additionally, boxplots were used to depict
the distribution of the training and test sets in different bands, as
illustrated in Figure 2. The horizontal orange line inside the box in the
boxplot represents the median of the sample data for the corresponding band.
The upper and lower limits of the box represent the upper quartile and lower
quartile of the sample data for the corresponding band, respectively. There is
a line above and below the box, which represents the maximum and minimum
values of the sample data in the corresponding band. Hollow dots indicate some
outliers in the sample data in the corresponding band. As illustrated in
Figure 2 , it can be observed that the two parts of the data exhibit a
homogeneous distribution.

Figure 1: The radial distance between the 275 symbiotic stars and the matched
sources in AllWISE.  Figure 2: The sequence of boxplots displays the magnitude
distribution of different sets of stars. Specifically, Boxplots (a) exhibit
the magnitude distribution of 25,159 non-symbiotic stars, with Boxplots (b)
and (c) presenting the magnitude distribution of the subset assigned to the
training and testing sets, respectively. Similarly, Boxplots (d) show the
magnitude distribution of 270 symbiotic stars, with Boxplots (e) and (f)
displaying the magnitude distribution of the subset assigned to the training
and validation sets, respectively. Lastly, Boxplots (g) illustrate the
magnitude distribution of 200 randomly selected non-symbiotic stars, with
Boxplots (h) and (i) depicting the magnitude distribution of the subset
assigned to the training and testing sets, respectively. The horizontal orange
line inside the box in the boxplot represents the median of the sample data
for the corresponding band. The upper and lower limits of the box represent
the upper quartile and lower quartile of the sample data for the corresponding
band, respectively. There is a line above and below the box, which represents
the maximum and minimum values of the sample data in the corresponding band.
Hollow dots indicate some outliers in the sample data in the corresponding
band. Figure 3: Distribution chart of feature importance for 16 best machine
learning models.

##  3 Model training

###  3.1  Model selection

In this work, we utilized three machine learning algorithms: the Decision Tree
algorithm, the XGBoost algorithm, and the Light Gradient Boosting Machine
(LightGBM) algorithm.

The Decision Tree algorithm is a method for approximating the value of a
discrete function (Rokach & Maimon 2005; Barros et al. 2012), and is a
commonly used classification technique. It begins by processing the data and
generating a set of readable rules and decision trees through an induction
algorithm. These rules are then used to analyze new data, effectively
classifying it. This algorithm is a popular method for predictive modeling in
fields such as statistics, data mining, and machine learning (Kotsiantis & S.
2013). The Decision Tree algorithm is a tree-like structure that can be used
to solve classification and regression problems. The construction process of a
decision tree is based on the training set. Firstly, a feature is chosen as
the root node, and then the dataset is divided into several subsets. Each
subset of data has the same feature value. Then, a feature is selected as a
node for classification in each data subset in turn. This process is repeated
until a complete decision tree is generated. The advantage of a decision tree
is that it is easy to understand and interpret, and the classification rules
can be clearly understood. However, decision trees also suffer from the
problem of overfitting, which needs to be optimized through methods such as
pruning (Barros et al. 2012). Vasconcellos et al. (2011) explored 13 Decision
tree algorithms for star/galaxy classification using SDSS DR7 data and
proposed a novel method that can accurately distinguish between stars and
galaxies with high precision.

The XGBoost algorithm, proposed by Tianqi Chen at the University of
Washington, is a powerful tool for classification and regression tasks (Chen &
Guestrin 2016; Wang et al. 2020). It is composed of multiple Classification
And Regression Tree decision trees, each of which learns the residual of the
target value and the sum of all previous tree predictions. The final
prediction is made by combining the results of all the trees (Friedman et al.
2000). Though each weak classifier may not have a high global prediction
accuracy, they can still have a very high prediction accuracy for specific
aspects of the data(Chen & Guestrin 2016). By combining many classifiers with
high local prediction accuracy, the XGBoost algorithm can achieve the effect
of a strong classifier with high global prediction accuracy. It has gained
popularity in data modeling competitions due to its excellent computing
efficiency and prediction accuracy. It is widely used in various fields such
as identifying stars, galaxies, and quasars from Beijing-Arizona Sky Survey
(BASS) DR3 with accuracy more than 90$\%$ and classifying stars and galaxies
using different models from SDSS DR7 (Li et al. 2022; Li et al. 2019).

The LightGBM algorithm is a scalable machine learning system developed by
Microsoft in 2017. It is an open-source project led by Guolin Ke, a winner of
the first Alibaba Big Data Competition in 2014. The algorithm is based on the
Gradient Boosting Decision Tree and is designed to reduce memory and
computational requirements while also minimizing communication costs when used
in parallel with multiple machines (Ke et al. 2017). LightGBM can
automatically identify effective data features and is considered an improved
version of the XGBoost algorithm, providing faster training speed and lower
memory consumption while maintaining a similar level of accuracy (Wang et al.
2020). Due to its efficient performance on large-scale datasets, LightGBM has
become a popular tool in data competitions. Malik et al. 2022 used LightGBM to
identify planets in simpler data and Transiting Exoplanet Survey Satellite
(TESS) data, with very good results.

###  3.2  Data Balancing Algorithms

During machine learning training, it has been observed that when the number of
negative samples exceeds that of positive samples, the model focuses more on
the characteristics of negative samples. Therefore, it is necessary to use
some methods to reduce the issues caused by the serious imbalance between the
number of positive and negative samples. To address this issue, we employed
the Synthetic Minority Oversampling Technique (SMOTE) algorithm (Castellanos
et al. 2018) and the Edited Nearest Neighbours (ENN) algorithm (Wilson 1972)
to balance the dataset.

SMOTE is an algorithm used to address imbalanced classification problems. It
generates synthetic samples of the minority class by interpolating between
existing samples. The steps are: select a sample, identify its k nearest
neighbors, randomly select one neighbor, generate a new synthetic sample, and
repeat until the desired number of samples is reached. The new samples are
combined with the original minority class samples to create a balanced dataset
(Chawla et al. 2002).

ENN is an undersampling technique commonly employed for addressing class
imbalance by reducing the majority class to match the minority class (Tang &
He 2015). In order to determine whether the majority class of an observation’s
k nearest neighbors is the same as the class of the observation itself, the
ENN technique identifies the k nearest neighbors for each observation. If the
majority class of an observation’s k nearest neighbors differs from the class
of the observation, both the observation and its k nearest neighbor are
removed from the dataset (Kim 2021).

SMOTE and ENN algorithms were applied to the training data, resulting in the
construction of 12 machine learning models. To compare with the generated 12
models and accurately identify symbiotic stars, we constructed a new training
set with a nearly 1:1 ratio of positive and negative samples. We randomly
selected 200 non-symbiotic stars from the training set and combined them with
our 198 symbiotic stars to create the new training set. We applied the
Decision Tree, XGBoost, and LightGBM algorithms to the new training set,
resulting in the construction of a total of 16 machine learning models
throughout our research process. Table 1 shows the algorithms and
constructions used for the 16 models.

###  3.3  Results

We randomly partitioned the dataset into a training set consisting of 80$\%$
of the data set and a test set consisting of 20$\%$ of the data set, with the
aim of ensuring a randomized partition. The training set was utilized for
training the machine learning models, while the test set was employed for
evaluating the performance of the machine learning models. We trained the
models with Scikit-learn. Scikit-learn is a Python-based open-source machine
learning library that offers an extensive collection of tools and algorithms
for data analysis, including classification, regression, clustering,
dimensionality reduction, and model selection (Pedregosa et al. 2011;Buitinck
et al. 2013). During the training process, we employ 5-fold cross-validation
and GridSearchCV to optimize the model parameters. Cross-validation is a
statistical analysis method commonly used to evaluate prediction performance
and maximize data utilization (Yadav & Shukla 2016). GridSearchCV is a
traditional approach for hyperparameter optimization in machine learning
(Müller & Guido 2016).

To evaluate the performance of our machine learning models, we used four key
evaluation metrics: Precision, Recall, F1-Score, and AUC. These metrics are
defined as follows:

  1. 1.

Precision: The proportion of true positive samples among the predicted
positive samples. It is calculated as TP / (TP + FP).

  2. 2.

Recall: The proportion of true positive samples that are correctly predicted
as positive. It is calculated as TP / (TP + FN).

  3. 3.

F1-Score: The harmonic mean of precision and recall. It is calculated as 2 *
(precision * recall) / (precision + recall).

  4. 4.

AUC: The area under the ROC curve, which can be used to measure the
performance of a classification model. The AUC value ranges from 0 to 1, with
a higher value indicating better model performance.

Here, TP represents the number of samples predicted by the model as symbiotic
stars and are actually symbiotic stars. FP represents the number of samples
predicted by the model as symbiotic stars but are actually non-symbiotic
stars. FN represents the number of samples predicted by the model as non-
symbiotic stars but are actually symbiotic stars. The primary evaluation
metric for our trained model in this study was Precision, as our goal was to
accurately identify a maximum number of symbiotic stars.

The performance of 16 models on the test set is summarized in Table 2. For a
comprehensive understanding of the parameters of these models, please refer to
Appendix A. Additionally, Figure 3 presents the feature importance of the
trained models. From Figure 3, it can be observed that the feature importance
of W2 is very high in the models that used decision trees (Models 1, 2, 5, 6,
9, 10, 13, and 14). The feature importance of other magnitudes is very low,
indicating that decision tree models, although easy to construct and
structurally simple, may not be stable enough. In the models that utilized
XGBoost (Models 3, 7, 11, and 15), W2 and W1 have relatively high feature
importance. For the models that employed LightGBM (Models 4, 8, 12, and 16),
the feature importance of W4 and W3 is relatively high. The performance of the
trained models was evaluated using a separate set of 72 symbiotic stars. Table
3 provides a clear view of the predictions made by each model for these 72
symbiotic stars.

Table 1: Summarizing the 16 best performing machine learning models | Decision Tree_gini |  | Decision Tree_entropy |  | XGBoost |  | LightGBM
---|---|---|---|---|---|---|---
Raw dataset | Model 1 |  | Model 2 |  | Model 3 |  | Model 4
SMOTE | Model 5 |  | Model 6 |  | Model 7 |  | Model 8
ENN | Model 9 |  | Model 10 |  | Model 11 |  | Model 12
200 non-symbiotic stars | Model 13 |  | Model 14 |  | Model 15 |  | Model 16
Table 2: The performance of the 16 best models in predicting symbiotic stars on the test set, presented as Precision, Recall, F1-Score, and the AUC scores. | model 1 | model 2 | model 3 | model 4 | model 5 | model 6 | model 7 | model 8
---|---|---|---|---|---|---|---|---
Precision | 0.94 | 0.94 | 0.92 | 0.94 | 0.96 | 0.92 | 0.91 | 0.94
Recall | 0.88 | 0.88 | 0.88 | 0.92 | 0.92 | 0.94 | 0.98 | 0.90
F1-Score | 0.91 | 0.91 | 0.90 | 0.93 | 0.94 | 0.93 | 0.94 | 0.92
AUC | 0.94 | 0.94 | 0.94 | 0.96 | 0.96 | 0.97 | 0.99 | 0.95
| model 9 | model 10 | model 11 | model 12 | model 13 | model 14 | model 15 | model 16
Precision | 0.94 | 0.96 | 0.94 | 0.94 | 0.97 | 0.97 | 0.97 | 1.00
Recall | 0.96 | 0.87 | 0.92 | 0.92 | 0.97 | 0.97 | 0.97 | 0.97
F1-Score | 0.95 | 0.91 | 0.93 | 0.93 | 0.97 | 0.97 | 0.97 | 0.99
AUC | 0.98 | 0.93 | 0.96 | 0.96 | 0.97 | 0.97 | 0.97 | 0.99
Table 3: The results presented in the table are the predictions made by the 16 trained models for 72 known symbiotic stars (SySts) | model 1 | model 2 | model 3 | model 4 | model 5 | model 6 | model 7 | model 8
---|---|---|---|---|---|---|---|---
ŷ = SySts | 60 | 59 | 63 | 62 | 59 | 62 | 66 | 63
| model 9 | model 10 | model 11 | model 12 | model 13 | model 14 | model 15 | model 16
ŷ = SySts | 62 | 53 | 64 | 62 | 70 | 70 | 70 | 70

##  4 Identifying Symbiotic Stars

The most reliable method for determining symbiotic stars is through
spectroscopic analysis. The earliest criteria for identifying symbiotic stars
were proposed by Merrill & Humason (1932), stating that a symbiotic star is a
binary system with a combined spectrum. As the study of symbiotic stars
progressed, more refined criteria for identifying symbiotic stars were
proposed, with the most current and widely accepted criteria being those
proposed by Belczyński et al. (2000). However, it is important to note that
these criteria are only applicable to burning symbiotic stars, and accreting-
only symbiotic stars may not show these spectral features unless an outburst
occurs (Merc et al. 2021). In this study, we used the criteria proposed by
Belczyński et al. (2000) to classify symbiotic stars. These criteria are as
follows:

  1. 1.

resence spectral features of late-type giants such as $\rm TiO$, $\rm H_{2}O$,
$\rm CO$, $\rm CN$ and $\rm VO$ bands as well as $\rm Ca$$\rm I$, $\rm Ca$$\rm
II$, $\rm Fe$$\rm I$ and $\rm Na$$\rm I$ absorption lines.

  2. 2.

the detection of some typical emission lines, for instance $\rm H$$\rm I$ and
$\rm He$$\rm I$. emission lines of ions with an ionization potential of at
least 35 eV (e.g. [$\rm O$$\rm III$], [$\rm Fe$$\rm
VII$]$\lambda$$\lambda$5727,6087, [$\rm He$$\rm II$]$\lambda$4686).

  3. 3.

the presence of strong emission lines of $\rm O$$\rm
VI$$\lambda$$\lambda$6830,7088 (Mikolajewska et al. 1997; Belczyński et al.
2000; Akras et al. 2019a).

Akras et al. (2019b) proposed a new method for determining symbiotic stars
using a mid-infrared criterion. This criterion was used to successfully
discover five previously unknown symbiotic stars in the galaxy (Akras et al.
2021).

We aimed to classify symbiotic stars among a sample of 11,226,252 sources from
LAMOST DR9 v1.0 using 16 machine learning models. We cross-matched the sources
with the AllWISE and 2MASS catalogs at a radius of 6 arcsec, and obtained
magnitude data for a total of 10,849,157 sources. The models were then
utilized to identify symbiotic stars. In order to indentifying more reliable
symbiotic star prediction, we employed a methodology that integrates the
results of multiple models to verify the classification of a star as a
symbiotic star. This ensures that the star is identified as a symbiotic star
by all of the models used in our analysis.

A total of 11,709 sources were jointly identify as symbiotic stars by the 16
models. These sources were then cross-matched with SDSS DR17 at a radius of 6
arcsec, and 15 of them were found to have spectral information. Among these 15
candidates, one was classified as a galaxy by both surveys, while another was
identified as a quasar by SDSS and a galaxy by LAMOST, and 13 were found to
have spectra similar to symbiotic stars. We have created a catalog of the
relevant information for these sources and made it available on the
website111https://doi.org/10.12149/101183. The spectra of 2 of the extent 13
sources are more in line with the criteria of Belczyński et al. (2000) for
determining the spectra of symbiotic stars. The spectra of the extent 11
sources are similar to the accreting-only symbiotic star V562Lyr.

Here we discussed the spectra of the two sources that have been newly
predicted as symbiotic stars.

###  4.1 V* V603 Ori

V* V603 Ori (= 2MASS J05393983-0233160; RA2000 = 05 39 39.8292920832, DEC2000
= -02 33 16.040160936; see also Table 4) displays more prominent $\rm
H$$\alpha$ , $\rm He$$\rm I$ lines, which increases the likelihood that it is
a symbiotic star. Additionally, the presence of more distinct $\rm He$$\rm
II$, $\rm H$$\beta$, $\rm He$$\rm I$ $\lambda$4930, $\rm O$$\rm III$
$\lambda$5007, and also $\rm H$$\gamma$(Figure 4) lines further supports this
possibility. However, V* V603 Ori differs from the newly discovered symbiotic
star DR2J141301.4-6533201.1 in Akras et al. (2021), as the latter lacks the
$\rm O$$\rm III$ $\lambda$4363 line, yet is still considered a symbiotic star.
V* V603 Ori also exhibits some spectral characteristics of red giants, such as
a molecular band containing $\rm TiO$ and absorption Na lines, as well as
emission lines like$\rm Ne$$\rm III$. According to the magnitude information
of AllWISE and 2MASS of V* V603 Ori, it is classified as an S+IR-type
symbiotic star. However, the TESS survey has not captured any obvious light
variation in V* V603 Ori, thus it cannot be confirmed as a symbiotic star
through light variation analysis. Fortunately, the renormalised unit weight
error (RUWE) parameter in GaiaDR3 is an essential indicator for determining
whether a star is binary. According to Hambly et al. (2021), when the RUWE
value is 1.4, it is likely that the star is not single. In the case of V* V603
Ori, the RUWE value is 1.4. Iłkiewicz & Mikołajewska (2017) explored various
other emission lines including [N II], [O III], [Ne III] and HeI lines, in
order to distinguish planetary nebulae from symbiotic stars and proposed
criteria for symbiotic stars based on emission line ratios. for example,
$\log([\mathrm{O}\text{ III] }5006/[\mathrm{N}\text{ II] }5755)<2.6\text{ and
}\log([\mathrm{Ne}\text{ III] }3869/[\mathrm{O}\text{ III }]4363)<0.45$. V*
V603 Ori meets this criterion. V* V603 Ori has been classified as an M0
spectral type star by LAMOST. The symbiotic stars were cross-matched with the
Gaia catalog within 5 arcsec , and corresponding diagnostic colour-colour
diagrams were plotted for The Gaia $\mathit{G}_{\mathit{BP}}$-$\mathit{G}$
versus $\mathit{G}_{\mathit{BP}}$-$\mathit{G}_{\mathit{RP}}$. In the figure5,
V* V603 Ori was highlighted in red. Based on the above information, we
classify V* V603 Ori as a newly discovered symbiotic star.

Table 4: Basic properties of V* V603 Ori and V* GN Tau. Data are from Gaia DR3 (Gaia Collaboration et al. 2023), 2MASS (Skrutskie et al. 2006), and AllWISE (Wright et al. 2010). Soucre | RA | DEC | J | H | Ks |  W1 |  W2 |  W3 |  W4
---|---|---|---|---|---|---|---|---|---
| (J2000) | (J2000) | (mag) | (mag) | (mag) | (mag) | (mag) | (mag) | (mag)
V* V603 Ori | 84.915955 | -02.554456 | 12.22 ± 0.03 | 10.96 ± 0.02 | 10.07 ± 0.02 | 8.96 ± 0.02 | 8.33 ± 0.03 | 6.76 ± 0.02 | 5.05 ± 0.04
V* GN Tau | 69.837176 | +25.750563 | 10.20 ± 0.03 | 8.89 ± 0.03 | 8.06 ± 0.03 | 7.16 ± 0.04 | 6.53 ± 0.02 | 4.91 ± 0.01 | 3.05 ± 0.02
Figure 4: Low resolution spectra of V* V603 Ori from SDSS. Top left panel
shows the V* V603 Ori observed spectra in SDSS. The top right panel displays
the images of the V* V603 Ori in SDSS. South is down, west to the right.
Bottom panels zoom in the $\rm H$$\gamma$ and $\rm O$$\rm III$ 4363Å lines,
$\rm He$$\rm II$ 4686Å line, $\rm H$$\beta$ and $\rm O$$\rm III$ 5007Å lines,
$\rm H$$\alpha$ and $\rm He$$\rm I$ emission lines.  Figure 5: The Gaia
$\mathit{G}_{\mathit{BP}}$-$\mathit{G}$ versus
$\mathit{G}_{\mathit{BP}}$-$\mathit{G}_{\mathit{RP}}$ for symbiotic stars. The
sources were identified through cross-matching 275 symbiotic stars with the
Gaia catalog within a radius of 5 arcsec and are represented in blue. V* V603
Ori and V* GN Tau are shown in red and orange, respectively.

###  4.2 V* GN Tau

The source J043920.90+254502.1 in LAMOST cross-matched with AllWISE is V* GN
Tau(see also Table 4), which is predicted to be a symbiotic star by our model.
The SDSS spectrogram of V* GN Tau displays prominent $\rm H$$\alpha$ and $\rm
He$$\rm I$ lines (Figure 6), suggesting that it is a strong candidate for
being a symbiotic star. Other noticeable lines in the spectrum include $\rm
He$$\rm II$ ,$\rm H$$\beta$, $\lambda$4930, $\rm O$$\rm III$ $\lambda$5007,
and also $\rm H$$\gamma$ and $\rm Na$$\rm I$ absorption, as well as a
molecular band of $\rm TiO$. Although there is a lack of $\rm O$$\rm III$
$\lambda$4363 lines, it does not necessarily exclude the possibility of V* GN
Tau being a symbiotic star. Other known symbiotic stars such as AS 201, V3811
Sgr, and V407 Cyg also display a similar absence of certain spectral lines
(refer to Table A.7 in Kenyon (2009)). The spectrum of V* GN Tau is similar to
that of DR2J175346.2-284826.16, which was previously identified as a symbiotic
candidate by Akras et al. (2021).

The magnitude information of V* GN Tau in AllWISE and 2MASS supports its
classification as an S+IR-type symbiotic star according to Akras’ mid-infrared
color standards. However, the lack of clear light variation in V* GN Tau as
captured by the TESS survey hinders us from fully confirming its status as a
symbiotic star through photometric analysis. The RUWE parameter value of V* GN
Tau is not available in GaiaDR3, thus it is not possible to determine whether
V* GN Tau is a binary star. V* GN Tau also meets Iłkiewicz & Mikołajewska
(2017) criterion. V* GN Tau has been classified as an M4/3 spectral type star
by LAMOST. In the figure5, V* GN Tau was highlighted in orange. But V* GN Tau
is still identified as a symbiotic star based on its spectral information.

Figure 6: Low resolution spectra of V* GN Tau Ori from SDSS. Top left panel
shows the V* GN Tau observed spectra in SDSS. The top right panel displays the
images of the V* GN Tau in SDSS. South is down, west to the right. Bottom
panels zoom in the $\rm H$$\gamma$ and $\rm O$$\rm III$ 4363Å lines, $\rm
He$$\rm II$ 4686Å line, $\rm H$$\beta$ and $\rm O$$\rm III$ 5007Å lines, $\rm
H$$\alpha$ and $\rm He$$\rm I$ emission lines.

##  5 Discussion and conclusions

In this study, the AllWISE and 2MASS magnitude data of known symbiotic stars
were used to identify potential symbiotic stars through a machine learning
approach. The constructed model processed 10,849,157 AllWISE and 2MASS
catalogs from LAMOST DR9 sources and identified 11,709 symbiotic stars.

We analyzed the SDSS spectra of these symbiotic star candidates and discovered
two new symbiotic stars, namely V* V603 Ori and V* GN Tau. The spectra of
these two symbiotic stars were found to be consistent with the spectral
classification criteria of Belczyński et al. (2000) and the mid-infrared color
classification criteria of Akras et al. (2019b).

Actually, the criteria for identifying symbiotic stars based on their spectra
are typically used for active, or “burning” symbiotic stars. However, some
symbiotic stars can remain hidden for a long period of time, referred to as
accreting-only symbiotic stars (Pujol et al. 2023). These stars do not exhibit
the spectroscopic characteristics of active symbiotic stars and do not have
distinct emission lines in the optical band, but instead, are bright in the
ultraviolet spectrum (Luna et al. 2013; Mukai et al. 2016; Munari et al. 2021;
Merc et al. 2021). An example of this is V1988 Sgr, whose spectrum was
analyzed by Merc et al. (2021) and found to not match the spectral features of
active symbiotic stars. Despite this, Merc et al. (2021) concluded that V1988
Sgr could not be ruled out as an accreting-only symbiotic star. Another
example is V562 Lyr, which was identified as a symbiotic star despite the
absence of prominent $\rm H$ and $\rm He$ lines. This weakening or
disappearance of optical emission lines in the spectra of symbiotic stars has
been found to be due to a decrease in the accretion rate by Pujol et al.
(2023).

Among the 11 remaining stars in our candidates catalog, we observed similar
spectra, tentatively classifying them as accreting-only symbiotic star
candidates. The next step in our research will be to observe these additional
11 candidates and gather more evidence to make a definitive classification.
Further observations and data are necessary to confirm this classification.

###### Acknowledgements.

This work received the generous support of the Natural Science Foundation of
Xinjiang No.2021D01C075, the National Natural Science Foundation of China,
project Nos. 12163005, 12003025, U2031204 and 11863005, the science research
grants from the China Manned Space Project with NO. CMS-CSST-2021-A10, the
Scientific Research Program of the Higher Education Institution of Xinjiang
(No. XJEDU2022P003). Data resources are supported by China National
Astronomical Data Center (NADC) and Chinese Virtual Observatory (China-VO).
This work is supported by Astronomical Big Data Joint Research Center, co-
founded by National Astronomical Observatories, Chinese Academy of Sciences
and Alibaba Cloud. This work made use of Astropy:222http://www.astropy.org a
community-developed core Python package and an ecosystem of tools and
resources for astronomy (Astropy Collaboration et al. 2013; Astropy
Collaboration et al. 2018; Astropy Collaboration et al. 2022). This
publication makes use of data products from the Wide-field Infrared Survey
Explorer, which is a joint project of the University of California, Los
Angeles, and the Jet Propulsion Laboratory/California Institute of Technology,
and NEOWISE, which is a project of the Jet Propulsion Laboratory/California
Institute of Technology. WISE and NEOWISE are funded by the National
Aeronautics and Space Administration. This publication makes use of data
products from the Two Micron All Sky Survey, which is a joint project of the
University of Massachusetts and the Infrared Processing and Analysis
Center/California Institute of Technology, funded by the National Aeronautics
and Space Administration and the National Science Foundation. Guoshoujing
Telescope (the Large Sky Area Multi-Object Fiber Spectroscopic Telescope
LAMOST) is a National Major Scientific Project built by the Chinese Academy of
Sciences. Funding for the project has been provided by the National
Development and Reform Commission. LAMOST is operated and managed by the
National Astronomical Observatories, Chinese Academy of Sciences. 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.

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##  Appendix A Algorithm and Parameter Details of the 16 Machine Learning
Models

Here is a detailed description of the parameters of these 16 models:

Models 1 through 4 were trained without using the SMOTE and ENN algorithms for
data balancing. The training set consisted of 146 symbiotic stars and 20,139
non-symbiotic stars. Model 1 was a Decision Tree model that used the Gini
index as the splitting criterion. Model 2 was a Decision Tree model that used
entropy as the splitting criterion. Model 3 was an XGBoost model, and Model 4
was a LightGBM model.

Models 5 through 8 were trained on a balanced dataset using the SMOTE
algorithm. We conducted multiple rounds of parameter selection and determined
the optimal parameter values for SMOTE algorithm using grid search, which are
k_neighbors = 1 and sampling_strategy = ’minority’. After applying SMOTE, the
training set consisted of 20,139 symbiotic stars and 20,139 non-symbiotic
stars. Model 5 was a DecisionTree model trained on the SMOTE-balanced data
using the Gini index as the splitting criterion, similar to Model 1. Model 6
was a DecisionTree model trained on the SMOTE-balanced data using the entropy
criterion as the splitting criterion, similar to Model 2. Model 7 was an
XGBoost model trained on the SMOTE-balanced data. Model 8 was a LightGBM model
trained on the SMOTE-balanced data.

Models 9 through 12 were trained using the ENN algorithm to balance the data.
We conducted multiple rounds of parameter selection and determined the optimal
parameter values for ENN algorithm using grid search, which are kind_sel =
’mode’, n_neighbors = 1 and sampling_strategy = ’majority’. After the
application of ENN, the training set consisted of 20,120 symbiotic stars and
146 non-symbiotic stars. Model 9 is a DecisionTree model trained on the ENN-
balanced data using the Gini index as the splitting criterion, similar to
Model 1. Model 10 is a DecisionTree model trained on the ENN-balanced data
using the entropy criterion as the splitting criterion, similar to Model 2.
Model 11 is an XGBoost model trained on the ENN-balanced data. Model 12 is a
LightGBM model trained on the ENN-balanced data.

Models 13 through 16 were trained without using the SMOTE and ENN algorithms
for data balancing. The training set consisted of 159 symbiotic stars and 159
non-symbiotic stars. Model 13 was a Decision Tree model that used the Gini
index as the splitting criterion. Model 14 was a Decision Tree model that used
entropy as the splitting criterion. Model 15 was an XGBoost model, and Model
16 was a LightGBM model.

The optimal model parameters obtained after training are as follows:

Model 1:  class_weight = None, criterion = ’gini’, max_depth = 7, max_features
= 6, min_samples_leaf = 5, min_samples_split = 51, splitter = ’best’.

Model 2:  class_weight = None, criterion = ’entropy’, max_depth = 10,
max_features = 3, min_samples_leaf = 2, min_samples_split = 3, splitter =
’best’.

Model 3:  colsample_bytree = 0.6, gamma = 0, learning_rate = 0.1, max_depth =
15, min_child_weight = 1, n_estimators = 580, reg_alpha = 0.1, reg_lambda =
0.1, scale_pos_weight = 300, subsample = 0.9.

Model 4:  colsample_bytree = 0.6, learning_rate = 0.1, max_depth = 11,
min_child_weight = 1, n_estimators = 500, reg_alpha = 0, reg_lambda = 0,
scale_pos_weight = 300, subsample = 0.9.

Model 5:  class_weight = None, criterion = ’gini’, max_depth = 15,
max_features = 5, min_samples_leaf = 2, min_samples_split = 6, splitter =
’best’.

Model 6:  class_weight = None, criterion = ’entropy’, max_depth = 15,
max_features = 7, min_samples_leaf = 2, min_samples_split = 6, splitter =
’best’.

Model 7:  colsample_bytree = 0.6, gamma = 0.1, learning_rate = 0.1, max_depth
= 15, min_child_weight = 0.1, n_estimators = 100, reg_alpha = 0, reg_lambda =
0, scale_pos_weight = 1, subsample = 0.8.

Model 8:  colsample_bytree = 0.6, learning_rate = 0.1, max_depth = 11,
min_child_weight = 1, n_estimators = 500, reg_alpha = 0, reg_lambda = 0,
scale_pos_weight = 1, subsample = 0.6.

Model 9:  class_weight = None, criterion = ’gini’, max_depth = 15,
max_features = 4, min_samples_leaf = 3, min_samples_split = 6, splitter =
’best’.

Model 10:  class_weight = None, criterion = ’entropy’, max_depth = 20,
max_features = 7, min_samples_leaf = 9, min_samples_split = 15, splitter =
’best’.

Model 11:  colsample_bytree = 0.6, gamma = 0.1, learning_rate = 0.1, max_depth
= 15, min_child_weight = 0.1, n_estimators = 100, reg_alpha = 0, reg_lambda =
0, scale_pos_weight = 200, subsample = 0.8.

Model 12:  colsampe_bytree = 0.6, learning_rate = 0.1, max_depth = 11,
min_child_weight = 1, n_estimators = 500, reg_alpha = 0, reg_lambda = 0,
scale_pos_weight = 300, subsample = 0.6.

Model 13:  class_weight = None, criterion = ’gini’, max_depth = 5,
max_features = 4, min_samples_leaf = 5, min_samples_split = 51, splitter =
’best’.

Model 14:  class_weight = None, criterion = ’entropy’, max_depth = 10,
max_features = 5, min_samples_leaf = 5, min_samples_split = 5, splitter =
’best’.

Model 15:  colsample_bytree = 0.6, gamma = 1, learning_rate = 0.1, max_depth =
15, min_child_weight = 1, n_estimators = 70, reg_alpha = 1, reg_lambda = 1,
scale_pos_weight = 1, subsample = 0.9.

Model 16:  colsample_bytree = 0.6, learning_rate = 0.1, max_depth = 10,
min_child_weight = 1, n_estimators = 50, reg_alpha = 0, reg_lambda = 0,
scale_pos_weight = 1, subsample = 0.9.