# Search for the edge-on galaxies using an artificial neural network

S.S. Savchenko  D.I. Makarov  A.V. Antipova  I.S. Tikhonenko

###### Abstract

We present an application of an artificial neural network methodology to a
modern wide-field sky survey Pan-STARRS1 in order to build a high-quality
sample of disk galaxies visible in edge-on orientation. Such galaxies play an
important role in the study of the vertical distribution of stars, gas and
dust, which is usually not available to study in other galaxies outside the
Milky Way. We give a detailed description of the network architecture and the
learning process. The method demonstrates good effectiveness with detection
rate about 97% and it works equally well for galaxies over a wide range of
brightnesses and sizes, which resulted in a creation of a catalogue of edge-on
galaxies with $10^{5}$ of objects. The catalogue is published on-line with an
open access.

###### keywords:

methods: data analysis , catalogs , galaxies:general , software: general

††journal: Astronomy $\&$ Computing

[spbu]organization=Saint Petersburg State University, Department of
Astrophysics, addressline=University Embankment, 7/9, city=St. Petersburg,
postcode=199034, country=Russia [gao]organization=Pulkovo Observatory of the
Russian Academy of Sciences, addressline=Pulkovskoye Shosse, 65, city=St.
Petersburg, postcode=196140, country=Russia [sao]organization=Special
Astrophysical Observatory, Russian Academy of Sciences, addressline=Nizhnii
Arkhyz, postcode=369167, state=Karachai-Cherkessian Republic, country=Russia
[mpe]organization=Max-Planck-Institut für extraterrestrische Physik,
addressline=Gießenbachstraße 1, postcode=D-85748, city=Garching,
country=Germany

##  1 Introduction

NGC 4244 NGC 4565 NGC 5529

Figure 1:  Examples of edge-on galaxies as seen in SDSS images. Thanks to the
orientation, we clearly see their substructures such as the dust lane in all
three galaxies, boxy/peanut bulge of NGC 4565 and X-structure of NGC 5529, as
well as a disk warp of NGC 5529. Otherwise, it would be extremely difficult to
detect these features.

Galaxies oriented almost edge-on to the observer form an important subset of
all disk galaxies, since only these extragalactic objects allow us to directly
observe the vertical distribution of stars, gas and dust. Some disk structures
like boxy/peanut shaped bulges (Burbidge and Burbidge, 1959), chimneys (Reach
et al., 2020), halos (Mosenkov et al., 2020), and some properties of disks
themselves like flaring and warping appear in all their glory only in edge-on
galaxies. Even if some galactic component is not a part of a disk, as in the
case of the polar rings (Whitmore et al., 1990) and the polar bulges
(Reshetnikov et al., 2015), it is still best seen in a highly inclined galaxy
due to the projection effects. Examples of edge-on galaxies obtained in the
Sloan Digital Sky Survey are shown in Fig. 1.

Within a framework of a comprehensive study of edge-on galaxies, it is
necessary to create a new representative sample of such galaxies. A sample
should be based on a wide-field survey to ensure uniformity of imaging data
across the sky, include as many objects as possible in an orientation as close
as possible to the edge-on orientation, and cover all Hubble types of disk
galaxies.

Figure 2: Examples of galaxies from the Galaxy Zoo 1 sample with their P_EDGE
values.

At the moment there were not many catalogs that satisfy this condition. For
example, the Revised Flat Galaxy Catalog (RFGC, Karachentsev et al., 1999) was
formed by a visual search for galaxies on photographic prints of the Palomar
Observatory (POSS-I) and the ESO/SERC sky surveys. It contains 4236 thin,
$a/b\geq 7$, mainly late-type spirals. Another example is the catalog of
genuine edge-on disk galaxies (EGIS, Bizyaev et al., 2014) that has been
prepared on a base of the Seventh Data Release of the Sloan Digital Sky Survey
(SDSS, Abazajian et al., 2009). In about one third of the sky, 5,747 edge-on
galaxies were detected without significant morphological discrimination. A
larger list of edge-on galaxies can be obtained via a crowdsource
classification of a big sample of galaxies. For example, the Galaxy Zoo 1
catalog (Lintott et al., 2008) contains such a classification for 667,945
galaxies. For each object, the percentage of votes given for it being an
edge=on galaxy is noted. The downside of this approach is that the
classification was made by non-specialists, and therefore substantial bias and
misclassifications are possible. Moreover, the strictness of the concept of
“the edge-on galaxy” can vary very significantly between volunteers, and as a
result, moderately inclined objects can be classified as the edge-on galaxies.
According to HyperLEDA111http://leda.univ-lyon1.fr/ database (Makarov et al.,
2014) the median inclination of 70,478 galaxies from the Galaxy Zoo 1 sample
with vote fraction $\mathrm{P\\_EDGE}>0.5$ is $72^{\circ}$. Figure 2 shows
examples of galaxies that have high P_EDGE values, but they fit poorly the
concept of “the edge-on orientation to the observer”: in all three cases a
disc structure is clearly visible. The situation improves, if one imposes a
more strict limit on the P_EDGE value, but this leads to significant decrease
of the number of selected galaxies: there are only 9,300 galaxies with
$\mbox{P\\_EDGE}>0.9$. Fig. 3 shows the distribution of galaxies from Galaxy
Zoo 1 project by their inclinations according to HyperLEDA database for all
galaxies with $\mbox{P\\_EDGE}>0.5$ and $\mbox{P\\_EDGE}>0.9$. One can see,
that these samples include galaxies with orientations far from edge-on.

Figure 3: A distributions of galaxies from Galaxy Zoo 1 catalogue by their
inclinations according to HyperLEDA database. The white histogram: galaxies
with $\mbox{P\\_EDGE}>0.5$, the green one – $\mbox{P\\_EDGE}>0.9$.

Our goal is to take advantage of the Panoramic Survey Telescope and Rapid
Response System (Pan-STARRS, Kaiser et al., 2010) survey to create a
specialized catalog of edge-on galaxies that is bigger than the EGIS and RFGC,
but cleaner than the one based on a crowdsource classification. The second
release of the survey is carried out in five broadband filters ($g$, $r$, $i$,
$z$, $y$) with the first 1.8-meter diameter telescope, Pan-STARRS1, of the the
Haleakala Observatory (Hawaii, US). The Pan-STARRS1 survey covers three
quarters of the sky above declination $\delta=-30^{\circ}$

The automatic detection of edge-on galaxies turns out to be a difficult task
for a set of reasons. First of all, they appear in a great diversity of
observed shapes: from bulge dominated red coloured Sa-type galaxies to almost
bulgeless blue Sd ones. They can be smooth and almost featureless, but can be
highly distorted and clumpy. Their disks can be perfectly flat, and can be
extremely warped and asymmetrical. The second problem comes from the fact that
the observed disk axis ratio does not unambiguously translate into its
inclination: a thick but perfectly edge-on galaxy can have a lower axis ratio
than a thin, but somewhat inclined one. Therefore, one can not rely solely on
this parameter to separate edge-on galaxies from a general population: a lower
value results in contamination of the sample by not perfectly edge-on
galaxies, while higher one skews the sample to late type galaxies. Some other
difficulties, such as contamination by foreground objects (mostly bright
stars), the existence of a dust lane leading to a fictitious splitting of the
galaxy into several separate objects, the presence of image artefacts that
mimic real galaxies, further complicate the task.

In this article, we describe our approach to finding and identifying edge-on
galaxies based on the use of artificial neural networks (ANN). This allowed us
to significantly improve the quality of the candidate selection, reduce the
project execution time, and to form the largest sample of edge-on galaxies to
date.

Machine learning algorithms proved to be efficient tools for classifications
of galaxies. There are numerous publications where neural networks were
applied both for annotating of growing samples of galaxies and for searching
for galaxies of some specific type. For example, Dieleman et al. (2015)
trained a convolutional neural network using visual morphological
classifications of 55,000 galaxies. The model predictions accuracy was more
than 99% for galaxies, where there was a consensus among human participants
annotating the training data. Domínguez Sánchez et al. (2018) used a
convolutional neural network to improve the results of visual classifications
of 14,034 galaxies published by Nair and Abraham (2010) and 304,122 galaxies
published by Willett et al. (2013). Similar work was made by Walmsley et al.
(2022), where an ensemble of Bayesian convolutional networks was trained on
visual classifications of 314,000 galaxies. An example of an unsupervised
classification is presented in Spindler et al. (2021), where a variational
autoencoder was used for galaxy clustering and generative purposes.

Some works are focused not on the general morphology classifications, but on
identifying specific features of galaxies or searching for galaxies of some
specific type. Thus, Abraham et al. (2018) used a neural network to detect bar
structures in images of almost face-on galaxies. Sarkar et al. (2023) trained
a model to distinguish between grand design and flocculent spiral patterns.
The works by Ackermann et al. (2018) and Domínguez Sánchez et al. (2023) were
dedicated to the detection of galaxy merging and tidal features. The work we
present in this paper falls into this class. We are creating a model to search
specifically for galaxies in an edge-on orientation.

##  2 First attempt

At a preliminary stage, we tried to extract edge-on galaxy candidates from a
catalog of extended sources found by the Pan-STARRS1 data processing pipeline
(Magnier et al., 2020). This catalogue contains the results of fitting of all
objects with Kron magnitudes smaller than $21.5$, $21.5$, $21.5$, $20.5$,
$19.5$ mag in $g$, $r$, $i$, $z$, $y$ bands respectively by the Sérsic profile
(Sérsic, 1963). Our search was carried out only outside the Zone of Avoidance
defined by
$|b|>20^{\circ}+15^{\circ}\exp(-\frac{1}{2}(\frac{\ell}{50^{\circ}})^{2})$.

Figure 4:  The left image illustrate a good match between size estimates in
Pan-STARRS and RFGC catalogs, while the case of the disagreement is shown in
the right image. Grey dashed ellipses, labelled ‘Reference’ indicate the
galaxy contour from RFGC, while orange ellipses are drawn from the parameters
of a Sersic fit in PanSTARRS data (gSerMajor, gSerAb).

To develop a selection criterion for the edge-on galaxies, we cross-matched
flat galaxies from the RFGC catalog (Karachentsev et al., 1999) with Pan-
STARRS1 extended sources in their common domain in the sky. Surprisingly, we
did not find clear correlations between the diameters of RFGC galaxies and the
half-light radii of automatically selected objects in Pan-STARRS survey. The
correlation between the axes ratios was not found as well. This discrepancy
rises from the difference in the source selection algorithms employed in the
catalogs. The sizes of the RFGC-galaxies have been measured by experts and
closely follow the apparent shape of the galaxies, while the Pan-STARRS1
pipeline focuses on compact objects and often selects only the brightest
central region of a galaxy or splits a galaxy into multiple pieces. In both
cases, this leads to an incorrect size estimate. The resulting candidates tend
to be smaller and rounder then their RFGC counterparts (see Fig. 4 for the
cases of a good match and the aforementioned problem).

As a result, we concluded that the desired catalog of edge-on galaxies can not
be easily constructed by constraining object parameters from the Pan-STARRS1
database, and a more advanced technique should be used instead.

##  3 Deep learning for images classification

Input $48\times 48\times 3$ Original images in g, r and i bands Conv $(5\times
5)$ $16\times 3$ Conv $(5\times 5)$ $16\times 3$ Batch norm Max-pool $2\times
2$ Dropout 0.3 Conv $(3\times 3)$ $32\times 3$ Conv $(3\times 3)$ $32\times 3$
Batch norm Max-pool $2\times 2$ Dropout 0.3 Conv $(3\times 3)$ $64\times 3$
Conv $(3\times 3)$ $64\times 3$ Batch norm Max-pool $2\times 2$ Dropout 0.3
Full 500 Full 2 Object type Downscaling+ normalisation
ReLUReLUReLUReLUReLUReLU

ReLU

SoftMax

Figure 5: Convolutional neural network architecture. The neural network
consists of three rounds of double convolutional blocks with batch
normalisation, max-pooling and dropout layers each, and two fully connected
layers at the end. For convolutional blocks, the first line shows the
convolution size, the second one – the number of convolutions in each block
(times three for three passbands). All max-pooling layers have $2\times 2$
size and all dropout layers have drop fraction equal to 0.3.

In this work we use an artificial neural network (ANN) algorithm to perform
the classification of the images. The network consists of interconnected
neurons, each with multiple inputs and an output that mimic the synapse of a
biological brain, and in its simplest form, it can be mathematically described
as a weighted sum:

$y=f\left(\sum_{j=1}^{n}w_{i}x_{i}+w_{0}\right),$

where $x_{i}$ are inputs and $w_{i}$ are so called weights, and $f(x)$ is an
activation function, that adds non-linearity to the model. The neurons of a
network are organised in layers such that the outputs of one layer neurons are
connected to the inputs of the next layer neurons. The first layer of neurons
is the input layer and its inputs $x_{i}$ are the data values. As it
propagates through the network, the data is modified at each layer according
to the weights until it reaches the last layer from which it can be read. In
other words, the network maps the input vector of the data to some output
vector.

The result of this data modification depends on the architecture of the neural
network (the number of neurons, the number of layers and their structure) and
the weights values. In general, a more complex network allows more complex
behaviour. Common sense is to start with relatively simple architecture and
build it up until the required level of complexity is reached. Once the
network architecture is fixed, the weights values can be tuned to achieve
desired network behaviour. This can be done through supervised learning
process. The key ingredient is a training dataset that consists of pairs of
vectors $\vec{x}_{i}$ that represent the input data and $\vec{y}_{i}$ that
represent the desired output for $\vec{x}_{i}$. For each training example the
weights of the network are modified using some optimisation technique (such as
the stochastic gradient descent algorithm) in a backpropagation manner:
weights are modified starting from the last layer back to the first one. As a
result, after each iteration the network becomes better in mapping of a given
input vector $\vec{x}_{i}$ to a given output vector $\vec{y}_{i}$. The
training process continues until the network converges to some steady state or
some specified precision is reached.

One of the most widely used applications of ANNs is the classification
problem. In this case, the input vector is the data to be classified and the
output vector represents the class, and the network is trained to properly map
the input data to the correct class. In the simplest case of two target
classes, the network output can be a scalar with different values for
different classes (usually 0 for one class and 1 for another). In the context
of our task of creating a catalog of edge-on galaxies, a natural approach is
to have two classes: the class 1 (positive case) corresponds to an image of
the edge-on galaxy, and class 0 (negative case) is an image of any other
object.

###  3.1 The network architecture

The architecture of a neural network is described by the number and type of
layers, the number of neurons in each layer, the size and number of a
convolutional kernels, etc. All these values together are called neural
network hyperparameters. During the training process, the hyperparameters are
fixed, and only the weights are changed. The best network architecture depends
on a specific problem, and there is no easy way to build the optimal network
for a given task.

The usual way to solve this is to use a trial and error approach: by modifying
the hyperparameters of a neural network and estimating its resulting
performance, one can gradually build a better network until the desired
quality is achieved. The common practice is to start with a relatively simple
network and move towards a more complex one keeping the track of the overall
performance. It is worth to note that a wide variety of different
architectures can provide the similar performance, but among them it is better
to choose one with a simpler architecture (with lower number of tunable
weights), as it is easier to train.

In this work, we use a convolutional neural network (CNN) to perform galaxy
classification. A CNN is a specialized type of ANN designed to process data
that has a spatial structure such as images. CNN neurons are organised in
spatial filters that perform discrete convolution of the image $F$ at
coordinates $m$, $n$ with the convolution matrix $K$:

$G\left[m,n\right]=(F*K)\left[m,n\right]=\sum_{i}\sum_{j}K\left[i,j\right]F\left[m-i,n-j\right],$

where indices $i$ and $j$ go over all elements of the kernel $K$. By sliding
the filter kernel over the entire input image, one can compute the full
response image $G$, the size of which depends on the convolution parameters:
the kernel size, the stride, and the padding (Dumoulin and Visin, 2016). The
output image can be fed forward as an input to the next layer (convolutional
or not) of the network. LeCun et al. (1989, 1990) showed that including such
convolutional layers into the network architecture greatly improves network
performance in case of the image processing.

Even though a network architecture can be fully convolutional, i.e. consisting
only of convolutional layers (for example, Long et al., 2015), the image
classification problem often involves a network in which several convolutional
layers are followed by one or more fully connected layers. These fully
connected layers map the output of the last convolutional layer into the
output of the network. In this approach, the convolutional part can be
considered as a feature detector trained to search for certain patterns in the
image, and the fully connected part is a classifier that uses these features
to make a decision.

Figure 5 shows the final architecture of our network, which was adopted after
the trial and error approach described above.

As an input, the network takes a stack of three images of an object with a
size of $48\times 48$ pixels in three $g$, $r$, $i$ Pan-STARRS1 passbands.
Therefore, the input is a 3D array of size $48\times 48\times 3$.

The network consists of three rounds of convolutional blocks. Each block has
two convolutional layers followed by batch normalisation, max-pooling and
dropout layers. The convolutional layers of the first block have 16 kernels of
$5\times 5$ pixels for each of the three bands. The convolutional layers of
the second and the third blocks have 32 and 64 kernels of $3\times 3$ pixels
for each band, respectively. We use the rectified linear unit (ReLU, Hahnloser
et al., 2000) as an activation function for the convolution layer neurons.

In each block, the second convolutional layer is followed by batch
normalisation, which normalizes the input using the mean and the standard
deviation over a subsample of training examples (called a batch). This reduces
the variation in hidden layers during training and allows the network to
converge faster (Ioffe and Szegedy, 2015).

In each convolution block, the batch normalization is followed by a max-
pooling layer. During the pooling process, the data is split in patches of
$2\times 2$ elements, and only maximal element of each patch is passed to the
output. The pooling reduces the number of network elements to train, because
only a quarter of neural connections are forwarded downstream, and also it
makes the network less sensitive to small spatial translations of the input
(Boureau et al., 2010).

The last layer in the block is the dropout layer. It randomly removes a
certain fraction of neurons along with all their connections on every pass
during the training process (Srivastava et al., 2014). Applying such
modifications to the network reduces the problem of overfitting when the
network remembers specific training examples rather than inferring general
patterns from the training data. An overfitted network has high score on the
training data, but does not generalize well to new data. We set the drop
fraction to 0.3 in all three dropout layers of the network.

After the third round of convolution, there are two fully connected layers
with 500 and 2 neurons, respectively, and the ReLU activation function. The
output of the last layer is the prediction of the type of the object, the
image of which is fed to the input of the entire network.

Putting together all of the above, we get that the network contains 206,894
trainable parameters.

###  3.2 Training dataset and data augmentation

To train a neural network as a classifier, one must provide it with a training
dataset consisting of labelled data: a set of training examples with the
correct class. Even though we are only interested in edge-on galaxies (i.e.
positive class), the training dataset must include both positive and negative
examples, otherwise the network will converge to a trivial solution that
always produces a positive output class.

As a source of positive examples, we used the EGIS catalog (Bizyaev et al.,
2014), which includes 5,747 visually selected edge-on galaxies. The vast
majority of objects in this catalog are genuine edge-on galaxies that can be
directly used as positive examples during the training process.

We used the Galaxy Zoo 1 catalog (Lintott et al., 2008) to build a list of
negative examples of non-edge-on galaxies. The Galaxy Zoo 1 catalog contains
rough visual classification of a large number of galaxies as fraction of votes
made for different morphological classes (elliptical galaxy, spiral galaxy,
edge-on galaxy, etc.). We selected all objects with a classification fraction
for a edge-on galaxy (P_EDGE) less than 0.1 (to exclude edge-on galaxies from
the list of negative examples) and a vote fraction for an elliptical galaxy or
a clockwise/anticlockwise spiral (P_EL, P_CW, P_ACW) greater than 0.1. This
step gave us a list of 270,000 galaxies.

Although the crowdsource classification used in the Galaxy Zoo 1 project is
subject to substantial bias, the main goal of this selection was achieved:
visual inspection of a random subsample confirmed the absence of edge-on
galaxies and the high diversity of all other galaxy types.

After cross-matching them with the HyperLEDA database, we also imposed
restrictions on the apparent diameter ($0.1<d_{25}<0.5$ arcmin) to exclude too
small and unresolved objects, as well as too big and oversaturated galaxies,
and on the apparent flattening ($q\geq 0.25$) to exclude disks close to edge-
on orientation. As a result, we formed a sample of negative examples for the
ANN training, consisting of more than 54,000 galaxies that are non-edge-on
disks.

Since most of the objects in the Pan-STARRS1 fields are stars, their images
must also be included in the training sample as negative examples. For this
purpose, we picked several dozens of stars from random Pan-STARRS1 fields.
Star images do not vary as much as galaxies do, therefore we do not need a
great number of them to represent this class.

The final component of the negative examples is empty background fields.
Spurious background variations can be detected as faint objects by image
segmentation algorithm. To take this into account, we extracted random regions
of the images that do not contain any objects.

The resulting training dataset consists of 5,747 positive examples (edge-on
galaxies) and over 54,000 negative examples (non-edge-on galaxies, stars and
empty fields).

This dataset still faces two major problems that prevent successful network
training. The first problem is its relatively small size. Even though there
are thousands of images, it is not enough to train a convolutional network
that is deep enough to solve our classification problem. A common solution in
a situation where the sample size can not be easily increased by adding new
objects is data augmentation. The main idea is to apply some modifications to
existing images to obtain new ones. We applied several modifications:

  * 1.

adding random Gaussian noise to the image;

  * 2.

random flipping of the image horizontally or/and vertically;

  * 3.

image rotation by a random angle;

  * 4.

image zoom by a random factor from 0.75 to 1.25;

  * 5.

shifting the image center randomly within 20% of the image size.

Although this process creates new images that contain essentially the same
objects, in practice, the sample augmented in this way leads to much better
results in a model training, but the trade-off is that this method can
introduce bias during the training process.

The second problem with the dataset is its skew in sample size (by about an
order of magnitude) towards negative examples. Having significantly more
negative examples during training, the network tends to converge to a solution
that will always predict a negative class (this would be true 9 times out of
10, so the formal testing score will be high even for this trivial solution).
To normalize the sample we adopted the following approach. Until the desired
size of the training set is reached, we take one random image of an edge-on
galaxy as a positive example and one random image of a negative one (with 80%
probability we take non-edge-on galaxy, 10% a star and 10% an empty field),
apply augmentation algorithm to them and add them to the training set. At the
end, the training sample will have exactly the same number of positive and
negative examples, and its size can be arbitrary large, so both problems are
solved.

Our tests showed that the training quality increased after applying described
above technique to our sample.

###  3.3 Training process

The dataset size described above was set to $3\cdot 10^{5}$ objects. We split
this entire dataset into two non-overlapping groups called the training
dataset ($2\cdot 10^{5}$ objects) and the test one ($10^{5}$ objects). The
first is used to provide examples during the network training, while the
latter is only used to evaluate the performance of the network. This approach
of using two independent datasets is extermely important, because the network
can overfit and demonstrate high performance score on the training data, but
will not perform well on new data that was not used during the training.
Computing the performance score on an independent dataset provides a less
biased estimation of the network performance.

Figure 6: The network training history: the accuracy (top) and loss function
value (bottom) as a function of epoch number.

The network was trained for 50 epochs (i.e. the training dataset was fed to
the network 50 times) with categorical cross-entropy as the loss function.
Fig. 6 shows the network performance computed on the test dataset as a
function of the epoch number. The upper panel of the figure shows the
prediction accuracy, and the bottom one presents the loss function value. It
is clearly seen that the accuracy of the network climbs rapidly to the level
of 99% during the first ten epochs, and after 20–30 epochs it reaches
approximately equilibrium state.

For comparison, before applying data augmentation, the accuracy saturated at
$\approx 95\%$ level.

Although $\approx 99\%$ accuracy seems rather good at first glance, it is not
good enough for our goal of the edge-on galaxies search in the Pan-STARRS1
survey. The problem is the small fraction of edge-on galaxies among all the
other objects on the celestial sphere: not all galaxies are disk ones, only a
small fraction of disk galaxies are visible edge-on, and many objects in the
processed images are not even galaxies (stars, asterisms, image artefacts). It
turned out that among the two hundred selected objects, on average there is
only one edge-on galaxy. This means that a trivial classifier that always
classify objects as not edge-on galaxies would have an accuracy of 99.5% (so
called ZeroR classification accuracy). Of course, our trained model greatly
surpasses this result, because its 99% accuracy is achieved on a balanced
training sample, for which the ZeroR classifier would only have accuracy of
50%. But if applied to the real data as it is, our model would result in more
false positive detections that there are real edge-on galaxies.

It is a challenge to improve the network accuracy above 99%, as it faces many
problems with limited number of training examples and the data overfitting is
possible. Instead, we used a different approach, sometimes called an ensemble
classifier. We created five independent training datasets using data
augmentation and trained five networks that have the same architecture on
them.

Even though all five networks have the identical architecture, they produce
different predictions when trained on large augmented datasets. We then use
these five predictions on the object type and take a simple majority of the
votes as the final result to reduce the chance of misclassification.

Thus, to get a false positive or false negative final classification, three
out of five networks must make an erroneous prediction. This approach
significantly improved the quality of classification.

Table 1:  The confusion matrix for our ensamble of 5 networks computed for 3027 edge-on galaxies from RFGC and the same amount of non-edge-on galaxies. Abbreviations are for true positive (TP), false negative (FN), false positive (FP) and true negative (TN).  | Predicted
---|---
| edge-on | non-edge-on
Actual edge-on | $\mathrm{TP}=3010$ | $\mathrm{FN}=17$
Actual non-edge-on | $\mathrm{FP}=25$ | $\mathrm{TN}=3002$

As a final independent quality check, we applied our classification procedure
to galaxies from the RFGC catalog (Karachentsev et al., 1999). This catalog
consists of 4236 thin edge-on galaxies and covers the entire sky. We used only
those RFGC-galaxies that are not included into the EGIS catalog and, as a
result, were not used for the network training. Among these 3027 unique RFGC
galaxies, our network misclassified only 17 galaxies, giving the error rate
less than 1% (see Table 1 for a full confusion matrix of the test).

##  4 Search for edge-on galaxies

Figure 7:  Examples of objects classified as edge-on galaxy by a single neural
network from of the entire ensemble. Objects in different rows are grouped by
the score assigned by the network, from the top row to the bottom:
$0.5<\mathrm{score}\leq 0.6$, $0.6<\mathrm{score}\leq 0.7$,
$0.7<\mathrm{score}\leq 0.8$, $0.8<\mathrm{score}\leq 0.9$, and
$0.9<\mathrm{score}\leq 1.0$.

###  4.1 Pipeline and the first run

The Pan-STARRS1 survey covers the celestial sphere north of declination
$\delta=-30^{\circ}$. Access to public data (Flewelling et al., 2020) is
provided by the Space Telescope Science Institute (STScI). The survey image
layout222https://outerspace.stsci.edu/display/PANSTARRS/PS1+Sky+tessellation+patterns
is organised as a regular grid of 2009 so-called projection cells. The
projection cell is an image of $63k\times 63k$ pixels. The pixel size is
$0.25^{\prime\prime}$. For convenience, each $4^{\circ}\times 4^{\circ}$
projection cell is split in turn into a $10\times 10$ grid of so-called
skycells, each $24^{\prime}\times 24^{\prime}$. Taking into account that we
are working in three photometric passbands, namely $g$, $r$ and $i$, we need
to process about 600,000 skycell images. Each skycell is a FITS-file (Wells et
al., 1981) about 65 Mb each, so the total amount of data to process is about 5
Tb.

The search pipeline was organized as follows. For each skycell, we download
its images in $g$, $r$, and $i$ filters. Next, we use the detect_sources
function of the Python package photutils (Bradley et al., 2020) to detect all
objects in the $r$-band image. This segmentation algorithm takes two main
parameters that govern the extraction of objects: the detection threshold
level and the number of connected pixels with flux values above a given
threshold. In our study, we choose the background variation threshold of
$4\sigma$, and the number of connected pixels brighter than this threshold to
be at least 15. Smaller values of these parameters lead to a large number of
spurious detections due to random background variations. Further, we filter
out all objects whose major axis is less than 48 pixels (the length of the
detected object may be bigger than the number of connected pixels, because in
the outer regions, some pixels may be disconnected from the main body of the
object, but still be attributed to the object). The size of 48 pixels,
corresponding to $12^{\prime\prime}$, was chosen to provide a reliable
thickness measurement for even thinnest galaxies, taking into account a
typical seeing of $1.19^{\prime\prime}$ in $r$-band. After that, we extract
the images of each object; scale them to $48\times 48$ pixels size according
to the size of the input layer of the network; stack $g$, $r$, and $i$ images
into a 3D array; and feed the array to our neural network quintet. Finally, if
at least three out of five networks score above 0.5 for the edge-on class, we
mark this object as the edge-on galaxy and add it to our catalog. The
downloaded field images can be deleted at this stage, so that the whole
pipeline goes ’on the fly’, without storing of the entire survey database
locally.

To speed up the process, we run the search simultaneously on a dozen
computers. One of them is used to keep track of processed skycells, to
distribute jobs to others in a form of skycells IDs, and to collect the
results.

###  4.2 Visual inspection

When the search was complete, our pipeline returned a list of 26,719 objects.
Figure 7 shows examples of the found objects grouped by the scores assigned to
them by the single network (i.e. without averaging over the whole ensemble of
networks). The top row shows objects with $0.5<\mathrm{score}\leq 0.6$, the
objects on the second one have $0.6<\mathrm{score}\leq 0.7$, etc. down to the
bottom row with objects $0.9<\mathrm{score}\leq 1.0$. It can be seen that the
score clearly correlates with the quality of the selection. For low scores
($\approx 0.5$–0.7), there are many false detections of completely wrong
objects, and even if an object is a disk galaxy, its orientation can be far
from the edge-on. For higher scores, the fraction of genuine edge-on galaxies
increases.

There are at least two types of false detections: asterisms (groups of stars
that occasionally form a line) and image artefacts in a form of bright strait
lines. It is clear how they ‘fool’ the network. Indeed, being narrow elongated
objects, especially at low-resolution network inputs of $48\times 48$, these
‘objects’ resemble edge-on galaxies, and we did not provide such images as
negative examples during the training process. More examples of false negative
detections are shown in Fig. 8. Similar to Fig. 7, they are also grouped into
rows according to their score. As the score increases, the appearance of false
detections becomes more and more ‘galaxy-like’.

Figure 8:  Examples of false positive detections arranged by the neural
network score similar to Fig. 7.

To separate false detections from real edge-on galaxies, we performed a visual
inspection of all candidates by 12 expert-astronomers. Each object was
examined at least 3 times. Experts assessed the proximity of the candidate to
the edge-on orientation by voting for one of the options: i) a genuine edge-on
galaxy, ii) a highly inclined galaxy, $i\gtrsim 80^{\circ}$, iii) a real non-
edge-on galaxy that does not satisfy the previous conditions, iv) image
artifact, asterism, bright oversaturated star, light reflection, etc. It
turned out that 3,992 detected objects are not galaxies. We also found 12,882
objects that are disk galaxies, but their inclination is not high enough to
hide the structure of their disks, and therefore they can not be considered as
edge-on galaxies. The relatively high percent of galaxies that deviate from
desired edge-on orientation can be explained by two facts. First, the network
input is low-resolution, so when the image is scaled, the minor axis shrinks
to just a few pixels, and thus the fine structure of the disk becomes
inaccessible to the network. Second, the EGIS catalog contains a certain
percentage of galaxies with inclinations well below 85 degrees, and the
network has learned to search for such galaxies.

###  4.3 Improvements and the second run

Our pipeline resulted in the largest sample of edge-on galaxies to date
(Makarov et al., 2022), but there is still room for improvement.

First, we have faced a large number of false detections of objects that are
not galaxies at all. Since most of these false positives form groups with a
characteristic shape (see fig. 8), if they were presented in the training
sample as negative examples, the network would learn to avoid them.

Second, the contamination of the training sample with galaxies that differ
from the edge-on orientation led to a large number of non-edge-on galaxies in
the final sample. A more accurate and ideally larger sample can provide better
search quality.

Third, the low resolution of the network input can also affects its
effectiveness by smearing out the fine details of the image.

Finally, automatic photometry performed with SExtractor (Bertin and Arnouts,
1996) showed a clear shortage of low surface brightness galaxies, especially
among ones with small angular sizes. We found that, as a rule, these galaxies
are lost even before applying the neural network at the stage of the source
extraction using the detect_sources function of photutils package. Due to the
low surface brightness, such galaxies do not meet the specified detection
criteria (see section 4.1).

To fix these issue, we have applied the following improvements to our
pipeline.

  * 1.

We included all non-galactic false detections as negative examples in the new
training sample. After this step, the training sample became more
representative regarding objects that resemble edge-on galaxies, but in fact
are not.

  * 2.

We extended a list of positive examples of our training sample by 3,482
objects detected during the first run and marked as genuine edge-on galaxy
during the visual inspection by at least two experts.

  * 3.

The resolution of the network input has been increased to $64\times 64$ pixels
to capture finer image details.

  * 4.

To improve the object selection by the detect_sources function, we apply it to
a combined $g+r+i$ image instead of a single $r$-band image. This step
significantly increases the detection rate of low surface brightness objects
due to a better signal-to-noise ratio of the combined image.

  * 5.

Finally, we increased the ensemble size from 5 to 11 models, because we found
that the three-out-of-five strategy still occasionally results in
misclassification, when three networks erroneously give low or high scores.
The new six-out-of-eleven approach should be more stable, as there is much
less chance of six networks producing a false positive.

We ran our modified pipeline again for the same data as described in Section
4.1.

The second run resulted in a significantly increased number of found edge-on
galaxies candidates: 132,528 objects have come through new detection procedure
on stacked images and received positive votes of six out of eleven networks.
The visual inspection showed that among these detections there are only 4,348
false positive detections of non-galactic objects. The full list of candidates
is available on the project page
333https://www.sao.ru/edgeon/catalogs.php?cat=PS1cand2 in the Edge-on Galaxy
Database (Makarov and Antipova, 2021).

##  5 The search completeness

It is obvious that any method can not find all galaxies in the survey images.
Therefore, it is important to evaluate the completeness of the search. We
assume that the two main parameters of a galaxy that can affect the
probability of detection are the central surface brightness of the galaxy and
the exponential scale of the light distribution. When a galaxy is too faint
and/or too small in angular size, the number of pixels above the $4\sigma$
detection level may fall below the 15 pixel threshold, and the total size of
the extracted object may fall below 48 pixel limit. Thus, such galaxy will be
discarded at the preliminary stage of the detect_objects function (see section
4.1) and, as a result, it will not be fed to the neural network for
classification. And even if a galaxy is detected by the image segmentation
algorithm as a separate object, the neural network may misclassify it due to
the low signal-to-noise ratio.

The exact detection level is rather difficult to estimate analytically,
because the level of background noise varies significantly between different
skycells. The same galaxy can be easily detected in an image with low
background noise, but may be completely missed in some fields with strong
background variations due to nearby bright stars, galactic nebulae, poor
atmospheric conditions, or in crowded fields such as near the plane of the
Milky Way. Even if a galaxy is big and bright enough to be selected, the
detection rate will not be 100%, because it can overlap with bright
oversaturated stars or image artifacts, such as satellite traces, clipping
artefacts, etc.

###  5.1 Artificial galaxy tests

To estimate the completeness of detection of the edge-on galaxies in the Pan-
STARRS1 fields by our method, we performed Monte-Carlo simulations. For this
purpose, we chose 1500 random skycells, evenly distributed throughout the
survey. To find the detection probability, we put an image of a real galaxy at
a random location on each field, and then perform a full cycle of the edge-on
galaxy search, including the objects detection and the neural classification.
This gives us the fraction of fields in which the galaxy was detected and
correctly classified as the edge-on galaxy. To find out the dependence of the
completeness on the galaxy properties, we scale its size and brightness before
placing it in the field. This allows us to estimate the completeness as a
function of the galaxy exponential scale and the central surface brightness.
To eliminate the possible influence of the features of an individual object,
we run this simulation for 20 random galaxies and average the results.

Figure 9:  Fraction of detected galaxies as a function of the disk exponential
scale and the central surface brightness. Black dots are galaxies from the
EGIS catalog (Bizyaev et al., 2014).

Figure 9 shows the results of the test for a grid of central surface
brightness ranging from 21 to 23.5 mag/sq.arcsec in the $r$-band and for an
exponential scale ranging from 3 to 10′′. One can see that, as expected, the
completeness is higher for large and bright galaxies and reaches almost 100%
for them, while for small and faint ones it decreases. We expect 90%
completeness for galaxies having the central surface brightness less than
$\approx 22$ mag/sq.arcsec in the $r$-band and the disk scale bigger than
$\approx 5^{\prime\prime}$. For comparison, we place EGIS-galaxies (Bizyaev et
al., 2014) on this diagram, which indicates that our sample should contain
more faint galaxies compared to this catalog.

###  5.2 Comparison with RFGC & EGIS

We test the efficiency of the method in finding real galaxies from the RFGC
(Karachentsev et al., 1999) and EGIS (Bizyaev et al., 2014) catalogs. Both
catalogs were created as a result of visual inspection of galaxy images. The
main difference is the selection criteria. In the older RFGC-catalog, the
galaxies were selected by their axis ratio, $a/b\geq 7$, measured on
photographic prints of the POSS-I and ESO/SERC surveys. While in the EGIS-
catalog the edge-on galaxies were chosen by visual inspection of a preselected
sample of objects automatically found in the SDSS survey, with $g$-band axes
ratio $a/b>3$ (for details see Bizyaev et al., 2014). As a result, the RFGC-
catalog contains predominantly late-type bulgeless galaxies. On the other
hand, the type distribution in the EGIS-catalog is more uniform, but due to
automatic selection, some known edge-on galaxies were lost and had to be added
manually.

|
---|---
|
Figure 10:  The search completeness for the RFGC galaxies (Karachentsev et
al., 1999). The gray squares correspond to the first run. The red circles show
the detection completeness in the second run. The bars correspond to the
1-sigma confidence interval (Wald interval) of the binomial proportion
(Wallis, 2013). The histogram shows the distribution of RFGC galaxies. The top
left panel is for the declination. The top right is for the major axis in
arcmin. The bottom left is for the axes ratio. The bottom right is for the
surface brightness class.

In the case of the RFGC catalog, we estimated completeness only for galaxies
with $\mathrm{Dec.}>-30^{\circ}$ in the region of intersection with the Pan-
STARRS1 survey. In the second pass, we were able not only to significantly
improve the level of object detection from 82 to 97%, but also the detection
quality. Figure 10 shows that the search completeness over the sky became much
more uniform as we approached the pole and the southern edge of the Pan-
STARRS1 survey (the top left panel).

The photometric depth of the Pan-STARRS1 survey (Chambers et al., 2016, see
fig. 17) drops slightly near the circumpolar region, as well as at low
latitudes. This reflects in a decrease of the detection completeness in the
first run, which was carried out only in one $r$-filter. The summation of the
three $g,r,i$ frames that was added in the second run increased the signal-to-
noise ratio of faint galaxies and solved this problem. The completeness of the
second run remains almost constant regardless of latitude.

Also there is no significant trends in the detection level with the object
size (the top right panel) and the axis ratio (the bottom left panel). The
greatest progress has been made in the detection of low surface brightness
galaxies. All galaxies in the RFGC catalog are divided into 4 classes of
surface brightness from the brightest (I) to the dimmest (IV). As it can be
seen from the bottom right panel, in the first version of the algorithm, we
were catastrophically short of low surface brightness galaxies. On the second
pass, the drop of the detection rate with surface brightness is very modest.

|
---|---
|
Figure 11:  The search completeness for the EGIS galaxies (Bizyaev et al.,
2014). The designations are similar to fig. 10. The top left panel is for the
exponential scale of the disk of EGIS-galaxies. The top right is for the
vertical-to-radial scale ratio of the disk. The bottom left is for the total
magnitude of the galaxy. The bottom right is for the central surface
brightness.

The area of the SDSS survey lies entirely within the Pan-STARRS1 survey.
Therefore, all EGIS-galaxies should have been passed through our algorithm.
For all EGIS-galaxies, aperture photometry, structural bulge-disk
decomposition, and parameters of the exponential disk (central brightness,
vertical and radial scales) were determined in the original work by Bizyaev et
al. (2014). This allows us to make more direct estimates of the completeness
depending on galaxy disk parameters. Figure 11 also shows huge improvements in
the second run compared to the first one. In the first run, the detection of
the smallest and faintest galaxies was extremely poor, falling below 50% for
galaxies with the radial disk scale less than 5 arcsec (the top left panel) or
fainter than 17 mag in the $r$-band (the bottom left panel). The second run
solved this issue. It is necessary to note a smooth decline of the
completeness for the thickest galaxies $z_{0}/h\gtrsim 0.4$ (the top right
panel). This happens for two reasons. The inspection shows that the some thick
EGIS-galaxies are not real edge-on galaxies and do not pass the classification
stage. The second reason is that the real thick edge-on galaxy is a quite rare
object. Since its axis ratio is similar to that of a normal galaxy inclined
less than $60^{\circ}$, this requires special attention during the training
process. The completeness is 98% if the thickest galaxies $z_{0}/h\gtrsim 0.4$
are excluded from the consideration (96% for the entire sample). One more
point that should be noted is the loss of the brightest (the bottom left) and
largest (the top left) galaxies with high central surface brightness (the
bottom right). Our methodology failed to select 23 out of 101 galaxies with
$r>13$ mag. The main reason of this is an upper limit that we imposed on the
candidate size on the stage of object selection with photutils. Adjacent Pan-
STARRS1 fields have a 2 arcminutes overlapping regions at their borders, so if
a galaxy image is less that 2 arcminutes in size, it is guaranteed to fit
entirely inside one or another Pan-STARRS1 field. Images of larger galaxies,
on the other hand, can be split between two or more adjacent fields depending
on their coordinates and orientation and to classify them properly one has to
concatenate these fields first. This would require a considerable amount of an
additional computational payload, whereas all such large galaxies are surely
already included in existing catalogues of edge-on galaxies.

##  6 Conclusions

In this work, we describe an algorithm for searching for a specific class of
objects, the so-called edge-on galaxies, in the Pan-STARRS1 survey images
using ANNs. This solution is an alternative to the classical approach based on
visual inspection of images or selection by axes ratio from automatically
generated object catalogs.

The final version of our pipeline consists of two main parts: the selection of
objects in an image using the python photometry package photutils (Bradley et
al., 2020) and the objects classification by an ensemble of ANN models trained
to find edge-on galaxies.

The search for objects is carried out in a combined image from three images in
the $g$, $r$ and $i$ bands of the Pan-STARRS1 survey. An object is considered
detected if its major axis exceeds 48 pixels with at least 15 connected pixels
are above $4\sigma$ of background noise. After that, we extract the object
images in the $g$, $r$, $i$ bands, scale them to $64\times 64$ pixels, and
combine them into a 3D array for ANN classification.

The resulting stack of $64\times 64\times 3$ pixels is fed to an ensemble of
eleven ANN models. Each model consists of three rounds of convolutional
blocks. Each block, in turn, consists of two convolutional layers, followed by
batch normalization, max-pooling and dropout layers. The network architecture
is completed with two fully connected layers with 500 and 2 neurons, which
perform image classification and evaluate the classification of the object as
the edge-on galaxy (see Section 3.1 for details).

Each network was independently trained on a sample of 9,229 positive examples.
This sample was formed by combining 5,747 edge-on galaxies from the EGIS
catalog (Bizyaev et al., 2014) and additional set of 3,482 true edge-on
galaxies selected during the visual inspection by experts of 26,719 candidates
received during the first run of the network (at least two experts had to mark
these objects as edge-on galaxies).

As negative examples, we used a sample of real non-edge-on galaxies,
supplemented by empty fields, images of stars, and, which turned out to be
extremely important, examples of image defects and various configurations that
mimic real edge-on galaxies.

All these steps allowed us to construct effective and reliable method for
searching for the edge-on galaxies. We found 128,180 real candidates in edge-
on galaxies with only 4,348 wrong detections (image artifacts, asterisms
etc.). The artificial galaxy test shows that the 90% completeness level is
achieved for edge-on galaxies with the central surface brightness of 22
mag$/\square^{\prime\prime}$ and the disk radial scale of $5^{\prime\prime}$.
Comparison with known catalogs of edge-on galaxies demonstrates 97% detection
rate in a wide range of parameters. There are no significant trends of the
completeness with position in the sky, object size and total magnitude, as
well as its surface brightness. The method works well for the disk galaxies
thinner than $z_{0}/h=0.4$, where $z_{0}$ and $h$ denote the vertical and
radial scales, respectively, of an isothermal exponential stellar disk.
Applying this method to the Pan-STARRS1 survey (Chambers et al., 2016) allowed
us to obtain the most complete and largest sample of galaxies to date. Data
access is provided by the Edge-on Galaxy Database (Makarov and Antipova, 2021)
on the web-page of the project
444https://www.sao.ru/edgeon/catalogs.php?cat=PS1cand2. For each candidate,
the score statistics of the proximity to the edge-on orientation, obtained by
the ANN, is given, as well as set of its photometric parameters (coordinates
of the center, the galaxy size along the major and minor semiaxes, aperture
magnitude).

## Acknowledgements

This research was supported by the Russian Science Foundation grant №
19–12–00145.

The authors thank the anonymous referees for their helpful comments that
improved the quality of the manuscript.

The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been
made possible through contributions by the Institute for Astronomy, the
University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society
and its participating institutes, the Max Planck Institute for Astronomy,
Heidelberg and the Max Planck Institute for Extraterrestrial Physics,
Garching, The Johns Hopkins University, Durham University, the University of
Edinburgh, the Queen’s University Belfast, the Harvard-Smithsonian Center for
Astrophysics, the Las Cumbres Observatory Global Telescope Network
Incorporated, the National Central University of Taiwan, the Space Telescope
Science Institute, the National Aeronautics and Space Administration under
Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA
Science Mission Directorate, the National Science Foundation Grant No.
AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), the
Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation.

We acknowledge the usage of the HyperLeda555http://leda.univ-lyon1.fr/
database (Makarov et al., 2014).

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