Image-based Classification of Variable Stars: First Results from Optical Gravitational Lensing Experiment Data
T. Szklenár, A. Bódi, D. Tarczay-Nehéz, K. Vida, G. Marton, Gy. Mező, A. Forró, R. Szabó
DDraft version July 7, 2020
Typeset using L A TEX twocolumn style in AASTeX63
Image-based classification of variable stars - First results on OGLE data
T. Szklen´ar,
1, 2
A. B´odi,
1, 2, 3
D. Tarczay-Neh´ez,
1, 2
K. Vida,
1, 2, 3
G. Marton,
1, 3
Gy. Mez˝o, A. Forr´o,
1, 2, 4 andR. Szab´o
1, 2, 3 Konkoly Observatory, Research Centre for Astronomy and Earth Sciences,H-1121 Budapest, Konkoly Thege Mikl´os ´ut 15-17, Hungary MTA CSFK Lend¨ulet Near-Field Cosmology Research Group ELTE E¨otv¨os Lor´and University, Institute of Physics, Budapest, Hungary E¨otv¨os Lor´and University, P´azm´any P´eter s´et´any 1/A, Budapest, Hungary (Received MM DD, 2020; Revised MM DD, 2020; Accepted 13 June 2020)
Submitted to ApJLABSTRACTRecently, machine learning methods presented a viable solution for automated classification of image-baseddata in various research fields and business applications. Scientists require a fast and reliable solution to beable to handle the always growing enormous amount of data in astronomy. However, so far astronomers havebeen mainly classifying variable star light curves based on various pre-computed statistics and light curveparameters. In this work we use an image-based Convolutional Neural Network to classify the different typesof variable stars. We used images of phase-folded light curves from the OGLE-III survey for training, validatingand testing and used OGLE-IV survey as an independent data set for testing. After the training phase, ourneural network was able to classify the different types between 80 and 99%, and 77–98% accuracy for OGLE-IIIand OGLE-IV, respectively.
Keywords: methods: data analysis — stars: variables: delta Scuti — stars: variables: general — stars:variables: RR Lyrae — (stars:) binaries: eclipsing INTRODUCTIONMost recent space-borne (e.g. Kepler, see Boruckiet al. 2010; Gaia, see Gaia Collaboration et al. 2016;TESS, see Ricker et al. 2014) and ground-based sky sur-veys (e.g. SDSS, see Gunn et al. 2006; and LSST, seeIvezi´c et al. 2019a) provide huge amount of data, thatleads to a new level of challenge in data processing. Thisenormous quantity of data need to be analysed with fastand effective automated computer programming tech-niques. As a consequence, several machine learning al-gorithms became popular in astronomy.Automatic classification of variable stars using ma-chine learning methods mostly uses photometric datasets where objects are represented by their light curves.The classical approach of variable star classification re-lies on carefully selected features of the light curves, suchas statistical metrics (like mean, standard deviation, [email protected] kurtosis, skewness; see e.g. Nun et al. 2015), Fourier-decomposition (Kim & Bailer-Jones 2016) or color infor-mation (Miller et al. 2015). The classifiers can be trainedon manually designed (Pashchenko et al. 2018; Hosenieet al. 2019) or computer-selected features (Becker et al.2020; Johnston et al. 2020) using known type of variablestars. Another opportunity to classify light curves is touse non-labeled data, which is called unsupervised learn-ing. This method clusters similar objects into groupsinstead of labelling them one-by-one (Mackenzie et al.2016; Valenzuela & Pichara 2018).Image-based classification is now in our everyday life:we use it in our phones, social network applications,cars, etc. Convolutional Neural Networks (CNNs, Le-Cun et al. 1999) – a class of deep neural networks –can distinguish humans, animals and various objects.If CNNs are well trained, they can learn very fine fea-tures of an image (e.g. face recognition), therefore thiskind of technology is now widely used in many scientificfields, for example geology, biology or even in medicineto recognise tumours and other diseases in the human a r X i v : . [ a s t r o - ph . S R ] J u l Szklen´ar et al. body (e.g. Alqudah et al. 2020). Recently, CNNs havebeen successfully applied to astronomical problems aswell, like real/bogus separation (Gieseke et al. 2017),cold gas study in galaxies (Dawson et al. 2020), super-nova classification (M¨oller & de Boissi`ere 2020), LIGOdata classification (George et al. 2018), and exoplanetcandidate classification (Osborn et al. 2020). Hon et al.(2018b) trained a convolutional network on 2D imagesof red giant power spectra to detect solar like oscilla-tions, and later used the method to classify the evolu-tionary states of red giants observed by Kepler (Honet al. 2018a). Carrasco-Davis et al. (2019) designed arecurrent convolutional neural network to classify astro-nomical objects using image sequences, however theirapproach does not compute the light curves itself.An approach similar to ours was used by Mahabalet al. (2017), who transformed the raw light curves into dmdt space and mapped the results to 2D images. Theseimages were then classified using a CNN. Moreover, twoother works also took advantage of neural networks toclassify variables stars. Aguirre et al. (2019a) used a re-current NN, which was fed by the light curve measure-ments one by one as individual points. Aguirre et al.(2019b) calculated the difference between consecutivemeasurement times and magnitude values, and classi-fied the resulted pair of one-dimensional vectors usinga CNN. However, the automatic classification of vari-able stars, which is fully based on the photometric lightcurves that are represented as images has not been per-formed so far to our knowledge.In this work, we present the first results of an image-based classification of phase-folded light curves of peri-odic variable stars with our deep neural network archi-tecture trained and validated on OGLE-III and testedon OGLE-III and independently on OGLE-IV databases(Udalski et al. 2008, 2015). The goal of our work wasto test whether we are able to classify the phase-foldedlight curve images, focusing only on the shape of thelight curves and neglecting period information. The ideais very similar to the way human perception works whena traditional astronomer visually evaluates a light curve,i.e. deciding based on distinctive features and patterns.In this study we demonstrate that a deep neural networktrained with light curve images can effectively used forclassification.The paper is structured as follows: In Section 2 wediscuss our data selection and handling, in Section 3 wepresent our neural network and data sampling, while inSections 4 and 6 we show and conclude our results. DATA
Figure 1.
Gallery of phase-folded light curve images of dif-ferent types of variables stars in OGLE-III. The phases are inthe [0..2] interval. From top to bottom: ACep, DSct, ECL,RRLyr and T2Cep. In case of pulsating variables the lightcurves are phased folded by their pulsation periods, whileeclipsing binaries are folded by the orbital periods (i.e. twicethe formal periods).
The aim of our project was to provide an effective andreliable solution for classifying variable stars by meansof an image-based classification technique. As a firststep, we restrict ourselves to use only periodic variablestars, so that images of phase-folded light curves can beused. Therefore, we need a data set that is classified in areliable way and contains enough observations to createwell-sampled phase-folded light curves.2.1.
Observational data
Many catalogs of variables stars are available from theliterature. Among these the Optical Gravitational Lens-ing Experiment (OGLE; Udalski et al. 2015) providesone of the most extensive data sets, which have suffi-cient number of labels and labelled samples to train andtest our neural networks. The survey is in its fourthphase, operating since 2010.OGLE observes the inner Galactic Bulge, the Magel-lanic Clouds and the Galactic disk. The observations areobtained in V and I bands, as the latter having aboutten times more data points we chose to work with the I -band data only.The obtained light curves mostly have high signal-to-noise ratios and their types are confirmed by experts,which makes the sample very reliable. The OGLE-III mage based classification of variable stars δ Scutis (DSct, Poleskiet al. 2010), eclipsing binaries (ECL, Graczyk et al.2011), RR Lyrae stars (RRLyr, Soszy´nski et al. 2009),and Type II Cepheids (T2Cep, Soszy´nski et al. 2008).The number of objects of each variable types is listed inTable 1.We converted the measured magnitudes of a given starinto flux values with a zero point of 25, then normal-ized this data with the maximum brightness. Using theepochs and periods from the OGLE catalog, the lightcurves have been phase-folded and transformed into 8bit images with a size of 128 ×
128 pixels, with blackbackground and white plotted dots (see Figure 1). Incase of pulsating variables we used the pulsation periods,while for eclipsing binaries we used the orbital periods(i.e. twice the formal periods) to phased-fold the lightcurves. Only the raw data were used, without sigmaclipping and measurement error handling. In order toensure that all of the representative light curve shapesare covered, the phased light curves are plotted in the[0..2] phase interval. These images served as the basisof our training sample.One other purpose of our research was to know howwell our trained model works with other observationaldata. This is why we generated light curves from theOGLE-IV database. Unfortunately, δ Scuti stars havenot been published yet, so we could use the followingtypes only: Anomalous Cepheids (ACep, Soszy´nski et al.2015), Eclipsing binaries (ECL, Pawlak et al. 2016), RRLyrae stars (RRLyr, Soszy´nski et al. 2016), and Type IICepheids (T2Cep, Soszy´nski et al. 2018). The subtypeswere not separated, we used the same method by theimage generation.2.2.
Data augmentation
Highly unbalanced number of representatives in dif-ferent classes, which is the case here (as it can seenin Table 1), may cause false machine learning output,therefore data augmentation was crucial in the pre-processing phase. The basic data augmentation meth-ods usually use e.g. Gaussian noise, elastic transform,
Table 1.
The number of variable stars in the original andin the augmented data set.Non-augmented AugmentedACep 83 25 000DSct 2 696 25 000ECL 26 121 25 000RRLyr 24 904 25 000T2Cep 203 25 000Total 54 007 125 000 random brightness or contrast changes (see e.g. Shorten& Khoshgoftaar 2019); the images can also be mirroredor rotated. These methods allow us to create more du-plicates, and it works well when classifying everyday ob-jects: a mirrored cat is still a cat – however, this is nottrue for light curves.To increase the sample of underrepresented classes,randomly generated noise was sampled from a Gaus-sian distribution with zero mean and standard devia-tion equal to the given measured error then added tothe original light curves. The augmented training datacontained 125 000 images, 25 000 from each variable startype (the number of the eclipsing binaries were reduced).We took precautions to ensure that the training, testingand validating sets contain non-overlapping samples ofthe generated dummy light curves, i.e. for one given starthe original light curve and its generated dummy multi-ples are used only in one of the aforementioned steps. METHODS AND MODELS3.1.
DarkNet
In order to investigate the effectiveness of a CNNon classifying the folded light curves, first we testedDarkNet (Redmon 2013–2016), a GPU supported open-source software. We used a built-in, very simple convo-lutional neural network for the first training of our data.This was originally created for the CIFAR-10 data set ,which is a test to classify images from 10 different classesof freely downloadable 28 ×
28 pixel images of cars, dogs,cats, ships, etc.Our first training package was not augmented, theclasses had large differences in the amount of data. Thisset contained 54 007 images, see Table 1.Training a deep neural network requires vast amountof computational time and capacity. To be able to testour first deep neural network on simple desktop com-puters, we created a much smaller image package. Thefirst training was made with less than 500 images, but ∼ kriz/cifar.html Szklen´ar et al.
Figure 2.
Schematic of the architecture of the designed CNN. it took 1.5 hours to complete one training. We useda high-performance computer for this task, containing4 Tesla V100 GPUs. Although the first results usingthe DarkNet framework were promising, due to the poordocumentation, the complexity of architecting a networkand the required time to preprocess data to match for-mat with the DarkNet requirements, we decided to moveto a more user-friendly framework.3.2.
TensorFlow/Keras
As the DarkNet package is poorly documented andnot being maintained, we moved to compile a new neu-ral network based on the TensorFlow/Keras framework.TensorFlow (Abadi et al. 2015) is a free and open-sourceframework which is widely used in different machinelearning applications. Keras (Chollet & others 2018) isan open-source, high-level language and neural-networklibrary for creating deep neural network with ease andit is officially supported in the TensorFlow core librarysince 2017. As a first step we recreated the previousCNN, now in Keras, using Python programming lan-guage. During the testing phase we used TensorBoard(Abadi et al. 2015) to be able to visualize the differences,track the changes in training loss and accuracy.3.3.
Our Convolutional Neural Network
Convolutional networks use convolution instead ofgeneral matrix multiplication in their layers. A typ-ical network architecture uses a mixture of convolu-tional, pooling and fully connected layers. Additionally,dropout layers can be added for regularization purposes.CNNs set the weights for the filter kernels during thelearning process instead of using pre-set kernels as e.g.in early optical character recognition solutions: this in-dependence from prior knowledge gives them great flex-ibility, and the ability to recognize features on differentspatial scales in their consecutive layers. Figure 2 shows a schematic view of our CNN. Ourmodel has a conventional structure, it consists of 2 con-volutional, 1 dropout and 1 pooling layers in all 4 blocks.The resolution of input images is 128 ×
128 pixels, thefirst two convolutional layers use a 16 ×
16 pixels widthconvolutional window (known as kernel/filtersize), with1 pixel stride to run through the images. After thisstep, the second, third and fourth pair of convolutionallayers use 8 ×
8, 4 × × . The output of the lastconvolution block is flattened and sent to a network offully connected layers (dense layers). The last one is asoftmax layer which is used to normalize the output andhence yields predictions (numbers between 0 −
1) for allthe 5 possible output labels. The total number of train-able parameters were 1 615 685 altogether. The testedhyperparameters and the final chosen ones are listed inTable 2. 3.3.1.
Convolutional layers
The input for the convolutional layer is a tensor withthe shape of the image height, width and depth. Whendata is passing trough this layer it becomes abstractedby a feature map. During this step a filter matrix –or kernel – of a given size is convolved with parts ofthe image, by moving it with a given stride until thewhole image is traversed. These layers can detect low-level features in the first steps, but can extract high-levelfeatures in later stages. f(x) = max(0,x) mage based classification of variable stars Table 2.
Hyperparameters of our Convolutional Neural NetworkParameter Tested values Chosen value
Architecture
Starting convolution window [8 ×
8, 16 ×
16 , 32 ×
32] 16 × ×
2, 3 ×
3] 2 × Optimization
Batch size [32, 64] 64Learning rate [10 − –10 − ] 10 − Optimizer [SGD, RMSProp, Adam] AdamLoss function Categorical crossentropy
Pooling layers
The pooling layer is responsible for reducing the spa-tial size of the convolved image. It reduces the requiredcomputational power and it is also important for theextraction of dominant features of the image. We usedmax pooling in our model, which returns the maximumvalue from each portion of an image: it selects importantfeatures as well as reduces noise.3.3.3.
Fully-connected layers
Fully-connected layers (also known as Dense layers)are responsible for the classification process as they canlearn the non-linear combinations of the high-level fea-tures represented by the convolutional layers. As a finalstep, we use a softmax classification (basically a general-ized version of a sigmoid function for multiple outputs),which classifies our images into separate classes of vari-able stars. 3.3.4.
Spatial Dropout
Data augmentation is crucial for a well-functioningdeep neural network in the pre-process phase (see Sec-tion 2.2). However, data augmentation alone is not al-ways enough. One serious obstacle in applied machinelearning is overfitting. A model is considered overfittedwhen it learned the features and their noise with highprecision, but it poorly fits a new, unseen data set. Tobe able to avoid it, one of the options is using Dropoutlayers. Dropout layers randomly neglect the output of anumber of randomly selected neurons during training, in our case this was 20 percent. We used Spatial Dropoutlayers, which drop not just the nodes but the entire fea-ture maps as well. These feature maps were not used bythe next pooling process. Dropout layers offer a compu-tationally cheap and remarkably effective regularizationmethod to reduce overfitting and improve generalizationerror in deep neural networks. It helped us to be able torun the training much longer, so we could achieve veryhigh accuracy.3.4.
Optimizers and Learning rate
We tested SGD (Stochastic Gradient Descent), RM-SProp (Root Mean Square Propagation) and Adam(Adaptive Moment estimation) optimizers with varioussetups. After thorough testing we chose Adam as theoptimizer in our model. For the learning rate we testedvarious values between 10 − and 10 − , in our model wechose a very low rate as 10 − .3.5. Early stopping
We built in an EarlyStopping callback into the train-ing method. This particular one is monitoring thechange of the validation loss value, which is a key pa-rameter by catching the signs of overfitting. In this caseif the validation loss does not decrease by 10 − , the call-back will run for another 7 additional epochs, stop thetraining process and save the best weight for furthertesting. Szklen´ar et al.
Random forest classifier
To compare our results with a method that only usespre-computer features, we trained a Random Forest(RF) classifier (Breiman 2001) as well. RF is a ma-chine learning algorithm that uses labeled (supervised)data and ensembles the results of several decision treesto classify the input into several classes. Here we use theRF that is implemented in the scikit-learn package(Pedregosa et al. 2011).The training set was created from the amplitude ( A )and R = A /A , φ = φ − φ Fourier-parameters ofthe original sample available in the OGLE-III database.The testing set is consist of the same parameters usingboth OGLE-III and OGLE-IV databases. As these val-ues for eclipsing binaries are not present in the catalog,we calculate them utilising the periods from the OGLEdatabase. To balance the number of samples in the fiveclasses, we sampled dummy parameters from Gaussiandistributions with means and standard deviations equalto the original parameters and 10 − (for A ), 10 − (for R , φ ), respectively. The ratio of training and testingsample was 80% − Evaluation Metrics
The performance of a trained machine-learning algo-rithm can be quantitatively characterised through sev-eral evaluation metrics. The one where the input andpredicted class labels are plotted against each other iscalled a confusion matrix, where the predicted class isindicated in each column and the actual class in eachrow. This method allows us to visualise the number oftrue/false positives and negatives. In the best-case sce-nario, if the matrix is normalised to unity, we expect theconfusion matrix to be purely diagonal, with non-zeroelements on the diagonal, and zero elements otherwise.Precision is defined as:Precision =
T PT P + F P , (1)where TP is the number of true positives and FP isthe number of false positives. Precision shows that howprecise the final model is out of those predicted positive,i.e. how many of predicted positives are actual positive.Recall is defined as:Recall =
T PT P + F N , (2)
Figure 3.
Accuracy and loss of the training and valida-tion process. Orange curve: training accuracy, red curve:validation accuracy. Blue curve: training loss, green curve:validation loss. where TP is the number of true positives and FN is thenumber of false negatives. Recall shows that how manyof the actual positives are labelled by the model as truepositives.From the last two metrics the F1-score can be calcu-lated, which is the harmonic average of the precision andrecall: F · Precision · RecallPrecision + Recall . (3)F1-score can measure the accuracy of the model, whichreturns a value between 0 and 1, where the latter corre-sponds to a better model. RESULTS4.1.
Training and validation
Our final data set contained 125 000 images, 25 000from each type. This data set was subdivided into threedifferent parts (70–15–15 %), choosing images withoutany overlap for training, validation and testing purposes,respectively. 87 500 images were used for training and18 750 for validation (see Table 7). The process thatgoes through these two phases (training and validation)is called an epoch. We used GPU-accelerated computersprovided by the MTA Cloud and the Konkoly Obser-vatory for this research. Each training and validationepoch took about 290 seconds on a NVidia Tesla K80GPU supported computer and 62 seconds with a NVidiaGeForce RTX 2080 Ti GPU card. We were constantlychecking the accuracy and loss values. An EarlyStop-ping callback stopped the training process after 173 fullepochs. Inspecting the log files in TensorBoard showedno overfitting, after the 173 rd epoch we reached 98.5%training accuracy for the complete model (see Figure 3). https://cloud.mta.hu mage based classification of variable stars Figure 4.
Test result on the OGLE-III data.
Figure 5.
Test result on the OGLE-IV data.
Testing the model
We made two separate prediction tests on our model,the first one ran on the previously mentioned OGLE-IIIdata.As our original data set was divided randomly intothree different parts, 87 500 images were used for train-ing and 18 750 for validation, the remaining 18 750 lightcurve images were for testing purposes. This test dataset contained 3 750 images from each variable star typeand the test method ran through all light curves, using
Table 3.
Classification report for the 5 classes in the OGLE-III data-set. Numbers correspond to the CNN and RF train-ings, respectively. The confusion matrix for this report isshown in Figure 4. Precision Recall F1 scoreACep 0.803 /0.93 0.972 /0.95 0.879 /0.94DSct 0.939 /0.87 0.949 /0.89 0.944 /0.88ECL 0.987 /0.98 0.992 /0.95 0.989 /0.96RRLyr 0.959 /0.88 0.702 /0.86 0.810 /0.87T2Cep 0.795 /0.96 0.966 /0.96 0.872 /0.96Average 0.897 /0.92 0.916 /0.92 0.899 /0.92 the weights from our trained model. We received a pre-dicted label for each image and in the end of the testwe could see how well our model is working with theOGLE-III LMC data (see Figure 4).For our second test we generated 10 000 augmentedsamples (2 500 from each type) from the OGLE-IVdatabase (see Table 7). The method was the same asbefore, we made predictions on each image, using theweights from the trained network (see Figure 5 and Ta-ble 4). Comparing the two confusion matrices it isclearly visible that our trained model is working welland can classify variable stars from a different database.Tables 3 and 4 show that a CNN trained on phase-folded light curves can classify variable stars with veryhigh accuracy. Based on our results, we conclude thatour model can efficiently distinguish between the eclips-ing binaries and the periodic variables, like RR Lyraestars. However, we note that due to similar light curveshapes and noise features, and due to the fact that werefrained from using the period as an input parameterwe got false predictions for the pulsating stars in our sec-ond test. ACep, RRLyr and T2Cep stars were especiallyvulnerable to false prediction, while DSct stars were notavailable for OGLE-IV, as we mentioned before.In this research we focused only on the light curveshapes, but it will be possible in the future to in-sert other data (most importantly, the period) into amore complex multi-channel network which could han-dle more inputs, image and numerical data as well. DISCUSSIONOur method uses a relatively new approach to clas-sify the light curves of periodic variable stars, on thecontrary of similar NNs, we do not use the time stampsof the measurements directly nor do we transform thelight curves into another space. Instead, we look only atthe light curve shape characteristics, which is achievedby phase-folding to increase the sampling within a cy-cle to be able to describe the shape more precisely. Tocompare our results with a more traditional method,
Szklen´ar et al.
Table 4.
Classification report for the 5 classes in the OGLE-IV data-set. Numbers correspond to the CNN and RF train-ings, respectively. The confusion matrix for this report isshown in Figure 5. Precision Recall F1 scoreACep 0.769 /0.89 0.914 /0.62 0.835 /0.73DSct · · · · · · · · ·
ECL 0.975 /0.96 0.994 /0.94 0.984 /0.95RRLyr 0.916 /0.72 0.790 /0.90 0.849 /0.80T2Cep 0.841 /0.99 0.900 /0.75 0.870 /0.85Average 0.875 /0.89 0.900 /0.80 0.885 /0.83
Table 5.
Classification report for the 5 classes in the OGLE-III data set of the RF method.Predicted classACep DSct ECL RRLyr T2Cep T r u e c l a ss ACep 95.46 0.08 0.00 4.46 0.00DSct 0.86 89.26 1.85 5.46 2.57ECL 0.00 3.91 95.11 0.14 0.85RRLyr 4.50 7.85 0.42 86.45 0.77T2Cep 2.12 0.89 0.00 1.46 95.53
Table 6.
Classification report for the 5 classes in the OGLE-IV data set of the RF method.Predicted classACep DSct ECL RRLyr T2Cep T r u e c l a ss ACep 62.02 9.41 0.00 28.57 0.00DSct · · · · · · · · · · · · · · ·
ECL 0.00 4.92 94.06 0.14 0.89RRLyr 4.62 5.16 0.07 89.92 0.24T2Cep 3.03 11.67 4.20 6.52 74.57
Table 7.
The number of images used in the various steps.Survey Training Validation TestingOGLE-III 87 500 18 750 18 750OGLE-IV · · · · · ·
10 000 we trained a RF algorithm using amplitudes and R , φ Fourier-parameters that best characterise the lightcurves shapes. Comparing Figure 4 to Table 3, and Fig-ure 5 to Table 4, i.e. OGLE-III and OGLE-IV results,respectively, we can see that overall our CNN algorithmpredicts better. Two cases where the CNN spectacu-larly preforms worse are the OGLE-III ACep and T2Cepclasses, but as we do a transfer learning, i.e. test thesemethods on the independent OGLE-IV data set, we find that our CNN gives similar results as before, while RFgives worse results by 15–16% for the mentioned classes.A major point that we should discuss is the qualityof training sets. As we described in Section 2, we didnot clear our sample, i.e. we included outliers and low-quality data, which makes the training more realisticand a harder task for the CNN to learn the weights.However, these bad values have a much subtle impacton the calculation of Fourier-parameters, making the RFresult more boosted.Anomalous Cepheids are relatively larger mass (1–2M (cid:12) ) variable stars that lie in the classical instabilitystrip. They follow a period-lumonisity relation, andtheir luminosity is between the classical and Type IICepheids’. They are pulsating in the fundamental modeor the first overtone with a period shorter than 2 days.Their light curve is characterized by a steeper ascend-ing branch which is followed by a shallower descend-ing branch. Usually a bump is present at the bottomof the ascending branch. These features make it veryhard or nearly impossible to distinguish them from RRLyrae stars without known distances, i.e. their absolutebrightness.One of the main goals of our work is to see whethera CNN can distinguish Anomalous Cepheids from othervariable stars based only on the light curve character-istics. From Figure 4 and Table 5 we can see that ourCNN was able to well-classify the 80.2%, while the RF,which is based on pre-computed features, well-classifiedthe 95.46% of ACeps in the OGLE-III sample. As itis expected, the majority of the misclassifications arelabeled as RR Lyrae stars (17.3% and 4.5%). These re-sults show that there are hints of differences that makeit possible to separate ACeps without known distances.Regarding our work, it is interesting that the CNN clas-sifies ACeps about 15% worse than the RF. However, ifwe test these methods using the independent OGLE-IVdatabase (see Figure 5 and Table 4), our CNN still per-forms near 80% (76.9%), while the performance of RFdrops down to 62%. However, this decrease is not en-tirely surprising, as RFs are restricted to predict withinthe range of input parameters, i.e. they are not usefulfor transfer learning.These results mean that image-based CNN classifica-tion may take place in applications where the trainingset slightly differs from the data set on which the pre-diction will be made. CONCLUSIONS AND FUTURE PROSPECTSIn this work we trained a deep neural network tobe able to distinguish different types of variable stars,based on light curve images generated from the OGLE- mage based classification of variable stars Table 8.
Approximate computational runtimes in minutes.Numbers correspond to the NVidia Tesla K80, and NVIDIARTX 2080 Ti GPU cards, respectively.Survey Preprocess Training TestingOGLE-III 265 167 /61 28 /12125 000 imagesOGLE-IV 30 · · ·
23 /510 000 images
III database. To be able to do this, we generated a data-augmented image data set, containing equal amount ofimages from the chosen 5 types of variable stars. Afterthorough testing, a Convolutional Neural Network wascreated, which learned the different light curve featureswith high level of accuracy.We demonstrated that image-based variable star clas-sification is a viable option using a Convolutional Neu-ral Network. This type of machine learning method canlearn both the high and low level features of a foldedvariable star light curve with high level of accuracy,in our case between 80 and 99 %, based on OGLE-IIIdata. It is clearly visible from our results that addi-tional data (e.g. period) could increase the classificationaccuracy. We are working on a multi-channel network,where additional important parameters can be addedas input, this way we expect that the classification ac-curacy of different variable star types will continue toincrease. Our future plans also include generating lightcurve images for all variable stars in the OGLE-III LMCand SMC fields and using their subtypes available (e.g.RRab/RRc/RRd instead of RRLyr), as well. This waywe would have a vast amount of training data and ourmodel could be more specific and reliable.Training and testing a Convolutional Neural Networkrequires vast amount of computational time and capac-ity. We used GPU-accelerated computers in this re-search. However, making predictions (i.e. classificationitself) is possible with the saved weight file on any com-mercial computers. Predicting a label for one imagetakes just a fraction of a second (e.g. 0.13 seconds on asimple laptop), meaning that predictions even on largeamount of light curve images can be made in a veryshort time (see Table 8).A novel way of variable star classification would makea difference in the interpretation of the billions of lightcurves available today (and more to come). The ZwickyTransient Facility (Masci et al. 2018, ZTF) produced ∼ ”Analysisof space-borne photometric data” project we thank forthe usage of MTA Cloud (https://cloud.mta.hu) thatsignificantly helped us achieving the results publishedin this paper. Software:
Python (van der Walt et al. 2011), Numpy(van der Walt et al. 2011), Pandas (McKinney 2010),Scikit-learn (Pedregosa et al. 2011), Tensorflow (Abadiet al. 2015), Keras (Chollet & others 2018)0
Szklen´ar et al.
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