Ensemble and deep learning on astronomical data with different modalities

Abstract

Light curves inform us how the brightness of an astronomical object changes over time. They are obtained by subtracting successive images of astronomical objects of a photometric band. In this thesis, the first task was to focus on the classification of 14 astronomical objects in the Photometric LSST Astronomical Time-series Classification Challenge (PLAsTiCC) data set which was prepared to model future observations of the Vera Rubin Observatory. The light curve of each object was divided into two separate parts using a Haar wavelet transform. By using these two wavelet components, statistical properties such as the mean, standard deviation, and minimum were obtained for each band. The classification was performed with boosted artificial neural networks and boosted decision trees by using extracted features and also including additional features such as the photometric redshift and its uncertainty. The training set was highly biased toward low-redshifted objects. Importance weights were estimated for each training object, and more representative data were given larger weights. The combination of boosted decision trees, random forests and extremely randomized trees was found to give the best performance for type Ia supernovae which are important indicators for cosmological measurements. The role of photometric redshift was examined by excluding the redshift parameter. The performance of superluminous supernovae (SLSN-I) was significantly affected by the omission of the redshift parameter with a 10% decrease in the area under the receiver operating characteristic curve (AUC) score. The relevant features of each object class were ranked using a neural network classifier. The time-frequency images were also obtained using a continuous wavelet transform as an alternative to discrete Haar wavelets. Since all data points of the light curves were used instead of utilizing feature extraction, a powerful model was needed to estimate the missing data. Gaussian process regression was employed for that task as one of the most successful models in filling the gaps of the light curves. As discussed previously in the literature, it is very difficult to accurately estimate 14 astronomical objects with only one kernel. Therefore we limited our attention to only include type Ia and II supernovae for the classification task. One of the difficulties that will be faced in future observations is that researchers will not be able to obtain any data on some photometric bands, depending on the status of the observation. Villar et al. proposed a 2D Gaussian process regression for this situation. The missing data in this part of the thesis was estimated using this two-dimensional kernel. The convolutional neural network (CNN) structures were decomposed using a tensor decomposition method (CP decomposition). It was observed that rank selection, which changes the number of parameters, also affects the classifier performance. While the classifier performed poorly on very small ranks, an optimal rank was determined for better performance. This indicates that tensor decomposition methods may be significant enough to include in the analysis of noisy light curves. This method provides an alternative to feature engineering that applies principal component analysis (PCA) to wavelet components. Another main task that was performed in this thesis was the morphological classification of Galaxy Zoo images. The images used in the Galaxy Zoo challenge were taken from the seventh data release (DR7) of the Sloan Digital Sky Survey (SDSS). SDSS made observations in 5 photometric bands which are labeled as u, g, r, i and z. The Galaxy Zoo photos are composite photos of galaxies observed in the r, g, and i bands. As galaxy images do not have a fixed or preferred orientation, any classifier that aims to correctly classify galaxies should be expected to properly detect when two galaxies are rotated versions of each other. Although convolutional layers are successful in processing images and preserve feature maps when encountering a translated version of an object, they fail in identifying rotated objects as the same. The convolution operation does not commute with rotation and this causes the feature map to change when it is generated for different orientations of the same galaxies. To overcome the problem of not identifying rotated versions of the same object, an equivariant structure is needed for an image classifier. Convolutional layers can be excellent ingredients in defining generalized equivariant architectures. Instead of using traditional convolution layers, it is possible to define a generalized convolution operation with group operations that preserve different symmetries. A dynamic structure using the p4m group convolutional layers (p4m is the plane symmetry group of translations, reflections, and rotations by 90 degrees) is proposed in this thesis, which introduces additional angles to the architecture after the initial training of the p4m group convolutional layers.