From Supervised to Unsupervised Support Vector Machines and Applications in Astronomy

Abstract

A common task in the field of machine learning is the classification of objects. The basis for such a task is usually a training set consisting of patterns and associated class labels. A typical example is, for instance, the automatic classification of stars and galaxies in the field of astronomy. Here, the training set could consist of images and associated labels, which indicate whether a particular image shows a star or a galaxy. For such a learning scenario, one aims at generating models that can automatically classify new, unseen images. In the field of machine learning, various classification schemes have been proposed. One of the most popular ones is the concept of support vector machines, which often yields excellent classification results given sufficient labeled data.However, for a variety of real-world tasks, the acquisition of sufficient labeled data can be quite time-consuming. In contrast to labeled training data, unlabeled one can often be obtained easily in huge quantities. Semi-and unsupervised techniques aim at taking these unlabeled patterns into account to generate appropriate models. In the literature, various ways of extending support vector machines to these scenarios have been proposed. One of these ways leads to combinatorial optimization tasks that are difficult to address.In this thesis, several optimization strategies will be developed for these tasks that (1) aim at solving them exactly or (2) aim at obtaining (possibly suboptimal) candidate solutions in an efficient kind of way. More specifically, we will derive a polynomial-time approach that can compute exact solutions for special cases of both tasks. This approach is among the first ones that provide upper runtime bounds for the tasks at hand and, thus, yield theoretical insights into their computational complexity. In addition to this exact scheme, two heuristics tackling both problems will be provided. The first one is based on least-squares variants of the original tasks whereas the second one relies on differentiable surrogates for the corresponding objective functions. While direct implementations of both heuristics are still computationally expensive, we will show how to make use of matrix operations to speed up their execution. This will result in two optimization schemes that exhibit an excellent classification and runtime performance.Despite these theoretical derivations, we will also depict possible application domains of machine learning methods in astronomy. Here, the massive amount of data given for today's and future projects renders a manual analysis impossible and necessitates the use of sophisticated techniques. In this context, we will derive an efficient way to preprocess spectroscopic data, which is based on an adaptation of support vector machines, and the benefits of semi-supervised learning schemes for appropriate learning tasks will be sketched. As a further contribution to this field, we will propose the use of so-called resilient algorithms for the automatic data analysis taking place aboard toda...