Statement of Research

Machine learning can be described as the discipline of automatically “learning” concepts from data eitherwith, or without human guidance. The goal ofmostmachine learning applications is to discover patterns within data so that properties of hitherto unseen data can be predicted reliably. However, the task of learning from data can often be very challenging (naturally contingent upon the concept that one is trying to learn), more so in the presence of vast amounts of data, where most approaches rapidly become infeasible. Therefore, it is imperative to either develop algorithms that are highly scalable, or to obtain approximate representations of data on which one can perform more sophisticated subsequent analyses. In my research, I deal with both the abovementioned aspects. My Ph.D. thesis is on Matrix Nearness Problems in Data Mining, wherein I develop important structured or pattern revealing approximations for the input data, along with efficient algorithms for computing them. Some examples of frequently arising matrix nearness problems are dimensionality reduction, sparse approximations, nonnegative matrix approximation, clustering, co-clustering, and kernel matrix approximation. Each of these problems has numerous applications in a diverse variety of fields ranging from bioinformatics, signal processing, text analysis, to astronomy. By developing new algorithms and efficient implementations for important nearness problems, my work enables several applications across all these domains, especially in the face of large amounts of data. In addition tomydoctoral research, I have alsoworked on obtaining highly scalable algorithms and implementations for fundamental machine learning problems such as classification and regression. The power of my approach can be gauged by considering a simple problem such as support vector regression; consider a dataset with several million high-dimensional vectors as input. None of the commonly available software implementations for support vector regression scale to such large data sizes, a problem that my approach overcomes. In what follows below, I have summarized some of my Ph.D. research work, as well as my non-doctoral research, the latter indicated by a ‘⋆’ suffixed to the section name.