Clustering is a fundamental task in unsupervised learning, which aims to partition the data set into several clusters. It is widely used for data mining, image segmentation, and natural language processing. One of the most popular clustering methods is centroid-based clustering, including k-medians and k-means clustering. k-medians and k-means clustering...
In this thesis we study two problems, one in unsupervised learning - k-means clustering and the other in a supervised learning setting with the presence of adversarial perturbations. We do a beyond-worst case style analysis and show that in either case instances that are resilient to adversarial perturbations are also...
The advent of sequencing technologies has generated a large amount of biological and medical data. These data such as genetic sequencing data and lab experimental evidence data can help understand critical biomedical problems. This dissertation makes contribution in three different but related applications in biomedical research. In Chapter 2, we...
Deep neural networks have shown impressive performance for many applications. In this dissertation, leveraging the capabilities of neural networks for modeling the non-linearity exists in the data, we propose several models that can project data into a low dimensional, discriminative, and smooth manifold. The suggested models can transfer knowledge from...
Cluster Analysis deals with classifying a sample of multivariate measurements into different categories. In this dissertation we study the effect of the correlation structure of the data on the performance of a clustering method. We begin with the analysis of two-component normal mixture models and then proceed to cluster analysis...