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...
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...