Algorithms for data mining

Abstract

Data of massive size are now available in a wide variety of fields and come with great promise. In theory, these massive data sets allow data mining and exploration on a scale previously unimaginable. However, in practice, it can be difficult to apply classic data mining techniques to such massive data sets due to their sheer size. In this thesis, we study three algorithmic problems in data mining with consideration to the analysis of massive data sets. Our work is both theoretical and experimental - we design algorithms and prove guarantees for their performance and also give experimental results on real data sets. The three problems we study are: 1) finding a matrix of low rank that approximates a given matrix, 2) clustering high-dimensional points into subsets whose points lie in the same subspace, and 3) clustering objects by pairwise similarities/distances.