Pattern extraction and clustering for high-dimensional discrete data

We explore connections of low-rank matrix factorizations with interesting problems in data mining and machine learning. We propose a framework for solving several low-rank matrix factorization problems, including binary matrix factorization, constrained binary matrix factorization, weighted constrained binary matrix factorization, densest k-subgraph, and orthogonal nonnegative matrix factorization. These combinatorial problems are NP-hard. Our goal is to develop effective approximation algorithms with good theoretical properties and apply them to solve various real application problems. We reformulate each of the problems as a special clustering problem that has the same optimal solution as the corresponding original problem. Making use of this property, we develop clustering algorithms to solve corresponding low-rank matrix factorization problems. We prove that most of our clustering algorithms have constant approximation ratios, which is a highly desirable property for NP-hard problems. We apply the proposed algorithms and compare them with existing methods for real applications in pattern extraction, document clustering, transaction data mining, recommender systems, bicluster discovery in gene expression data, social network mining, and image representation.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Jiang, Peng

Contributors dc:contributor

• Heath, Michael T.
• Olson, Luke N.
• Zhai, ChengXiang
• Park, Haesun

• low-rank matrix factorization
• binary matrix factorization
• k-means clustering
• approximation algorithm
• pattern extraction
• association rule mining
• document clustering
• weighted binary matrix factorization
• bicluster discovery
• densest k-subgraph
• social network mining

Statement dc:rights

• Copyright 2013 Peng Jiang

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/46604

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/46604