A New Geometric Approach to Latent Topic Modeling and Discovery

Abstract

A new geometrically-motivated algorithm for nonnegative matrix factorization is developed and applied to the discovery of latent "topics" for text and image "document" corpora. The algorithm is based on robustly finding and clustering extreme points of empirical cross-document word-frequencies that correspond to novel "words" unique to each topic. In contrast to related approaches that are based on solving non-convex optimization problems using suboptimal approximations, locally-optimal methods, or heuristics, the new algorithm is convex, has polynomial complexity, and has competitive qualitative and quantitative performance compared to the current state-of-the-art approaches on synthetic and real-world datasets.

This paper was submitted to the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2013 on November 30, 2012

References in corpus (6)

• Probabilistic Latent Semantic Analysis
• A geometric analysis of subspace clustering with outliers
• A convex model for non-negative matrix factorization and dimensionality reduction on physical space
• Factoring nonnegative matrices with linear programs
• Topic Discovery through Data Dependent and Random Projections
• Automatic Relevance Determination in Nonnegative Matrix Factorization with the β-Divergence

Cited by in corpus (1)

• Necessary and Sufficient Conditions and a Provably Efficient Algorithm for Separable Topic Discovery