---
title: "Locality Preserving Nonnegative Matrix Factorization"
authors:
  - "Deng Cai"
  - "Xiaofei He"
  - "Xuanhui Wang"
  - "Hujun Bao"
  - "Jiawei Han"
doi: ""
url: "https://ijcai.org/proceedings/2009/171"
pdf: "https://ijcai.org/proceedings/2009/0171.pdf"
venue: "Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence"
year: 2009
pages: "1010-1014"
track: ""
keywords:
---

# Locality Preserving Nonnegative Matrix Factorization

Deng Cai, Xiaofei He, Xuanhui Wang, Hujun Bao, Jiawei Han

*Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence*, pages 1010-1014.

## Abstract

Matrix factorization techniques have been frequently applied in information processing tasks. Among them, Non-negative Matrix Factorization (NMF) have received considerable attentions due to its psychological and physiological interpretation of naturally occurring data whose representation may be parts-based in human brain. On the other hand, from geometric perspective the data is usually sampled from a low dimensional manifold embedded in high dimensional ambient space. One hopes then to find a compact representation which uncovers the hidden topics and simultaneously respects the intrinsic geometric structure. In this paper, we propose a novel algorithm, called {em Locality Preserving Non-negative Matrix Factorization} (LPNMF), for this purpose. For two data points, we use KL-divergence to evaluate their similarity on the hidden topics. The optimal maps are obtained such that the feature values on hidden topics are restricted to be non-negative and vary smoothly along the geodesics of the data manifold. Our empirical study shows the encouraging results of the proposed algorithm in comparisons to the state-of-the-art algorithms on two large high-dimensional databases.Deng Cai, Xiaofei He, Xuanhui Wang, Hujun Bao, Jiawei Han