Laplacian Regularized Gaussian Mixture Model for Data Clustering

Gaussian Mixture Models (GMMs) are among the most statistically mature methods for clustering. Each cluster is represented by a Gaussian distribution. The clustering process thereby turns to estimate the parameters of the Gaussian mixture, usually by the Expectation-Maximization algorithm. In this p...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on knowledge and data engineering 2011-09, Vol.23 (9), p.1406-1418
Main Authors: He, Xiaofei, Cai, Deng, Shao, Yuanlong, Bao, Hujun, Han, Jiawei
Format: Article
Language:English
Subjects:
Applied sciences
Clustering
Clustering algorithms
Clusters
Computer science
control theory
systems
Data models
Data processing. List processing. Character string processing
Exact sciences and technology
Gaussian
Gaussian mixture model
Geometry
graph laplacian
Graphs
Information retrieval. Graph
Laplace equations
manifold structure
Manifolds
Mathematical models
Mathematics
Memory organisation. Data processing
Nearest neighbor searches
Probability distribution
Software
Studies
Theoretical computing
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Gaussian Mixture Models (GMMs) are among the most statistically mature methods for clustering. Each cluster is represented by a Gaussian distribution. The clustering process thereby turns to estimate the parameters of the Gaussian mixture, usually by the Expectation-Maximization algorithm. In this paper, we consider the case where the probability distribution that generates the data is supported on a submanifold of the ambient space. It is natural to assume that if two points are close in the intrinsic geometry of the probability distribution, then their conditional probability distributions are similar. Specifically, we introduce a regularized probabilistic model based on manifold structure for data clustering, called Laplacian regularized Gaussian Mixture Model (LapGMM). The data manifold is modeled by a nearest neighbor graph, and the graph structure is incorporated in the maximum likelihood objective function. As a result, the obtained conditional probability distribution varies smoothly along the geodesics of the data manifold. Experimental results on real data sets demonstrate the effectiveness of the proposed approach.
ISSN:1041-4347
1558-2191
DOI:10.1109/TKDE.2010.259