Bayesian Nonparametric Clustering for Positive Definite Matrices

Anoop Cherian, Vassilios Morellas, Nikolaos P Papanikolopoulos

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Symmetric Positive Definite (SPD) matrices emerge as data descriptors in several applications of computer vision such as object tracking, texture recognition, and diffusion tensor imaging. Clustering these data matrices forms an integral part of these applications, for which soft-clustering algorithms (K-Means, expectation maximization, etc.) are generally used. As is well-known, these algorithms need the number of clusters to be specified, which is difficult when the dataset scales. To address this issue, we resort to the classical nonparametric Bayesian framework by modeling the data as a mixture model using the Dirichlet process (DP) prior. Since these matrices do not conform to the Euclidean geometry, rather belongs to a curved Riemannian manifold,existing DP models cannot be directly applied. Thus, in this paper, we propose a novel DP mixture model framework for SPD matrices. Using the log-determinant divergence as the underlying dissimilarity measure to compare these matrices, and further using the connection between this measure and the Wishart distribution, we derive a novel DPM model based on the Wishart-Inverse-Wishart conjugate pair. We apply this model to several applications in computer vision. Our experiments demonstrate that our model is scalable to the dataset size and at the same time achieves superior accuracy compared to several state-of-the-art parametric and nonparametric clustering algorithms.

Original languageEnglish (US)
Article number7159063
Pages (from-to)862-874
Number of pages13
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Volume38
Issue number5
DOIs
StatePublished - May 1 2016

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Bayesian Nonparametrics
Positive definite matrix
Symmetric Positive Definite Matrix
Dirichlet Process
Clustering
Mixture Model
Computer Vision
Process Model
Clustering Algorithm
Dirichlet Process Prior
Wishart Distribution
Euclidean geometry
Dissimilarity Measure
Expectation Maximization
Data Clustering
Object Tracking
K-means
Number of Clusters
Clustering algorithms
Computer vision

Keywords

  • Dirichlet process
  • Region covariances
  • nonparametric methods
  • positive definite matrices

Cite this

Bayesian Nonparametric Clustering for Positive Definite Matrices. / Cherian, Anoop; Morellas, Vassilios; Papanikolopoulos, Nikolaos P.

In: IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 38, No. 5, 7159063, 01.05.2016, p. 862-874.

Research output: Contribution to journalArticle

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