Canonical correlation analysis on spd(n) manifolds

Hyun Woo Kim, Nagesh Adluru, Barbara B. Bendlin, Sterling C. Johnson, Vikas Singh, Baba C. Vemuri

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)

Abstract

Canonical correlation analysis (CCA) is a widely used statistical technique to capture correlations between two sets of multivariate random variables and has found a multitude of applications in computer vision, medical imaging, and machine learning. The classical formulation assumes that the data live in a pair of vector spaces which makes its use in certain important scientific domains problematic. For instance, the set of symmetric positive definite matrices (SPD), rotations, and probability distributions all belong to certain curved Riemannian manifolds where vector-space operations are in general not applicable. Analyzing the space of such data via the classical versions of inference models is suboptimal. Using the space of SPD matrices as a concrete example, we present a principled generalization of the well known CCA to the Riemannian setting. Our CCA algorithm operates on the product Riemannian manifold representing SPD matrix-valued fields to identify meaningful correlations. As a proof of principle, we present experimental results on a neuroimaging data set to show the applicability of these ideas.

Original languageEnglish
Title of host publicationRiemannian Computing in Computer Vision
PublisherSpringer International Publishing
Pages69-100
Number of pages32
ISBN (Electronic)9783319229577
ISBN (Print)9783319229560
DOIs
Publication statusPublished - 2015 Jan 1
Externally publishedYes

Fingerprint

Canonical Correlation Analysis
Symmetric Positive Definite Matrix
Vector space
Riemannian Manifold
Neuroimaging
Vector spaces
Valued Fields
Medical Imaging
Computer Vision
Machine Learning
Probability Distribution
Random variable
Medical imaging
Random variables
Formulation
Probability distributions
Computer vision
Experimental Results
Learning systems
Model

ASJC Scopus subject areas

  • Engineering(all)
  • Computer Science(all)
  • Mathematics(all)

Cite this

Kim, H. W., Adluru, N., Bendlin, B. B., Johnson, S. C., Singh, V., & Vemuri, B. C. (2015). Canonical correlation analysis on spd(n) manifolds. In Riemannian Computing in Computer Vision (pp. 69-100). Springer International Publishing. https://doi.org/10.1007/978-3-319-22957-7_4

Canonical correlation analysis on spd(n) manifolds. / Kim, Hyun Woo; Adluru, Nagesh; Bendlin, Barbara B.; Johnson, Sterling C.; Singh, Vikas; Vemuri, Baba C.

Riemannian Computing in Computer Vision. Springer International Publishing, 2015. p. 69-100.

Research output: Chapter in Book/Report/Conference proceedingChapter

Kim, HW, Adluru, N, Bendlin, BB, Johnson, SC, Singh, V & Vemuri, BC 2015, Canonical correlation analysis on spd(n) manifolds. in Riemannian Computing in Computer Vision. Springer International Publishing, pp. 69-100. https://doi.org/10.1007/978-3-319-22957-7_4
Kim HW, Adluru N, Bendlin BB, Johnson SC, Singh V, Vemuri BC. Canonical correlation analysis on spd(n) manifolds. In Riemannian Computing in Computer Vision. Springer International Publishing. 2015. p. 69-100 https://doi.org/10.1007/978-3-319-22957-7_4
Kim, Hyun Woo ; Adluru, Nagesh ; Bendlin, Barbara B. ; Johnson, Sterling C. ; Singh, Vikas ; Vemuri, Baba C. / Canonical correlation analysis on spd(n) manifolds. Riemannian Computing in Computer Vision. Springer International Publishing, 2015. pp. 69-100
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