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Related Experiment Video

Cross-Modal Multivariate Pattern Analysis
13:51

Cross-Modal Multivariate Pattern Analysis

Published on: November 9, 2011

Multivariate multilinear regression.

Ya Su1, Xinbo Gao, Xuelong Li

  • 1Department of Electronic Engineering, Tsinghua University, Beijing 100084, China. thsuya@gmail.com

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|June 9, 2012

View abstract on PubMed

Summary
This summary is machine-generated.

This study investigates the under-sample problem (USP) in principal component regression (PCR) and proposes a new multivariate multilinear regression (MMR) model. MMR alleviates USP by reducing the required sample size and avoiding principal component selection.

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Area of Science:

  • Statistics
  • Machine Learning
  • Computer Vision

Background:

  • Conventional regression methods like multivariate linear regression (MLR) and principal component regression (PCR) struggle with high-dimensional data where the number of features exceeds training samples, leading to the under-sample problem (USP).
  • The USP in PCR, characterized by a high-dimensional feature space relative to the number of training samples, has received limited attention, impacting regression accuracy and stability.

Purpose of the Study:

  • To conduct an in-depth investigation into the under-sample problem (USP) within principal component regression (PCR).
  • To propose a novel multivariate multilinear regression (MMR) model as an alternative to MLR for multilinear data.
  • To address the principal component selection challenge in PCR and alleviate the USP.

Main Methods:

  • Analysis of the causes, conditions, and influence of USP in PCR.
  • Development of a multivariate multilinear regression (MMR) model by incorporating the multilinear structure of objects as a constraint on regression coefficients.
  • Design of an alternative projection procedure for obtaining regression matrices in MMR due to the absence of a closed-form solution.

Main Results:

  • The study elucidates the underlying reasons and conditions for USP in PCR and its impact on regression.
  • The proposed MMR model effectively reduces the regression problem to finding low-dimensional coefficients, thereby avoiding principal component selection.
  • MMR significantly reduces the necessary sample size, thereby alleviating the USP, and experimental validation on synthetic and AAM fitting data confirms its efficacy.

Conclusions:

  • The multivariate multilinear regression (MMR) model offers a viable solution for high-dimensional data with multilinear structures, overcoming limitations of traditional PCR.
  • MMR's ability to reduce sample size requirements and avoid principal component selection makes it a powerful tool for addressing the under-sample problem.
  • The proposed projection procedure for MMR is computationally analyzed and proven to converge, demonstrating practical applicability, particularly in areas like Active Appearance Model fitting.