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Higher order partial least squares (HOPLS): a generalized multilinear regression method.

Qibin Zhao1, Cesar F Caiafa, Danilo P Mandic

  • 1Brain Science Institute, RIKEN, Saitama, Japan. qbzhao@brain.riken.jp

IEEE Transactions on Pattern Analysis and Machine Intelligence
|May 18, 2013
PubMed
Summary

A new regression model, higher order partial least squares (HOPLS), predicts tensor data by projecting it onto a latent space. HOPLS offers improved prediction, handles small datasets, and is robust to noise compared to existing methods.

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Area of Science:

  • Multilinear regression
  • Tensor analysis
  • Machine learning

Background:

  • Predicting tensor data (multiway arrays) is challenging.
  • Existing regression models may struggle with complex, multi-dimensional datasets.
  • Overfitting and noise are common issues in high-dimensional data analysis.

Purpose of the Study:

  • Introduce a novel generalized multilinear regression model, higher order partial least squares (HOPLS).
  • Enable prediction of a tensor Y from a tensor X using latent variable regression.
  • Enhance predictive accuracy, small sample size suitability, and noise robustness.

Main Methods:

  • Projecting data onto an optimized latent space.
  • Sequential optimization of the low-dimensional latent space via deflation.
  • Utilizing higher order singular value decomposition on a generalized cross-covariance tensor.
  • Explaining data as a sum of orthogonal Tucker tensors.

Main Results:

  • HOPLS demonstrates superior predictive ability compared to existing methods.
  • The model is well-suited for datasets with a small number of samples.
  • HOPLS exhibits significant robustness to noise in the data.
  • Validation on synthetic and real-world electrocorticogram data confirms advantages.

Conclusions:

  • HOPLS provides a powerful new tool for tensor-based regression.
  • The model effectively balances model complexity and predictive performance.
  • HOPLS offers significant advantages for analyzing complex, multi-dimensional scientific data.