Local Dimensionality Reduction for Non-Parametric Regression

Heiko Hoffmann, Stefan Schaal, Sethu Vijayakumar

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

Locally-weighted regression is a computationally-efficient technique for non-linear regression. However, for high-dimensional data, this technique becomes numerically brittle and computationally too expensive if many local models need to be maintained simultaneously. Thus, local linear dimensionality reduction combined with locally-weighted regression seems to be a promising solution. In this context, we review linear dimensionalityreduction methods, compare their performance on non-parametric locally-linear regression, and discuss their ability to extend to incremental learning. The considered methods belong to the following three groups: (1) reducing dimensionality only on the input data, (2) modeling the joint input-output data distribution, and (3) optimizing the correlation between projection directions and output data. Group 1 contains principal component regression (PCR); group 2 contains principal component analysis (PCA) in joint input and output space, factor analysis, and probabilistic PCA; and group 3 contains reduced rank regression (RRR) and partial least squares (PLS) regression. Among the tested methods, only group 3 managed to achieve robust performance even for a non-optimal number of components (factors or projection directions). In contrast, group 1 and 2 failed for fewer components since these methods rely on the correct estimate of the true intrinsic dimensionality. In group 3, PLS is the only method for which a computationally-efficient incremental implementation exists.
Original languageEnglish
Pages (from-to)109-131
Number of pages23
JournalNeural Processing Letters
Issue number2
Early online date13 Feb 2009
Publication statusPublished - Apr 2009

Keywords / Materials (for Non-textual outputs)

  • Correlation
  • Dimensionality reduction
  • Factor analysis
  • Incremental learning
  • Kernel function
  • Locally-weighted regression
  • Partial least squares
  • Principal component analysis
  • Principal component regression
  • Reduced-rank regression


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