Dimension Reduction by Local Principal Component Analysis

1997/10/01 by Nandakishore Kambhatla, Todd K. Leen · 8 citations
Computer Science · #Blind Source Separation Techniques #Image and Signal Denoising Methods #Neural Networks and Applications

paper · doi:10.1162/neco.1997.9.7.1493

openalex publication_date 1997/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Reducing or eliminating statistical redundancy between the components of high-dimensional vector data enables a lower-dimensional representation without significant loss of information. Recognizing the limitations of principal component analysis (PCA), researchers in the statistics and neural network communities have developed nonlinear extensions of PCA. This article develops a local linear approach to dimension reduction that provides accurate representations and is fast to compute. We exercise the algorithms on speech and image data, and compare performance with PCA and with neural network implementations of nonlinear PCA. We find that both nonlinear techniques can provide more accurate representations than PCA and show that the local linear techniques outperform neural network implementations.

Citations

• Auto-association by multilayer perceptrons and singular value decomposition
• An Algorithm for Finding Intrinsic Dimensionality of Data
• The JPEG still picture compression standard
• Detection of signals by information theoretic criteria
• Multilayer feedforward networks are universal approximators

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