Adaptive Principal Component Analysis

  • Authors:
  • Cynthia Archer;Todd K. Leen

  • Affiliations:
  • -;-

  • Venue:
  • Adaptive Principal Component Analysis
  • Year:
  • 2002

Quantified Score

Hi-index 0.00

Visualization

Abstract

We develop a new signal modeling method, entropy-constrained adaptive PCA, that has the flexibility to accurately model the cluster structure of non-stationary data. Using a latent data framework, we derive a statistical model for a broad category of real world signals that includes images and measurements from natural processes. Data of this type consists of a collection of low-dimensional patterns embedded in a high-dimensional observation or measurement space. We use this statistical model to develop our adaptive PCA algorithm. Our algorithm adjusts the model parameters to minimize the dimension reduction error between the model and sample data subject to a constraint on the entropy. We evaluate the quality of models porduced by adaptive PCA using image texture data and salinity and temperature measurements from the Columbia river. Compated to entropy-constrained vector quantization, local PCA and full-covariance models, adaptive PCA proved to be a more effective tool for analyzing the salinity and temperature data. In addition, our results show that our model segments texture images as well as entropy-constrained vector quantizers, yet uses substantially fewer model components. Adaptive PCA models conform to the data structure better than full covariance models when training data is sparse.