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.

This paper presents an analysis/synthesis model for sound that is based on nonlinear dynamics, or chaos, theory. The inspiration is that since chaos and fractals can represent many complex naturally occurring forms, can the same be found for sound? Evidence is examined that shows how nonlinear dynamics plays a fundamental role in the generation of sounds, both musical and non-musical. Presented is a novel model that consists of an autonomous nonlinear feedback system and a way of analysing a sound to find parameters for the model. Encouraging results are presented showing the analysis and resynthesis of air noises, wind instrument and gong sounds. 1. Introduction It is now well known that simple nonlinear dynamical systems can produce complex and beautiful behaviour that often replicates natural phenomena. A striking example of this can be seen in the wide range of abstract and natural looking computer images that may be generated with such systems. Could the same be done for sound? F...