Dimensionality Reduction (DR) has found many applications in hyperspectral image processing. This book chapter investigates Projection Pursuit (PP)-based Dimensionality Reduction, (PP-DR) which includes both Principal Components Analysis (PCA) and Independent Component Analysis (ICA) as special cases. Three approaches are developed for PP-DR. One is to use a Projection Index (PI) to produce pro...

The projection pursuit index defined by a sum of squares of the third and the fourth sample cumulants is known as the moment index proposed by Jones and Sibson (1987). The limiting distribution of the maximum of the moment index under the null hypothesis that the population is multivariate normal is shown to be the maximum of a Gaussian random field with a finite Karhunen-Loève expansion. An ap...

Independent component analysis (ICA) and projection pursuit (PP) are two related techniques for separating mixtures of source signals into their individual components. These rapidly evolving techniques are currently nding applications in speech separation, ERP, EEG, fMRI, and low-level vision. Their power resides in the simple and realistic assumption that diierent physical processes tend to ge...

This article uses Projection Pursuit methods to develop a procedure for detecting outliers in a multivariate time series. We show that testing for outliers in some projection directions could be more powerful than testing the multivariate series directly. The optimal directions for detecting outliers are found by numerical optimization of the kurtosis coefficient of the projected series. We pro...

Auto-associative models have been introduced as a new tool for building nonlinear Principal component analysis (PCA) methods. Such models rely on successive approximations of a dataset by manifolds of increasing dimensions. In this chapter, we propose a precise theoretical comparison between PCA and autoassociative models. We also highlight the links between auto-associative models, projection ...

Matching Pursuit is a greedy algorithm that decomposes any signal into a linear expansion of waveforms taken from a redundant dictionary. Computing the projection of the signal on every element of the basis has a high computational cost. To reduce this computational cost, optimized computational error minimization methods have to be found. Genetic Algorithms have shown to be a good tool to this...

Recently, many authors have proposed new algorithms to improve the accuracy of certain classifiers on artificial and real data sets. The goal is to assemble a collection of individual classifiers based on resampling of data set. Bagging (Breiman, 1996) and AdaBoost (Freund & Schapire, 1997) are the most used procedures: the first fits many classifiers to bootstrap samples of data and classifies...

In this article we use projection pursuit methods to develop a procedure for detecting outliers in a multivariate time series. We show that testing for outliers in some projection directions can be more powerful than testing the multivariate series directly. The optimal directions for detecting outliers are found by numerical optimization of the kurtosis coefficient of the projected series. We ...

A natural multivariate extension of the two-sided cumulative sum chart is proposed via projection pursuit. A modification is given for improving its performance for the special situation in which the process mean is already shifted at the time the charting begins. Simulation studies show that the new charts have slightly better performance than the competing charts (MC1, MEWMA1 and MEWMA2) in t...

We study and compare two types of connectionist learning methods for model-free regression problems: 1) the backpropagation learning (BPL); and 2) the projection pursuit learning (PPL) emerged in recent years in the statistical estimation literature. Both the BPL and the PPL are based on projections of the data in directions determined from interconnection weights. However, unlike the use of fi...