For the rapid analysis of complicated heterogeneous mixtures, we have developed a method to acquire and intuitively display hyperspectral coherent anti-Stokes Raman scattering (CARS) images. The imaging is performed with a conventional optical setup based around an optical parametric oscillator. Color coding each frame of the resulting hyperspectral data cube according to vibrational frequency ...

This article describes the adaption of exploratory projection pursuit for use with functional data. The aim is to nd \interesting" projections of functional data: e.g. to separate curves into meaningful clusters. Functional data are projected onto low-dimensional subspaces determined by a projection function using a suitable inner product. Such a projection is rapidly computed by representing d...

Recent theory of compressed sensing (CS) tells us that sparse signals can be reconstructed from a small number of random samples. In reconstruction of sparse signals, greedy algorithms, such as the orthogonal matching pursuit (OMP), have been shown to be computationally efficient. In this paper, the performance of OMP is shown to be dependent on how well information of the underlying signals is...

Based on CART, we introduce a recursive partitioning method for high dimensional space which partitions the data using low dimensional features. The low dimensional features are extracted via an exploratory projection pursuit (EPP) method, localized to each node in the tree. In addition, we present an exploratory splitting rule that is potentially less biased to the training data. This leads to...

Tensor methods are of great interest since the development of multicomponent sensors. The acquired multicomponent data are represented by tensors, that is, multiway arrays. This paper presents advances on filtering methods to improve tensor data denoising. Channel-by-channel and multiway methods are presented. The first multiway method is based on the lower-rank (K1, . . . ,KN ) truncation of t...

This article provides a historic review of the forward and backward projection pursuit algorithms, previously thought to be equivalent, and points out an important difference between the two. In doing so, a small error in the original exploratory projection pursuit article by Friedman [J. Amer. Statist. Assoc. 82 (1987) 249–266] is corrected. The implication of the difference is briefly discuss...

Projection pursuit is an exploratory data-analytic method in multivariate (MV) analysis. It is similar to the well-known principal components analysis (PCA) in that it can be used to nd interesting structure within a MV data set. However, unlike PCA, which nds linear projections of maximum variance, projection pursuit nds linear projections of maximum non-normality, which sometimes is better at...

The development and usage of a three-dimensional projection pursuit software package is discussed. The well-established Jones and Sibson moments index is chosen as a computationally efficient projection index to extend to 3D. Computer algebraic methods are extensively employed to handle the long and complex formulae that constitute the index and are explained in detail. A discussion of importan...

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