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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Transforming complex multivariate geological data to be multivariate Gaussian is an important and challenging problem in geostatistics. A variety of transforms are available to accomplish this goal, but may struggle with data sets of high dimensional and sample sizes. Projection Pursuit Density Estimation (PPDE) is a well-established non-parametric method for estimating the joint PDF of multiva...

Parameter estimation becomes difficult in high-dimensional spaces due to the increasing sparseness of the data. Therefore, when a low-dimensional representation is embedded in the data, dimensionality reduction methods become useful. One such method-projection pursuit regression (Friedman and Stuetzle 1981 (PPR)-is capable of performing dimensionality reduction by composition, namely, it constr...

Projection pursuit regression (PPR) can be used to estimate a smooth function of several variables from noisy and scattered data. The estimate is a sum of smoothed one-dimensional projections of the variables. This paper discusses an extension of PPR to exponential family distributions, called generalized projection pursuit regression (GPPR). The proposed model allows multiple responses and non...

The goal of this thesis is to modify projection pursuit by trading accuracy for interpretability. The modification produces a more parsimonious and understandable model without sacrificing the structure which projection pursuit seeks. The method retains the nonlinear versatility of projection pursuit while clarifying the results. Following an introduction which outlines the dissertation, the fi...

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This paper examines the implementation of projection pursuit regression (PPR) in the context of machine learning and neural networks. We propose a parametric PPR with direct training which achieves improved training speed and accuracy when compared with nonparametric PPR. Analysis and simulations are done for heuristics to choose good initial projection directions. A comparison of a projection ...

Graphical inspection of multimodality is demonstrated using unsupervised lateral-inhibition neural networks. Three projection pursuit indices are compared on low dimensional simulated and real-world data: principal components 22], Legendre polynomial 6] and projection pursuit network 16].