In this paper, we present a L1 regularized projection pursuit algorithm for additive model learning. Two new algorithms are developed for regression and classification respectively: sparse projection pursuit regression and sparse Jensen-Shannon Boosting. The introduced L1 regularized projection pursuit encourages sparse solutions, thus our new algorithms are robust to overfitting and present be...

In high-dimensional data, one often seeks a few interesting low-dimensional projections that reveal important features of the data. Projection pursuit is a procedure for searching high-dimensional data for interesting low-dimensional projections via the optimization of a criterion function called the projection pursuit index. Very few projection pursuit indices incorporate class or group inform...

Friedman and Stuetzle (JASA, 1981) developed a methodology for modeling a response surface by the sum of general smooth functions of linear combinations of the predictor variables. Here multiplicative models for regression and categorical regression are explored. The construction of these models and their performance relative to additive models are examined. CHAPTER 0 INTRODUCTION In recent wor...

Projection pursuit (PP) is an interesting concept, which has been found in many applications. It uses a so-called projection index (PI) as a criterion to seek directions that may lead to interesting findings for data analysts. Unlike the principal components analysis (PCA), which uses variance as a measure to find directions that maximizes data variances, the PI used by the PP finds interesting...

\Ve present a novel classifica t.ioll and regression met.hod that combines exploratory projection pursuit. (unsupervised traiuing) with projection pursuit. regression (supervised t.raining), t.o yield a. nev,,' family of cost./complexity penalLy terms . Some improved generalization properties are demonstrat.ed on real \vorld problems.

Abstract: This paper develops projection pursuit for discrete data using the discrete Radon transform. Discrete projection pursuit is presented as an exploratory method for finding informative low dimensional views of data such as binary vectors, rankings, phylogenetic trees or graphs. We show that for most data sets, most projections are close to uniform. Thus, informative summaries are ones d...

The present work addresses the issue of accurate stochastic approximations in high-dimensional parametric space using tools from uncertainty quantification (UQ). basis adaptation method and its accelerated algorithm polynomial chaos expansions (PCE) were recently proposed to construct low-dimensional adapted specific quantities interest (QoI). paper one difficulty with these adaptations, namely...

Principal Component Analysis is a technique often found to be useful for identifying structure in multivariate data. Although it has various characterizations (Rao 1964), the most familiar is as a variance-maximizing projection. Projection pursuit is a methodology for selecting low-dimensional projections of multivariate data by the optimization of some index of \interestingness" over all proje...