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Keywords: density estimation; empirical distribution function; exploratory data analysis; Gaussian mixture; ICA; PCA.
Finding a suitable representation of multivariate data is fundamental in many scientific disciplines. The projection pursuit (PP) aims to extract interesting "non-Gaussian" features from multivariate data, and tends to be computationally intensive even for low-dimensional data points. In high-dimensional settings, a recent work by Bickel etal (2018, PNAS) on PP addresses asymptotic characterization and conjectures of the feasibility of PP as the dimension grows with the sample size. To gain practical utility of and learn theoretical insights into PP in an integral way, data analytic tools needed to evaluate phase transitions of PP in high dimensions become increasingly desirable but are less explored in the literature. This paper focuses on developing computationally fast and effective approaches central to finite sample studies for (i) visualizing the feasibility of PP in extracting features from high-dimensional data, as compared with alternative methods like principal component analysis (PCA) and independent component analysis (ICA), and (ii) assessing the plausibility of PP in cases where asymptotic studies are lacking or unavailable, with the goal of better understanding the practicality, limitation and challenge of PP in the analysis of large data sets.