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Improving Performance and Accuracy of Local PCA
Author(s) -
Gassenbauer Václav,
Křivánek Jaroslav,
Bouatouch Kadi,
Bouville Christian,
Ribardière Mickaël
Publication year - 2011
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2011.02047.x
Subject(s) - initialization , computer science , cluster analysis , principal component analysis , point (geometry) , curse of dimensionality , dimensionality reduction , focus (optics) , computation , artificial intelligence , algorithm , data mining , mathematics , physics , geometry , optics , programming language
Abstract Local Principal Component Analysis (LPCA) is one of the popular techniques for dimensionality reduction and data compression of large data sets encountered in computer graphics. The LPCA algorithm is a variant of k‐means clustering where the repetitive classification of high dimensional data points to their nearest cluster leads to long execution times. The focus of this paper is on improving the efficiency and accuracy of LPCA. We propose a novel SortCluster LPCA algorithm that significantly reduces the cost of the point‐cluster classification stage, achieving a speed‐up of up to 20. To improve the approximation accuracy, we investigate different initialization schemes for LPCA and find that the k‐means++ algorithm [AV07] yields best results, however at a high computation cost. We show that similar ideas that lead to the efficiency of our SortCluster LPCA algorithm can be used to accelerate k‐means++. The resulting initialization algorithm is faster than purely random seeding while producing substantially more accurate data approximation.