Improving Performance and Accuracy of Local PCA

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 kmeans 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.

Principal Autoparallel Analysis: Data Analysis in Weitzenböck Space

“…However, we are using locality to refer to points within the dataset, rather than treating the problem as a variant of k-means clustering. In local PCA it is common to approximate the whole data distribution by some set of PCA subspaces, and then has to decide which subspace to assign a point to (i.e., which cluster), then doing PCA again for each cluster (Gassenbauer et al, 2011). The method also differs from neighbourhood-preserving methods such as Local Linear Embedding (Roweis & Saul, 2000), where locally flat patches of the manifold are identified and linked together, since we make no linear approximation.…”