Accelerating a Lloyd-Type k-Means Clustering Algorithm with Summable Lower Bounds in a Lower-Dimensional Space

Abstract

This paper presents an efficient acceleration algorithm for Lloyd-type k-means clustering, which is suitable to a large-scale and high-dimensional data set with potentially numerous classes. The algorithm employs a novel projection-based filter (PRJ) to avoid unnecessary distance calculations, resulting in high-speed performance keeping the same results as a standard Lloyd's algorithm. The PRJ exploits a summable lower bound on a squared distance defined in a lower-dimensional space to which data points are projected. The summable lower bound can make the bound tighter dynamically by incremental addition of components in the lower-dimensional space within each iteration although the existing lower bounds used in other acceleration algorithms work only once as a fixed filter. Experimental results on large-scale and high-dimensional real image data sets demonstrate that the proposed algorithm works at high speed and with low memory consumption when large k values are given, compared with the state-of-the-art algorithms.