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

Kazuo AOYAMA  Kazumi SAITO  Tetsuo IKEDA  

IEICE TRANSACTIONS on Information and Systems   Vol.E101-D   No.11   pp.2773-2783
Publication Date: 2018/11/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.2017EDP7392
Type of Manuscript: PAPER
Category: Artificial Intelligence, Data Mining
algorithm,  clustering,  k-means,  lower bound,  singular value decomposition,  principal component analysis,  dimensionality reduction,  performance,  

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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.