BICO: BIRCH Meets Coresets for k-Means Clustering

Abstract

We design a data stream algorithm for the k-means problem, called BICO, that combines the data structure of the SIGMOD Test of Time award winning algorithm BIRCH [27] with the theoretical concept of coresets for clustering problems. The k-means problem asks for a set C of k centers minimizing the sum of the squared distances from every point in a set P to its nearest center in C. In a data stream, the points arrive one by one in arbitrary order and there is limited storage space.BICO computes high quality solutions in a time short in practice. First, BICO computes a summary S of the data with a provable quality guarantee: For every center set C, S has the same cost as P up to a (1 + ε)-factor, i. e., S is a coreset. Then, it runs k-means ++ [5] on S.We compare BICO experimentally with popular and very fast heuristics (BIRCH, MacQueen [24]) and with approximation algorithms (Stream-KM ++ [2], StreamLS [16,26]) with the best known quality guarantees. We achieve the same quality as the approximation algorithms mentioned with a much shorter running time, and we get much better solutions than the heuristics at the cost of only a moderate increase in running time.

A Hierarchical Algorithm for Extreme Clustering

“…A natural adaptation of these agglomerative methods is the mini-batch version that PERCH outperforms in our empirical evaluation. BIRCH [38] and its extensions [19] comprise state of the art online hierarchical methods that, like PERCH, incrementally insert points into a cluster tree data structure. However, unlike PERCH, these methods parameterize internal nodes with means and variances as opposed to bounding boxes, and they do not implement rotations, which our empirical and theoretical results justify.…”

Coresets-Methods and History: A Theoreticians Design Pattern for Approximation and Streaming Algorithms

“…Many of these decompositions are based on packing arguments and range spaces. We will illustrate one approach via the k-means problem, based on the papers by Har-Peled and Mazumdar [58] and Fichtenberger et al [51].…”

“…The geometric approach was also popular when coresets were introduced to k-median and k-means clustering and generalizations, see for instance [44,51,52,57,58]. Due to the exponential dependency inherent in all known constructions, the focus later shifted to sampling.…”

“…Certain geometric decompositions avoid this, see [51,52], but have a much larger offline space dependency compared to other constructions. See Table 1 for an overview.…”

Applying K-Means Clustering Algorithm Using Oracle Data Mining to Banking Data

“…Koupaie et al [4] proposed cluster based outlier detection in data stream. Fichtenberger et al [3] proposed a data stream algorithm for the k-means problem called BICO (BIRCH Meets Core sets for k-means Clustering), that combines the data structure of the SIGMOD test of time award winning algorithm birch with the theoretical concept of corsets for clustering problems. Vijayarani and Jothi [11] two clustering algorithms namely BIRCH with k-means and Birch with CLARANS are used for clustering the data items and finding the outliers in data streams.…”