A clustering algorithm for multivariate data streams with correlated components

Common clustering algorithms require multiple scans of all the data to achieve convergence, and this is prohibitive when large databases, with data arriving in streams, must be processed. Some algorithms to extend the popular K-means method to the analysis of streaming data are present in literature since 1998 (Bradley et al. in Scaling clustering algorithms to large databases. In: KDD. p. 9-15, 1998; O'Callaghan et al. in Streaming-data algorithms for high-quality clustering. In: Proceedings of IEEE international conference on data engineering. p. 685, 2001), based on the memorization and recursive update of a small number of summary statistics, but they either don't take into account the specific variability of the clusters, or assume that the random vectors which are processed and grouped have uncorrelated components. Unfortunately this is not the case in many practical situations. We here propose a new algorithm to process data streams, with data having correlated components and coming from clusters with different covariance matrices. Such covariance matrices are estimated via an optimal double shrinkage method, which provides positive definite estimates even in presence of a few data points, or of data having components with small variance. This is needed to invert the matrices and compute the Mahalanobis distances that we use for the data assignment to the clusters. We also estimate the total number of clusters from the data.Comment: title changed, rewritte

A K-means clustering algorithm for multivariate big data with correlated components

Common clustering algorithms require multiple scans of all the data to achieve convergence, and this is prohibitive when large databases, with millions of data, must be processed. Some algorithms to extend the popular K-means method to the analysis of big data are present in literature since the publication of (Bradley et al, Scaling clustering algorithms to large databases, 1998) but they assume that the random vectors which are processed and grouped have uncorrelated components. Unfortunately this is not the case in many practical situations. We here propose an extension of the algorithm of Bradley, Fayyad and Reina to the processing of massive multivariate data, having correlated components

On The Effect of Hyperedge Weights On Hypergraph Learning

Hypergraph is a powerful representation in several computer vision, machine learning and pattern recognition problems. In the last decade, many researchers have been keen to develop different hypergraph models. In contrast, no much attention has been paid to the design of hyperedge weights. However, many studies on pairwise graphs show that the choice of edge weight can significantly influence the performances of such graph algorithms. We argue that this also applies to hypegraphs. In this paper, we empirically discuss the influence of hyperedge weight on hypegraph learning via proposing three novel hyperedge weights from the perspectives of geometry, multivariate statistical analysis and linear regression. Extensive experiments on ORL, COIL20, JAFFE, Sheffield, Scene15 and Caltech256 databases verify our hypothesis. Similar to graph learning, several representative hyperedge weighting schemes can be concluded by our experimental studies. Moreover, the experiments also demonstrate that the combinations of such weighting schemes and conventional hypergraph models can get very promising classification and clustering performances in comparison with some recent state-of-the-art algorithms

Finding groups in data: Cluster analysis with ants

Wepresent in this paper a modification of Lumer and Faieta’s algorithm for data clustering. This approach mimics the clustering behavior observed in real ant colonies. This algorithm discovers automatically clusters in numerical data without prior knowledge of possible number of clusters. In this paper we focus on ant-based clustering algorithms, a particular kind of a swarm intelligent system, and on the effects on the final clustering by using during the classification differentmetrics of dissimilarity: Euclidean, Cosine, and Gower measures. Clustering with swarm-based algorithms is emerging as an alternative to more conventional clustering methods, such as e.g. k-means, etc. Among the many bio-inspired techniques, ant clustering algorithms have received special attention, especially because they still require much investigation to improve performance, stability and other key features that would make such algorithms mature tools for data mining. As a case study, this paper focus on the behavior of clustering procedures in those new approaches. The proposed algorithm and its modifications are evaluated in a number of well-known benchmark datasets. Empirical results clearly show that ant-based clustering algorithms performs well when compared to another techniques

Methods of Hierarchical Clustering

We survey agglomerative hierarchical clustering algorithms and discuss efficient implementations that are available in R and other software environments. We look at hierarchical self-organizing maps, and mixture models. We review grid-based clustering, focusing on hierarchical density-based approaches. Finally we describe a recently developed very efficient (linear time) hierarchical clustering algorithm, which can also be viewed as a hierarchical grid-based algorithm.Comment: 21 pages, 2 figures, 1 table, 69 reference

Linear, Deterministic, and Order-Invariant Initialization Methods for the K-Means Clustering Algorithm

Over the past five decades, k-means has become the clustering algorithm of choice in many application domains primarily due to its simplicity, time/space efficiency, and invariance to the ordering of the data points. Unfortunately, the algorithm's sensitivity to the initial selection of the cluster centers remains to be its most serious drawback. Numerous initialization methods have been proposed to address this drawback. Many of these methods, however, have time complexity superlinear in the number of data points, which makes them impractical for large data sets. On the other hand, linear methods are often random and/or sensitive to the ordering of the data points. These methods are generally unreliable in that the quality of their results is unpredictable. Therefore, it is common practice to perform multiple runs of such methods and take the output of the run that produces the best results. Such a practice, however, greatly increases the computational requirements of the otherwise highly efficient k-means algorithm. In this chapter, we investigate the empirical performance of six linear, deterministic (non-random), and order-invariant k-means initialization methods on a large and diverse collection of data sets from the UCI Machine Learning Repository. The results demonstrate that two relatively unknown hierarchical initialization methods due to Su and Dy outperform the remaining four methods with respect to two objective effectiveness criteria. In addition, a recent method due to Erisoglu et al. performs surprisingly poorly.Comment: 21 pages, 2 figures, 5 tables, Partitional Clustering Algorithms (Springer, 2014). arXiv admin note: substantial text overlap with arXiv:1304.7465, arXiv:1209.196