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Clustering Time Series Data with Distance Matrices

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Optimization and Data Analysis in Biomedical Informatics

Part of the book series: Fields Institute Communications ((FIC,volume 63))

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Abstract

Clustering is a frequently used method in unsupervised analysis of various data types including time series data. In this study, we first present a discrete k-median (DKM) method based on uncoupled bilinear programming algorithm and modify it for faster implementation, which becomes a variant of the Lloyds algorithm. We also introduce the fuzzy discrete k-median (FDKM) method which is the fuzzy version of the modified algorithm. The main draw for the these two efficient algorithms is that they do not require any input but a matrix of distances as a measure of dissimilarity between pairs of samples to avoid the complications that may arise from working with the actual domain that the data samples reside in. We also include a hiearchical cluster tree (HCT) method and partition around medoids (PAM) method, both of which can use the distance matrix for clustering. The output of all four methods are median samples, which define clusters by assigning each sample to the closest median sample using the distance matrix. We consider four different distance measures, rectilinear, Euclidean, squared-Euclidean and dynamic time warping (DTW) to create the distance matrix, and also mention how the calculation of the distance matrix can be extended to any kernel induced feature space. The main application domain in this study is time series data, where actual samples in the data set are better cluster representations than mean or median points whose components are independently calculated for each dimension of the domain. We present computational results on a public time series benchmark data set and a real life local field potential (LFP) recordings collected from a macaque monkey brain during a visuomotor task.

Mathematics Subject Classification (2010):Primary 62H30, Secondary 68W25

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Authors and Affiliations

  1. Business Information Technology, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061, USA

    Onur Şeref

  2. Department of Industrial and Systems Engineering, Department of Radiology, University of Washington, Seattle, WA, 98195, USA

    W. Art Chaovalitwongse

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  1. Onur Şeref
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  2. W. Art Chaovalitwongse
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Correspondence to Onur Şeref .

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Editors and Affiliations

  1. , Department of Industrial & Systems Engin, University of Florida, Weil Hall 401, Gainesville, 32611, Florida, USA

    Panos M. Pardalos

  2. , Department of Mathematics, University of Waterloo, University Avenue West 200, Waterloo, N2L 3G1, Ontario, Canada

    Thomas F. Coleman

  3. , Department of Industrial Engineering, University of Central Florida, Central Florida Blvd 4000, Orlando, 32816, Florida, USA

    Petros Xanthopoulos

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Şeref, O., Chaovalitwongse, W.A. (2013). Clustering Time Series Data with Distance Matrices. In: Pardalos, P., Coleman, T., Xanthopoulos, P. (eds) Optimization and Data Analysis in Biomedical Informatics. Fields Institute Communications, vol 63. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4133-5_2

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