Elsevier

Pattern Recognition Letters

Volume 75, 1 May 2016, Pages 63-69
Pattern Recognition Letters

Generalized k-means-based clustering for temporal data under weighted and kernel time warp

https://doi.org/10.1016/j.patrec.2016.03.007Get rights and content

Highlights

  • Generalize k-means-based clustering to temporal data under time warp.

  • Extend time warp measures and temporal kernels to capture local temporal differences.

  • Propose a tractable estimation of the cluster representatives under extended measures.

  • Propose fast solutions that capture both global and local temporal features.

  • Deep analysis on a wide range of 20 non-isotropic, linearly non-separable public data.

Abstract

Temporal data naturally arise in various emerging applications, such as sensor networks, human mobility or internet of things. Clustering is an important task, usually applied a priori to pattern analysis tasks, for summarization, group and prototype extraction; it is all the more crucial for dimensionality reduction in a big data context. Clustering temporal data under time warp measures is challenging because it requires aligning multiple temporal data simultaneously. To circumvent this problem, costly k-medoids and kernel k-means algorithms are generally used. This work investigates a different approach to temporal data clustering through weighted and kernel time warp measures and a tractable and fast estimation of the representative of the clusters that captures both global and local temporal features. A wide range of 20 public and challenging datasets, encompassing images, traces and ecg data that are non-isotropic (i.e., non-spherical), not well-isolated and linearly non-separable, is used to evaluate the efficiency of the proposed temporal data clustering. The results of this comparison illustrate the benefits of the method proposed, which outperforms the baselines on all datasets. A deep analysis is conducted to study the impact of the data specifications on the effectiveness of the studied clustering methods.

Section snippets

Introduction and related work

Temporal data naturally arise in various emerging applications, such as sensor networks, human mobility or internet of things. Clustering is an important task, usually applied priori to any pattern analysis tasks, for summarization, cluster and prototype extraction, and is crucial for big data dimensionality reduction.

k-means-based clustering, viz. standard k-means, k-means++, fuzzy c-means, and all its variations, is among the most popular clustering algorithms, because it provides a good

Generalized k-means for temporal data clustering

The k-means algorithm aims at providing a partition of a set of data points in distinct clusters such that the inertia within each cluster is minimized, the inertia being defined as the sum of distances between any data point in the cluster and the centroid (or representative) of the cluster. The k-means algorithm was originally developed with the Euclidean distance, the representative of each cluster being defined as the center of gravity of the cluster. This algorithm can, however, be

Centroid estimation for time warp measures

We first describe here the general strategy followed to estimate the representatives (or centroids) of a cluster of data points (X), prior to studying the solution this strategy leads to for the three extended measures introduced above.

Experiments

In this section, we first describe the datasets retained to conduct our experiments prior to comparing the generalized k-means algorithms, based on the extended wdtw(Eq. (4)) and wkdtak (Eq. (5)) and the centroid estimations given in Section 3, to two alternative approaches i) k-medoids with the standard unweighted dtw and ii) kernel k-means with the standard unweighted kdtak and kga temporal kernels.

Conclusion

This work introduces a generalized centroid-based clustering algorithm for temporal data under time warp measures. For this, we propose i) an extension of the common time warp measures and ii) a tractable, fast and efficient estimation of the cluster representatives, under the extended time warp measures, that captures local temporal features. The efficiency of this algorithm is analyzed on a wide range of challenging datasets, which are non-isotropic (i.e., non-spherical), not well-isolated

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