Generalized Clustering via Kernel Embeddings

Jegelka, Stefanie; Gretton, Arthur; Schölkopf, Bernhard; Sriperumbudur, Bharath K.; Luxburg, Ulrike von

doi:10.1007/978-3-642-04617-9_19

Cited by 30 publications

(19 citation statements)

References 11 publications

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“…EMD and other spatially aware (i.e., based on the underlying metric space) distances have been applied to clustering of points in space [5,9]. However, in these cases the clusters of points are treated as distributions and EMD is used to compute/compare these clusters.…”

Section: Related Workmentioning

confidence: 99%

Ep-Means

Henderson

Gallagher

Eliassi-Rad

2015

Proceedings of the 30th Annual ACM Symposium on Applied Computing

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Given a collection of m continuous-valued, one-dimensional empirical probability distributions {P1, . . . , Pm}, how can we cluster these distributions efficiently with a nonparametric approach? Such problems arise in many real-world settings where keeping the moments of the distribution is not appropriate, because either some of the moments are not defined or the distributions are heavy-tailed or bi-modal. Examples include mining distributions of inter-arrival times and phone-call lengths. We present an efficient algorithm with a non-parametric model for clustering empirical, onedimensional, continuous probability distributions. Our algorithm, called ep-means, is based on the Earth Mover's Distance and k-means clustering. We illustrate the utility of ep-means on various data sets and applications. In particular, we demonstrate that ep-means effectively and efficiently clusters probability distributions of mixed and arbitrary shapes, recovering ground-truth clusters exactly in cases where existing methods perform at baseline accuracy. We also demonstrate that ep-means outperforms momentbased classification techniques and discovers useful patterns in a variety of real-world applications.

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Section: Related Workmentioning

confidence: 99%

Ep-Means

Henderson

Gallagher

Eliassi-Rad

2015

Proceedings of the 30th Annual ACM Symposium on Applied Computing

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“…The Maximum Mean Discrepancy (MMD) [35] between the two sets of data with probability distributionsP 1 andP 2 is a metric representative of the distance between the means of those distributions and it has been defined as…”

Section: Maximum Mean Discrepancymentioning

confidence: 99%

“…It has been also shown by Jegelka et al [35] that MMD can be expressed in terms of the dependency between two sets of variables:…”

Section: Maximum Mean Discrepancymentioning

confidence: 99%

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Adapting Component Analysis

Dorri

Ghodsi

2012

2012 IEEE 12th International Conference on Data Mining

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“…One can derive HSIC as a measure of (in)dependence between two random variables X and Y using two different approaches: first by computing the Hilbert-Schmidt norm of the cross-covariance operators in RKHSs as shown in [32,33]; or second, by computing maximum mean discrepancy (MMD) of two distributions mapped to a high dimensional space, i.e., computed in RKHSs [67,68]. I believe that this latter approach is more straightforward and hence, use it to describe HSIC.…”

Section: Hilbert Schmidt Independence Criterionmentioning

confidence: 99%