Convex Clustering Analysis for Histogram-Valued Data

Park, Cheolwoo; Choi, Ho Sun; Delcher, Chris; Wang, Yanning; Yoon, Young Il

doi:10.1111/biom.13004

Cited by 6 publications

(3 citation statements)

References 34 publications

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“…Due to the Frobenious loss function, Problem (1) performs based for Gaussian-like (continuous, symmetric) data. By replacing this loss function, this convex clustering framework has been extended to a variety of other structured data types including: histogram-valued data [11], wavelet basis (sparse) data [12], time series data [13], and data drawn from arbitrary exponential families [14]. The major contribution of this paper is to extend the convex clustering framework to situations where each observation is represented by a network, as discussed in more detail below.…”

Section: Background: Convex Clusteringmentioning

confidence: 99%

Network Clustering for Latent State and Changepoint Detection

Madeline¹,

Allen²,

Weylandt³

2021

Preprint

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Network models provide a powerful and flexible framework for analyzing a wide range of structured data sources. In many situations of interest, however, multiple networks can be constructed to capture different aspects of an underlying phenomenon or to capture changing behavior over time. In such settings, it is often useful to cluster together related networks in attempt to identify patterns of common structure. In this paper, we propose a convex approach for the task of network clustering. Our approach uses a convex fusion penalty to induce a smoothly-varying tree-like cluster structure, eliminating the need to select the number of clusters a priori. We provide an efficient algorithm for convex network clustering and demonstrate its effectiveness on synthetic examples.

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Section: Background: Convex Clusteringmentioning

confidence: 99%

Network Clustering for Latent State and Changepoint Detection

Madeline¹,

Allen²,

Weylandt³

2021

Preprint

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“…Sui et al [10] use a Mahalanobis-type distance and embed convex clustering in a metric learning scheme. Extending convex clustering to non-vector-valued data, Park et al [11] use an earth-mover's distance to cluster histogram-valued observations arising in genomic sequencing. Building on this line of research, we propose a novel automatic spectral-registration distance metric suitable for use with temporal data and investigate its use in a convex clustering context.…”

Section: Introduction 1convex Clusteringmentioning

confidence: 99%

Automatic Registration and Clustering of Time Series

Weylandt

Michailidis

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Clustering of time series data exhibits a number of challenges not present in other settings, notably the problem of registration (alignment) of observed signals. Typical approaches include preregistration to a user-specified template or time warping approaches which attempt to optimally align series with a minimum of distortion. For many signals obtained from recording or sensing devices, these methods may be unsuitable as a template signal is not available for pre-registration, while the distortion of warping approaches may obscure meaningful temporal information. We propose a new method for automatic time series alignment within a clustering problem. Our approach, Temporal Registration using Optimal Unitary Transformations (TROUT), is based on a novel dissimilarity measure between time series that is easy to compute and automatically identifies optimal alignment between pairs of time series. By embedding our new measure in a optimization formulation, we retain well-known advantages of computational and statistical performance. We provide an efficient algorithm for TROUT-based clustering and demonstrate its superior performance over a range of competitors.

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“…The idea has been extended to many related tasks including tensors, metric versions, co-clustering, multi-view and histogram-valued data. (Wu et al, 2016;Chi et al, 2018;Park et al, 2019;Wang and Allen, 2019).…”

Section: Introductionmentioning

confidence: 99%

Biconvex Clustering

Chakraborty,

2020

Preprint

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Convex clustering has recently garnered increasing interest due to its attractive theoretical and computational properties. While it confers many advantages over traditional clustering methods, its merits become limited in the face of high-dimensional data. In such settings, not only do Euclidean measures of fit appearing in the objective provide weaker discriminating power, but pairwise affinity terms that rely on k-nearest neighbors become poorly specified. We find that recent attempts which successfully address the former difficulty still suffer from the latter, in addition to incurring high computational cost and some numerical instability. To surmount these issues, we propose to modify the convex clustering objective so that feature weights are optimized jointly with the centroids. The resulting problem becomes biconvex and as such remains well-behaved statistically and algorithmically. In particular, we derive a fast algorithm with closed form updates and convergence guarantees, and establish finite-sample bounds on its prediction error that imply consistency. Our biconvex clustering method performs feature selection throughout the clustering task: as the learned weights change the effective feature representation, pairwise affinities can be updated adaptively across iterations rather than precomputed within a dubious feature space. We validate the contributions on real and simulated data, showing that our method effectively addresses the challenges of dimensionality while reducing dependence on carefully tuned heuristics typical of existing approaches.

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Convex Clustering Analysis for Histogram-Valued Data

Cited by 6 publications

References 34 publications

Network Clustering for Latent State and Changepoint Detection

Network Clustering for Latent State and Changepoint Detection

Automatic Registration and Clustering of Time Series

Biconvex Clustering

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