Bregman Power k-Means for Clustering Exponential Family Data

• URL: http://arxiv.org/abs/2206.10860v1
• Date: Wed, 22 Jun 2022 06:09:54 GMT
• Title: Bregman Power k-Means for Clustering Exponential Family Data
• Authors: Adithya Vellal, Saptarshi Chakraborty and Jason Xu
• Abstract summary: We bridge algorithmic advances to classical work on hard clustering under Bregman divergences. The elegant properties of Bregman divergences allow us to maintain closed form updates in a simple and transparent algorithm. We consider thorough empirical analyses on simulated experiments and a case study on rainfall data, finding that the proposed method outperforms existing peer methods in a variety of non-Gaussian data settings.
• Score: 11.434503492579477
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent progress in center-based clustering algorithms combats poor local minima by implicit annealing, using a family of generalized means. These methods are variations of Lloyd's celebrated $k$-means algorithm, and are most appropriate for spherical clusters such as those arising from Gaussian data. In this paper, we bridge these algorithmic advances to classical work on hard clustering under Bregman divergences, which enjoy a bijection to exponential family distributions and are thus well-suited for clustering objects arising from a breadth of data generating mechanisms. The elegant properties of Bregman divergences allow us to maintain closed form updates in a simple and transparent algorithm, and moreover lead to new theoretical arguments for establishing finite sample bounds that relax the bounded support assumption made in the existing state of the art. Additionally, we consider thorough empirical analyses on simulated experiments and a case study on rainfall data, finding that the proposed method outperforms existing peer methods in a variety of non-Gaussian data settings.

Related papers

• GCC: Generative Calibration Clustering [55.44944397168619]
  We propose a novel Generative Clustering (GCC) method to incorporate feature learning and augmentation into clustering procedure. First, we develop a discrimirative feature alignment mechanism to discover intrinsic relationship across real and generated samples. Second, we design a self-supervised metric learning to generate more reliable cluster assignment.
  arXiv  Detail & Related papers  (2024-04-14T01:51:11Z)
• Deep Embedding Clustering Driven by Sample Stability [16.53706617383543]
  We propose a deep embedding clustering algorithm driven by sample stability (DECS) Specifically, we start by constructing the initial feature space with an autoencoder and then learn the cluster-oriented embedding feature constrained by sample stability. The experimental results on five datasets illustrate that the proposed method achieves superior performance compared to state-of-the-art clustering approaches.
  arXiv  Detail & Related papers  (2024-01-29T09:19:49Z)
• Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers [143.6249073384419]
  In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.
  arXiv  Detail & Related papers  (2024-01-29T02:08:40Z)
• A provable initialization and robust clustering method for general mixture models [6.806940901668607]
  Clustering is a fundamental tool in statistical machine learning in the presence of heterogeneous data. Most recent results focus on optimal mislabeling guarantees when data are distributed around centroids with sub-Gaussian errors.
  arXiv  Detail & Related papers  (2024-01-10T22:56:44Z)
• Robust and Automatic Data Clustering: Dirichlet Process meets Median-of-Means [18.3248037914529]
  We present an efficient and automatic clustering technique by integrating the principles of model-based and centroid-based methodologies. Statistical guarantees on the upper bound of clustering error suggest the advantages of our proposed method over existing state-of-the-art clustering algorithms.
  arXiv  Detail & Related papers  (2023-11-26T19:01:15Z)
• A One-shot Framework for Distributed Clustered Learning in Heterogeneous Environments [54.172993875654015]
  The paper proposes a family of communication efficient methods for distributed learning in heterogeneous environments. One-shot approach, based on local computations at the users and a clustering based aggregation step at the server is shown to provide strong learning guarantees. For strongly convex problems it is shown that, as long as the number of data points per user is above a threshold, the proposed approach achieves order-optimal mean-squared error rates in terms of the sample size.
  arXiv  Detail & Related papers  (2022-09-22T09:04:10Z)
• Kernel Biclustering algorithm in Hilbert Spaces [8.303238963864885]
  We develop a new model-free biclustering algorithm in abstract spaces using the notions of energy distance and the maximum mean discrepancy. The proposed method can learn more general and complex cluster shapes than most existing literature approaches. Our results are similar to state-of-the-art methods in their optimal scenarios, assuming a proper kernel choice.
  arXiv  Detail & Related papers  (2022-08-07T08:41:46Z)
• Gradient Based Clustering [72.15857783681658]
  We propose a general approach for distance based clustering, using the gradient of the cost function that measures clustering quality. The approach is an iterative two step procedure (alternating between cluster assignment and cluster center updates) and is applicable to a wide range of functions.
  arXiv  Detail & Related papers  (2022-02-01T19:31:15Z)
• Lattice-Based Methods Surpass Sum-of-Squares in Clustering [98.46302040220395]
  Clustering is a fundamental primitive in unsupervised learning. Recent work has established lower bounds against the class of low-degree methods. We show that, perhaps surprisingly, this particular clustering model textitdoes not exhibit a statistical-to-computational gap.
  arXiv  Detail & Related papers  (2021-12-07T18:50:17Z)
• Deep Conditional Gaussian Mixture Model for Constrained Clustering [7.070883800886882]
  Constrained clustering can leverage prior information on a growing amount of only partially labeled data. We propose a novel framework for constrained clustering that is intuitive, interpretable, and can be trained efficiently in the framework of gradient variational inference.
  arXiv  Detail & Related papers  (2021-06-11T13:38:09Z)
• Clustering Binary Data by Application of Combinatorial Optimization Heuristics [52.77024349608834]
  We study clustering methods for binary data, first defining aggregation criteria that measure the compactness of clusters. Five new and original methods are introduced, using neighborhoods and population behavior optimization metaheuristics. From a set of 16 data tables generated by a quasi-Monte Carlo experiment, a comparison is performed for one of the aggregations using L1 dissimilarity, with hierarchical clustering, and a version of k-means: partitioning around medoids or PAM.
  arXiv  Detail & Related papers  (2020-01-06T23:33:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.