Debolina Paul

All Publications

• Implicit Annealing in Kernel Spaces: A Strongly Consistent Clustering Approach. IEEE transactions on pattern analysis and machine intelligence Paul, D., Chakraborty, S., Das, S., Xu, J. 2023; 45 (5): 5862-5871

  Abstract

  Kernel k-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Its merits are thoroughly validated on a suite of simulated datasets and real data benchmarks that feature nonlinear and multi-view separation. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from the non-convexity of the underlying objective function. In this paper, we generalize recent results leveraging a general family of means to combat sub-optimal local solutions to the kernel and multi-kernel settings. Called Kernel Power k-Means, our algorithm uses majorization-minimization (MM) to better solve this non-convex problem. We show that the method implicitly performs annealing in kernel feature space while retaining efficient, closed-form updates. We rigorously characterize its convergence properties both from computational and statistical points of view. In particular, we characterize the large sample behavior of the proposed method by establishing strong consistency guarantees as well as finite-sample bounds on the excess risk of the estimates through modern tools in learning theory. The proposal's efficacy is demonstrated through an array of simulated and real data experiments.

  View details for DOI 10.1109/TPAMI.2022.3217137

  View details for PubMedID 36282831

• On Consistent Entropy-Regularized k-Means Clustering With Feature Weight Learning: Algorithm and Statistical Analyses. IEEE transactions on cybernetics Chakraborty, S., Paul, D., Das, S. 2022; PP

  Abstract

  Clusters in real data are often restricted to low-dimensional subspaces rather than the entire feature space. Recent approaches to circumvent this difficulty are often computationally inefficient and lack theoretical justification in terms of their large-sample behavior. This article deals with the problem by introducing an entropy incentive term to efficiently learn the feature importance within the framework of center-based clustering. A scalable block-coordinate descent algorithm, with closed-form updates, is incorporated to minimize the proposed objective function. We establish theoretical guarantees on our method by Vapnik-Chervonenkis (VC) theory to establish strong consistency along with uniform concentration bounds. The merits of our method are showcased through detailed experimental analysis on toy examples as well as real data clustering benchmarks.

  View details for DOI 10.1109/TCYB.2022.3166975

  View details for PubMedID 35609103

• On the uniform concentration bounds and large sample properties of clustering with Bregman divergences STAT Paul, D., Chakraborty, S., Das, S. 2021; 10 (1)

  View details for DOI 10.1002/sta4.360

  View details for Web of Science ID 000634461800001

• Automated Clustering of High-dimensional Data with a Feature Weighted Mean Shift Algorithm Chakraborty, S., Paul, D., Das, S., Assoc Advancement Artificial Intelligence ASSOC ADVANCEMENT ARTIFICIAL INTELLIGENCE. 2021: 6930-6938

  View details for Web of Science ID 000680423507005

• t-Entropy: A New Measure of Uncertainty with Some Applications Chakraborty, S., Paul, D., Das, S., IEEE IEEE. 2021: 1475-1480

  View details for DOI 10.1109/ISIT45174.2021.9518114

  View details for Web of Science ID 000701502201095

• Uniform Concentration Bounds toward a Unified Framework for Robust Clustering Thirty-fifth Conference on Neural Information Processing Systems (NeurIPS), 2021. Paul, D., Chakraborty, S., Das, S., Xu, J. 2021
• Hierarchical clustering with optimal transport STATISTICS & PROBABILITY LETTERS Chakraborty, S., Paul, D., Das, S. 2020; 163

  View details for DOI 10.1016/j.spl.2020.108781

  View details for Web of Science ID 000543291300013

• Entropy Weighted Power k-Means Clustering Chakraborty, S., Paul, D., Das, S., Xu, J., Chiappa, S., Calandra, R. ADDISON-WESLEY PUBL CO. 2020: 691-700

  View details for Web of Science ID 000559931300048

• A Bayesian non-parametric approach for automatic clustering with feature weighting STAT Paul, D., Das, S. 2020; 9 (1)

  View details for DOI 10.1002/sta4.306

  View details for Web of Science ID 000614806100049

• A New Visual Cryptography Scheme with Perfect Contrast using Galois Fields Paul, D., Chakraborty, S., IEEE IEEE. 2019: 7-11

  View details for Web of Science ID 000546171800002

• On the Non-convergence of Differential Evolution: Some Generalized Adversarial Conditions and A Remedy Paul, D., Chakraborty, S., Das, S., Zelinka, I., ACM ASSOC COMPUTING MACHINERY. 2019: 265-266

  View details for DOI 10.1145/3319619.3322007

  View details for Web of Science ID 000538328100133