Honors & Awards

  • EDGE: Enhancing Diversity in Graduate Education Doctoral Fellowship, Stanford University, CA, USA (09/20/2021)
  • First Prize in Madhava Mathematics Competition, Tata Institute of Fundamental Research, India (03/24/2019)
  • Usri Gangopadhay Memorial Gold Medal, Indian Statistical Institute, Kolkata, India (01/23/2020)
  • Mukul Chaudhury Memorial Award, Indian Statistical Institute, Kolkata, India (01/10/2019)
  • Mukul Chaudhuri Memorial Award, Indian Statistical Institute, Kolkata, India (01/09/2018)

Education & Certifications

  • M.Stat, Indian Statistical Institute, Kolkata, India (2021)
  • B.Stat (Hons.), Indian Statistical Institute, Kolkata, India (2019)

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


    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


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