Date of Submission

6-23-2026

Date of Award

6-23-2026

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Master's Dissertation

Degree Name

Master of Technology

Subject Name

Computer Science

Department

Electronics and Communication Sciences Unit (ECSU-Kolkata)

Supervisor

Das, Swagatam

Abstract (Summary of the Work)

A fundamental challenge in modern unsupervised learning is adapting classical clustering algorithms to handle complex, real-world data constraints. Traditional models often assume data resides in a flat, Euclidean space and optimize strictly for cluster cohesion, thereby failing to capture intrinsic hierarchical structures and ignoring sociotechnical demographic biases. This thesis addresses these critical limitations by extending generalized mean-shift dynamics into two novel clustering frameworks. First, to natively accommodate data with tree-like structures (e.g., taxonomies and social networks), we propose Hyperbolic Gaussian Blurring Mean Shift (HypeGBMS). By projecting data into the Poincar´e ball model and utilizing M¨obius vector space operations, HypeGBMS successfully generalizes density-based clustering to non-Euclidean manifolds. Second, to tackle algorithmic bias in noisy datasets, we introduce Fair Possibilistic C-Means (F-PCM). By embedding a group-fairness Kullback-Leibler divergence penalty into the possibilistic objective function, F-PCM explicitly enforces demographic parity without sacrificing the outlier-robust nature of possibilistic typicalities. We provide rigorous theoretical proofs for both methodologies, including convergence guarantees, statistical consistency, and optimization bounds via Majorization-Minimization. Extensive experiments on complex real-world datasets demonstrate that HypeGBMS dramatically improves cluster quality on hierarchical data, while F-PCM maintains strict fairness criteria while matching the computational efficiency of traditional baselines.

Control Number

CS2408

DOI

https://dspace.isical.ac.in/items/21f52607-2c11-4a2d-bd45-ad51faf5c25c

DSpace Identifier

http://hdl.handle.net/10263/7757

Download

Share

COinS