Jyotishka Ray Choudhury

Jyotishka Ray Choudhury, Aytijhya Saha, Sarbojit Roy et al.

Classification of high-dimensional low sample size (HDLSS) data poses a challenge in a variety of real-world situations, such as gene expression studies, cancer research, and medical imaging. This article presents the development and analysis of some classifiers that are specifically designed for HDLSS data. These classifiers are free of tuning parameters and are robust, in the sense that they are devoid of any moment conditions of the underlying data distributions. It is shown that they yield perfect classification in the HDLSS asymptotic regime, under some fairly general conditions. The comparative performance of the proposed classifiers is also investigated. Our theoretical results are supported by extensive simulation studies and real data analysis, which demonstrate promising advantages of the proposed classification techniques over several widely recognized methods.

Supratik Basu, Jyotishka Ray Choudhury, Debolina Paul et al.

Clustering stands as one of the most prominent challenges in unsupervised machine learning. Among centroid-based methods, the classic $k$-means algorithm, based on Lloyd's heuristic, is widely used. Nonetheless, it is a well-known fact that $k$-means and its variants face several challenges, including heavy reliance on initial cluster centroids, susceptibility to converging into local minima of the objective function, and sensitivity to outliers and noise in the data. When data contains noise or outliers, the Median-of-Means (MoM) estimator offers a robust alternative for stabilizing centroid-based methods. On a different note, another limitation in many commonly used clustering methods is the need to specify the number of clusters beforehand. Model-based approaches, such as Bayesian nonparametric models, address this issue by incorporating infinite mixture models, which eliminate the requirement for predefined cluster counts. Motivated by these facts, in this article, we propose an efficient and automatic clustering technique by integrating the strengths of model-based and centroid-based methodologies. Our method mitigates the effect of noise on the quality of clustering; while at the same time, estimates the number of clusters. Statistical guarantees on an upper bound of clustering error, and rigorous assessment through simulated and real datasets, suggest the advantages of our proposed method over existing state-of-the-art clustering algorithms.