arXiv subjects

Jhareswar Maiti

Publications and source records attributed to Jhareswar Maiti.

3 recordsLinked to original sources

arXiv2026

An Algorithm to perform Covariance-Adjusted Support Vector Classification in Non-Euclidean Spaces

Traditional Support Vector Machine (SVM) classification is carried out by finding the max-margin classifier for the training data that divides the margin space into two equal sub-spaces. This study demonstrates limitations of performing Support Vector Classification in non-Euclidean spaces by establishing that the underlying principle of max-margin classification and Karush Kuhn Tucker (KKT) boundary conditions are optimal only in the Euclidean vector spaces. The study establishes a methodology to perform Support Vector Classification in Non-Euclidean Spaces by incorporating data covariance into the optimization problem using Cholesky Decomposition of respective class covariance structure. It also demonstrates that in non-Euclidean spaces KKT modelling is sub-optimal as the principle of maximum margin is a function of intra-class data covariances and the classifier obtained separates the margin space in ratio of the respective class population covariance matrix. The study proposes an algorithm to iteratively estimate the population covariance-adjusted SVM classifier in non-Euclidean space from sample covariance matrices of the training data. The effectiveness of this SVM classification approach is demonstrated by applying the classifier on multiple datasets and comparing the performance with traditional SVM kernels and whitening algorithms. The Cholesky-SVM model shows marked improvement in the accuracy, precision, F1 scores and ROC performance compared to linear and other kernel SVMs.

cs.LG↗

arXiv2025

Multivariate Gaussian Topic Modelling: A novel approach to discover topics with greater semantic coherence

An important aspect of text mining involves information retrieval in form of discovery of semantic themes (topics) from documents using topic modelling. While generative topic models like Latent Dirichlet Allocation (LDA) or Latent Semantic Analysis (LSA) elegantly model topics as probability distributions and are useful in identifying latent topics from large document corpora with minimal supervision, they suffer from difficulty in topic interpretability and reduced performance in shorter texts. Here we propose a novel Multivariate Gaussian Topic Model (MGTM). In this approach topics are presented as Multivariate Gaussian Distributions and documents as Gaussian Mixture Models. Applying EM algorithm on a document corpus, the various constituent Multivariate Gaussian distributions corresponding to the latent topics and their respective parameters are identified. Analysis of the parameters of each distribution helps identify the respective topic keywords, and from these key-words topic annotations are carried out. This approach is applied on 20 newsgroups dataset to demonstrate the interpretability benefits vis-`a-vis 4 other benchmark models. The effectiveness of this model in capturing the semantic theme of the topics with high interpretability is examined by calculating the topic coherence and comparing the coherence values with benchmark models. This model achieves a highest mean topic coherence (0.7) and median topic coherence (0.76) vis-`a-vis the benchmark models, demonstrating high effectiveness in identifying interpretable, semantically coherent topics.

cs.LG↗

arXiv2025

Variance-Adjusted Cosine Distance as Similarity Metric

Cosine similarity is a popular distance measure that measures the similarity between two vectors in the inner product space. It is widely used in many data classification algorithms like K-Nearest Neighbors, Clustering etc. This study demonstrates limitations of application of cosine similarity. Particularly, this study demonstrates that traditional cosine similarity metric is valid only in the Euclidean space, whereas the original data resides in a random variable space. When there is variance and correlation in the data, then cosine distance is not a completely accurate measure of similarity. While new similarity and distance metrics have been developed to make up for the limitations of cosine similarity, these metrics are used as substitutes to cosine distance, and do not make modifications to cosine distance to overcome its limitations. Subsequently, we propose a modified cosine similarity metric, where cosine distance is adjusted by variance-covariance of the data. Application of variance-adjusted cosine distance gives better similarity performance compared to traditional cosine distance. KNN modelling on the Wisconsin Breast Cancer Dataset is performed using both traditional and modified cosine similarity measures and compared. The modified formula shows 100% test accuracy on the data.

stat.ML↗