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@article{190441,
        author = {Samiksha Khemka},
        title = {Investigating Sparsity-Induced Rank Inflation and Similarity Stability in Recommendation Systems},
        journal = {International Journal of Innovative Research in Technology},
        year = {2026},
        volume = {12},
        number = {8},
        pages = {817-822},
        issn = {2349-6002},
        url = {https://ijirt.org/article?manuscript=190441},
        abstract = {The rapid expansion of digital streaming platforms has intensified reliance on algorithmic recommendation systems, foregrounding a problem of the estimation of unobserved entries in a highly sparse user-item rating matrix. This paper develops a mathematical framework for analysing collaborative filtering methods under sparsity, focusing on cosine similarity, Pearson correlation, and latent factor models based on Singular Value Decomposition (SVD). The paper provides formal derivations that explain how sparsity alters their underlying mathematical properties. Sparsity is modelled as a projection operator acting on the true rating matrix, inducing a structured perturbation that distorts similarity measures and low-rank approximations. We introduce and analyse the concept of sparsity-induced rank inflation and formally demonstrate why classical guarantees such as the Eckart-Young theorem fail under naive treatment of missing data, namely the direct application of standard algorithms to zero-filled observed matrices. The results establish that similarity-based methods possess intrinsic geometric robustness to sparsity, while SVD-based approaches suffer from structural instability unless specialised matrix completion techniques are employed. The paper contributes a mathematically grounded explanation for observed performance differences in recommendation systems and clarifies the theoretical conditions under which standard models remain valid.},
        keywords = {Collaborative Filtering; Sparse Matrices; Cosine Similarity; Pearson Correlation; Singular Value Decomposition; Matrix Perturbation Theory; Numerical Rank; Recommendation Systems},
        month = {January},
        }