Non-negative Sparse Matrix Factorization for Soft Clustering of Territory Risk Analysis

Developing effective methodologies for territory design and relativity estimation is crucial in auto insurance rate filings and reviews. This study introduces a novel approach utilizing fuzzy clustering to enhance the design process of territories for auto insurance rate-making and regulation. By adopting a soft clustering method, we aim to overcome the limitations of traditional hard clustering techniques and improve the assessment of territory risk. Furthermore, we employ non-negative sparse matrix approximation techniques to refine the estimates of risk relativities for basic rating units. This method promotes sparsity in the fuzzy membership matrix by eliminating small membership values, leading to more robust and interpretable results. We also compare the outcomes with those obtained using non-negative sparse principal component analysis, a technique explored in our previous research. Integrating fuzzy clustering with non-negative sparse matrix decomposition offers a promising approach for auto insurance rate filings. The combined methodology enhances decision-making and provides sparse estimates, which can be advantageous in various data science applications where fuzzy clustering is relevant.