Custom Score Function: Projection of Structural Attention in Stochastic Structures

Abstract

This study introduces a novel approach to correlation-based feature selection and dimensionality reduction in high-dimensional data structures. To this end, a customized scoring function is proposed, designed as a dual-objective structure that simultaneously maximizes the correlation with the target variable while penalizing redundant information among features. The method is built upon three main components: correlation-based preliminary assessment, feature selection via the tailored scoring function, and integration of the selection results into a t-SNE visualization guided by Rel/Red ratios. Initially, features are ranked according to their Pearson correlation with the target, and then redundancy is assessed through pairwise correlations among features. A priority scheme is defined using a scoring function composed of relevance and redundancy components. To enhance the selection process, an optimization framework based on stochastic differential equations (SDEs) is introduced. Throughout this process, feature weights are updated using both gradient information and diffusion dynamics, enabling the identification of subsets that maximize overall correlation. In the final stage, the t-SNE dimensionality reduction technique is applied with weights derived from the Rel/Red scores. In conclusion, this study redefines the feature selection process by integrating correlation-maximizing objectives with stochastic modeling. The proposed approach offers a more comprehensive and effective alternative to conventional methods, particularly in terms of explainability, interpretability, and generalizability. The method demonstrates strong potential for application in advanced machine learning systems, such as credit scoring, and in broader dimensionality reduction tasks.