Multi-Scale Fuzzy Fusion-Based Heterogeneous Granular-Ball Flexible Representation Learning for Multi-View Feature Selection

Representation learning serves as a critical bridge between human cognition and the data world, constituting an essential component of machine learning architectures where comprehensiveness and flexibility are paramount. However, existing multi-view feature selection methods are constrained by the raw-scale representations, neglecting comprehensive depth-breadth integration and flexible adaptability. This paper presents multi-scale fuzzy fusion-based heterogeneous granular-ball flexible representation learning for multi-view feature selection (MFHGBFR). A comprehensive multi-view, multi-scale analytical foundation is established to promote depth-breadth representation learning, where views represent breadth and scales represent depth in human cognition. Heterogeneous granular ball-based flexible representations are adaptively developed via multi-scale fuzzy fusion, effectively capturing intricate data manifolds and implicit fuzzy patterns across multi-granularity spaces. Intricate data manifolds are fitted with heterogeneous rather than conventional homogeneous structures to improve the adaptability of representations' multi-granularity. Implicit fuzzy patterns are extracted with fuzzy approximation operators to mitigate fuzziness and uncertainty in a multi-granularity space. For the first time, granular-ball representation learning and feature selection are adaptively optimized in a unified one-step framework, rather than the conventional two-step frameworks, for flexible adaptability. An effective optimization algorithm with proven convergence is derived. Through the learned high-quality representations, the MFHGBFR manifests superior performance, robustness, and efficiency. Comparative experiments against contemporary state-of-the-art algorithms substantiate these advantages quantitatively and qualitatively.