Fractional Graph Spectral Filtering Based on Unified Graph Representation Matrix

Graph spectral filtering relies on a representation matrix to define the frequency-domain transformations. Conventional approaches use fixed graph representations, which limit their adaptability to complex structures. Although fractional spectral filtering enhances flexibility via fractional-order parameters, it remains constrained by fixed matrices. This letter proposes a fractional graph spectral filtering method based on a unified graph representation matrix. By parameterizing the representation matrix, the proposed method dynamically adapts to diverse graph structures and jointly optimizes the fractional order and graph representation parameters, ensuring a deeper integration between spectral properties and graph topology. Experimental results demonstrate that the proposed approach consistently outperforms existing methods in terms of filtering effectiveness.