Hierarchical Clustering and Signal Denoising on Digraphs
This study addresses the challenges of directed graph clustering and signal denoising by proposing a spectral clustering framework that jointly accounts for connectivity and directionality. Methodologically, a Hermitian matrix is constructed to represent the directed graph structure, enabling hierarchical clustering through spectral decomposition combined with recursive K-means. Furthermore, the approach integrates hierarchical filtering with B-spline quasi-interpolation, achieving multiscale denoising and reconstruction of graph signals via adaptive thresholding. Experimental results on both synthetic and real-world datasets demonstrate that the proposed method significantly enhances clustering consistency while effectively improving signal recovery performance in terms of RMSE and SNR metrics.