Weighted Least Squares Design of Graph Filter Using Generalized Laguerre Polynomial

This article presents a weighted least squares (WLS) method based on the generalized Laguerre polynomial (GLP) for designing graph filters capable of processing irregular data collected from various networks. The design process involves several key steps: First, the problem of graph filter design is introduced, along with the discussions of conventional least squares approaches. Second, the generalized Laguerre polynomial is defined, and its key properties are discussed. Third, the details of the WLS-based graph filter design are presented, where the filter coefficients are determined by minimizing the WLS errors between the ideal spectral response and the actual filter response. Finally, the effectiveness of the proposed WLS design is demonstrated through its application to graph signal denoising in sensor networks, where signal-to-noise ratio (SNR) is used to evaluate the performance of the Proposed method.