Spectral methods for graph neural networks (GNNs) have achieved great success. Despite their success, many works have shown that existing approaches are mainly focused on low-frequency information which may not be pertinent to the task at hand. Recent efforts have been made to design new graph filters for wider frequency profiles, but it remains an open problem how to learn multi-scale disentangled node embeddings in the graph Fourier domain. In this paper, we propose a graph (signal) sampling and filtering framework, entitled Pyramid Graph Neural Network (PyGNN), which follows the Downsampling-Filtering-Upsampling-Decoding scheme. To be specific, we develop an ω-bandlimited downsampling approach to split input graph into subgraphs for the reduction of high-frequency components, then perform spectral graph filters on subgraphs to achieve node embeddings with different frequency bands, and propose a Laplacian smoothing-based upsampling approach to extrapolate the node embedding on subgraphs to the full set of vertices on the original graph. In the end, we add frequency-aware gated units to decode node embeddings of different frequencies for downstream tasks. Results on both homophilic and heterophilic graph datasets show its superiority over state-of-the-art methods.

Adapting the parameters of a statistical speaker independent continuous speech recognizer to the speaker can significantly improve the recognition performance and robustness of the system. In this paper, we propose a novel target-driven speaker adaptation method, Generalized Joint Maximum a Posteriori (GJMAP), which extends and improves the previous successful method JMAP. GJMAP partitions the HMM parameters with respect to the adaptation data, using the priori phonetic knowledge. The generation of regression class trees is dynamically constructed on the target-driven principle in order to obtain the maximum increase of the auxiliary function. An off-line adaptation experiment on large vocabulary continuous speech recognition is carried out. The experimental results show GJMAP has more advantages than the conventional methods.

A vector statistical piecewise polynomial (VPP) approximation algorithm is proposed for environment compensation in speech signals that are degraded by both additive and convolutive noise. By investigating the model of the telephone environment, we address a piecewise polynomial, namely two linear polynomials and a quadratic polynomial, to approximate the environment function precisely. The VPP is applied either to stationary noise, or to non-stationary noise. In the first case, batch EM is used in the log-spectral domain; in the second case, recursive EM with iterative stochastic approximation is developed in the cepstral domain. Both approaches are based on the minimum mean squared error (MMSE) sense. Experimental results are presented on the application of this approach in improving the performance of Mandarin large vocabulary continuous speech recognition (LVCSR) in background noise and different transmission channels (such as fixed telephone line and GSM). The method can reduce the average character error rate (CER) by about 18%.