First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper presents a extension in the family of low-rank spectrogram-factorization models of sound decomposition that generalizes the latent factors over an arbitrary (potentially overcomplete) set of bases, meaning that decomposition can be performed on multiresolution (e.g. This is argued to help with source separation and denoising. It starts from Gaussian Composite Model of Fevotte et al, which models the variance of each cell of a spectrogram with a low-rank matrix factorization, but then expands the implicit convolution with the multiple gabor impulse responses corresponding to each row of the spectrogram to give a purely time-domain expression for what is being estimated, that can then be modified to work for different sets of impulse responses, including nonorthogonal ones. An EM (local optimum) analysis procedure is presented.

Ranked data sets, where m judges/voters specify a preference ranking of n objects/candidates, are increasingly prevalent in contexts such as political elections, computer vision, recommender systems, and bioinformatics. The vote counts for each ranking can be viewed as an n! data vector lying on the permutahedron, which is a Cayley graph of the symmetric group with vertices labeled by permutations and an edge when two permutations differ by an adjacent transposition. Leveraging combinatorial representation theory and recent progress in signal processing on graphs, we investigate a novel, scalable transform method to interpret and exploit structure in ranked data. We represent data on the permutahedron using an overcomplete dictionary of atoms, each of which captures both smoothness information about the data (typically the focus of spectral graph decomposition methods in graph signal processing) and structural information about the data (typically the focus of symmetry decomposition methods from representation theory). These atoms have a more naturally interpretable structure than any known basis for signals on the permutahedron, and they form a Parseval frame, ensuring beneficial numerical properties such as energy preservation. We develop specialized algorithms and open software that take advantage of the symmetry and structure of the permutahedron to improve the scalability of the proposed method, making it more applicable to the high-dimensional ranked data found in applications.