Summary The fused lasso, also known as totalvariation denoising, is a locally adaptive function estimator over a regular grid of design points. In this article, we extend the fused lasso to settings in which the points do not occur on a regular grid, leading to a method for nonparametric regression. This approach, which we call the $K$nearestneighbours fused lasso, involves computing the $K$nearestneighbours graph of the design points and then performing the fused lasso over this graph. We show that this procedure has a number of theoretical advantages over competing methods: specifically, it inherits local adaptivity from its connection to the fused lasso, and it inherits manifold adaptivity from its connection to the $K$nearestneighbours approach. In a simulation study and an application to flu data, we show that excellent results are obtained. For completeness, we also study an estimator that makes use of an $\epsilon$graph rather than a $K$nearestneighbours graph and contrast it with the $K$nearestneighbours fused lasso.
Learning the Helix Topology of Musical Pitch
To explain the consonance of octaves, music psychologists represent pitch as a helix where azimuth and axial coordinate correspond to pitch class and pitch height respectively. This article addresses the problem of discovering this helical structure from unlabeled audio data. We measure Pearson correlations in the constantQ transform (CQT) domain to build a Knearest neighbor graph between frequency subbands. Then, we run the Isomap manifold learning algorithm to represent this graph in a threedimensional space in which straight lines approximate graph geodesics. Experiments on isolated musical notes demonstrate that the resulting manifold resembles a helix which makes a full turn at every octave. A circular shape is also found in English speech, but not in urban noise. We discuss the impact of various design choices on the visualization: instrumentarium, loudness mapping function, and number of neighbors K.
 Award ID(s):
 1633206
 Publication Date:
 NSFPAR ID:
 10301445
 Journal Name:
 ICASSP 2020  2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
 Page Range or eLocationID:
 11 to 15
 Sponsoring Org:
 National Science Foundation
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