Exploring the signal manifold of super-imposed pulses

Charles Sutton, M.Sc. Thesis Seminar
Thursday, 25.10.2018, 14:00
Taub 401
Prof. A. Bruckstein

Large points cloud X in $R^{n\times D}$ are often assumed to be sampled from a k-dimensional manifold where $k 1$). However, there is no evidence that this technique extends to other manifolds. This work aims to verify how the multi-scale singular value analysis of a manifold can extend to any manifold. In this work, we focus our effort on signal manifolds of super-imposed pulses (SIPS), due to their generic nature and widespread use in signal processing applications. First, we examine why the current state of the art cannot be extended to SIPS manifolds. We prove that the current approaches rely upon averaging methods that are too sensitive to the manifold’s shape. Then, we propose a method that is agnostic to the shape of manifold by utilizing the k-medoids clustering algorithm. We then present a method to tackle the problem of the estimation of the intrinsic dimensionality, including manifolds constructed out of rather noisy signals. Our method improves upon the state of the art in estimating the intrinsic dimensionality and shows promising results for an extension to any manifold.

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