2018/01/02 by Sunrita Poddar, Poddar, Sunrita, Mathews Jacob +1
Computer Science · Physics and Astronomy · #Advanced Graph Neural Networks #Matrix Theory and Algorithms #Complex Network Analysis Techniques
paper · pdf · doi:10.48550/arxiv.1801.00890
We introduce a continuous domain framework for the recovery of points on a\nsurface in high dimensional space, represented as the zero-level set of a\nbandlimited function. We show that the exponential maps of the points on the\nsurface satisfy annihilation relations, implying that they lie in a finite\ndimensional subspace. The subspace properties are used to derive sampling\nconditions, which will guarantee the perfect recovery of the surface from\nfinite number of points. We rely on nuclear norm minimization to exploit the\nlow-rank structure of the maps to recover the points from noisy measurements.\nSince the direct estimation of the surface is computationally prohibitive in\nvery high dimensions, we propose an iterative reweighted algorithm using the\n"kernel trick". The iterative algorithm reveals deep links to Laplacian based\nalgorithms widely used in graph signal processing; the theory and the sampling\nconditions can serve as a basis for discrete-continuous domain processing of\nsignals on a graph.\n