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DESCRIPTION:Speaker: Akshay Gadde, University of Southern California
Talk Title: Sampling and Filtering of Signals on Graphs with Applications to Active Learning and Image Processing
Abstract: Processing of signals defined over the nodes of a graph has generated a lot of interest recently. This is due to the emergence of modern application domains such as social networks, web information analysis, sensor networks and machine learning, in which graphs provide a natural representation for the data. Traditional data such as images and videos can also be represented as signals on graphs. A frequency domain representation for graph signals can be obtained using the eigenvectors and eigenvalues of operators which measure the variation in signals taking into account the underlying connectivity in the graph. Spectral filtering can then be defined in this frequency domain. Based on this, we develop a sampling theory for graph signals by answering the following questions: 1. When can we uniquely and stably reconstruct a bandlimited graph signal from its samples on a subset of the nodes? 2. What is the best subset of nodes for sampling a signal so that the resulting bandlimited reconstruction is most stable? 3. How to compute a bandlimited reconstruction efficiently from a subset of samples? The algorithms developed for sampling set selection and reconstruction do not require explicit eigenvalue decomposition of the variation operator and admit efficient, localized implementation. Using graph sampling theory, we propose effective graph based active semi-supervised learning techniques. We also give a probabilistic interpretation for the proposed techniques. Based on this interpretation, we generalize the framework of active learning on graphs using Bayesian methods to give an adaptive sampling method. Additionally, we study the application graph spectral filtering in image processing by representing the image as a graph, where the nodes correspond to the pixels and edge weights capture the similarity between them given by the coefficients of the bilateral filter. We show that the bilateral filter is a low pass graph spectral filter with linearly decaying spectral response. We then generalize the bilateral filter by defining filters on the above graph with different spectral responses depending on the application. We also consider the problem of constructing a sparse graph from the given data efficiently, which can be used in graph based learning and fast image adaptive filtering.\n
Biography: Akshay Gadde received his Bachelor of Technology degree in Electrical Engineering from Indian Institute of Technology (IIT), Kharagpur, India in 2011. He has been working towards a Ph.D. in Electrical Engineering at the University of Southern California (USC), Los Angeles since 2011. His work (with Prof. Antonio Ortega and Aamir Anis) won the Best Student Paper Award at ICASSP 2014. His research interests include graph signal processing and machine learning with applications to multimedia data processing and compression.
Host: Dr. Antonio Ortega
SEQUENCE:5
DTSTART:20170427T130000
LOCATION:EEB 248
DTSTAMP:20170427T130000
SUMMARY:PhD Defense
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DTEND:20170427T150000
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