32,955 research outputs found
Graph Signal Processing: Overview, Challenges and Applications
Research in Graph Signal Processing (GSP) aims to develop tools for
processing data defined on irregular graph domains. In this paper we first
provide an overview of core ideas in GSP and their connection to conventional
digital signal processing. We then summarize recent developments in developing
basic GSP tools, including methods for sampling, filtering or graph learning.
Next, we review progress in several application areas using GSP, including
processing and analysis of sensor network data, biological data, and
applications to image processing and machine learning. We finish by providing a
brief historical perspective to highlight how concepts recently developed in
GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE
Gains in Power from Structured Two-Sample Tests of Means on Graphs
We consider multivariate two-sample tests of means, where the location shift
between the two populations is expected to be related to a known graph
structure. An important application of such tests is the detection of
differentially expressed genes between two patient populations, as shifts in
expression levels are expected to be coherent with the structure of graphs
reflecting gene properties such as biological process, molecular function,
regulation, or metabolism. For a fixed graph of interest, we demonstrate that
accounting for graph structure can yield more powerful tests under the
assumption of smooth distribution shift on the graph. We also investigate the
identification of non-homogeneous subgraphs of a given large graph, which poses
both computational and multiple testing problems. The relevance and benefits of
the proposed approach are illustrated on synthetic data and on breast cancer
gene expression data analyzed in context of KEGG pathways
Discrete Signal Processing on Graphs: Frequency Analysis
Signals and datasets that arise in physical and engineering applications, as
well as social, genetics, biomolecular, and many other domains, are becoming
increasingly larger and more complex. In contrast to traditional time and image
signals, data in these domains are supported by arbitrary graphs. Signal
processing on graphs extends concepts and techniques from traditional signal
processing to data indexed by generic graphs. This paper studies the concepts
of low and high frequencies on graphs, and low-, high-, and band-pass graph
filters. In traditional signal processing, there concepts are easily defined
because of a natural frequency ordering that has a physical interpretation. For
signals residing on graphs, in general, there is no obvious frequency ordering.
We propose a definition of total variation for graph signals that naturally
leads to a frequency ordering on graphs and defines low-, high-, and band-pass
graph signals and filters. We study the design of graph filters with specified
frequency response, and illustrate our approach with applications to sensor
malfunction detection and data classification
Algorithm engineering for optimal alignment of protein structure distance matrices
Protein structural alignment is an important problem in computational
biology. In this paper, we present first successes on provably optimal pairwise
alignment of protein inter-residue distance matrices, using the popular Dali
scoring function. We introduce the structural alignment problem formally, which
enables us to express a variety of scoring functions used in previous work as
special cases in a unified framework. Further, we propose the first
mathematical model for computing optimal structural alignments based on dense
inter-residue distance matrices. We therefore reformulate the problem as a
special graph problem and give a tight integer linear programming model. We
then present algorithm engineering techniques to handle the huge integer linear
programs of real-life distance matrix alignment problems. Applying these
techniques, we can compute provably optimal Dali alignments for the very first
time
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