93,921 research outputs found
Tight Continuous Relaxation of the Balanced -Cut Problem
Spectral Clustering as a relaxation of the normalized/ratio cut has become
one of the standard graph-based clustering methods. Existing methods for the
computation of multiple clusters, corresponding to a balanced -cut of the
graph, are either based on greedy techniques or heuristics which have weak
connection to the original motivation of minimizing the normalized cut. In this
paper we propose a new tight continuous relaxation for any balanced -cut
problem and show that a related recently proposed relaxation is in most cases
loose leading to poor performance in practice. For the optimization of our
tight continuous relaxation we propose a new algorithm for the difficult
sum-of-ratios minimization problem which achieves monotonic descent. Extensive
comparisons show that our method outperforms all existing approaches for ratio
cut and other balanced -cut criteria.Comment: Long version of paper accepted at NIPS 201
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
Algorithmic and Statistical Perspectives on Large-Scale Data Analysis
In recent years, ideas from statistics and scientific computing have begun to
interact in increasingly sophisticated and fruitful ways with ideas from
computer science and the theory of algorithms to aid in the development of
improved worst-case algorithms that are useful for large-scale scientific and
Internet data analysis problems. In this chapter, I will describe two recent
examples---one having to do with selecting good columns or features from a (DNA
Single Nucleotide Polymorphism) data matrix, and the other having to do with
selecting good clusters or communities from a data graph (representing a social
or information network)---that drew on ideas from both areas and that may serve
as a model for exploiting complementary algorithmic and statistical
perspectives in order to solve applied large-scale data analysis problems.Comment: 33 pages. To appear in Uwe Naumann and Olaf Schenk, editors,
"Combinatorial Scientific Computing," Chapman and Hall/CRC Press, 201
- …