Topic
Spectral graph theory
About: Spectral graph theory is a research topic. Over the lifetime, 1334 publications have been published within this topic receiving 77373 citations.
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TL;DR: In this paper, the idea of graph coloration from spectral graph theory is employed in conjunction with group theoretical concepts for efficient eigensolution of adjacency matrices of graphs.
11 citations
TL;DR: For a fixed real number r, the authors gave several necessary and/or sufficient conditions for a graph to have the second largest eigenvalue of the adjacency matrix, or signless Laplacian matrix, less then or equal to r.
11 citations
TL;DR: This work proposes a graph-based approach to cell image analysis and applies it to quantify the degree of partial fragmentation of mitochondria in collections of fluorescent cell images, revealing that squamocin induces more fragmented mitochondria than muricin A.
Abstract: Motivation: High-throughput image-based assay technologies can rapidly produce a large number of cell images for drug screening, but data analysis is still a major bottleneck that limits their utility. Quantifying a wide variety of morphological differences observed in cell images under different drug influences is still a challenging task because the result can be highly sensitive to sampling and noise.
Results: We propose a graph-based approach to cell image analysis. We define graph transition energy to quantify morphological differences between image sets. A spectral graph theoretic regularization is applied to transform the feature space based on training examples of extremely different images to calibrate the quantification. Calibration is essential for a practical quantification method because we need to measure the confidence of the quantification. We applied our method to quantify the degree of partial fragmentation of mitochondria in collections of fluorescent cell images. We show that with transformation, the quantification can be more accurate and sensitive than that without transformation. We also show that our method outperforms competing methods, including neighbourhood component analysis and the multi-variate drug profiling method by Loo et al. We illustrate its utility with a study of Annonaceous acetogenins, a family of compounds with drug potential. Our result reveals that squamocin induces more fragmented mitochondria than muricin A.
Availability: Mitochondrial cell images, their corresponding feature sets (SSLF and WSLF) and the source code of our proposed method are available at http://aiia.iis.sinica.edu.tw/.
Contact: chunnan@iis.sinica.edu.tw
Supplementary information:Supplementary data are available at Bioinformatics online.
11 citations
Posted Content•
TL;DR: In this article, a new formulation for the short-time Fourier transform (STFT) for signals defined over graphs is proposed, which uses personalized PageRank vectors as its fundamental building block and establishes the connection between local spectral graph theory and localized spectral analysis of graph signals.
Abstract: The short-time Fourier transform (STFT) is widely used to analyze the spectra of temporal signals that vary through time. Signals defined over graphs, due to their intrinsic complexity, exhibit large variations in their patterns. In this work we propose a new formulation for an STFT for signals defined over graphs. This formulation draws on recent ideas from spectral graph theory, using personalized PageRank vectors as its fundamental building block. Furthermore, this work establishes and explores the connection between local spectral graph theory and localized spectral analysis of graph signals. We accompany the presentation with synthetic and real-world examples, showing the suitability of the proposed approach.
11 citations
01 Dec 2009
TL;DR: By merging control theory and spectral graph theory, it is proved that, when the nonlinear protocol is strictly increasing, consensus can be achieved if and only if the underlying directed interaction graph has a spanning tree.
Abstract: In a consensus problem, autonomous agents constituting a dynamical system communicate with one another to reach agreement on certain quantities of interest. By merging control theory and spectral graph theory, we generalize the previous consensus problems under nonlinear protocols for networks with undirected graphs to directed graphs. We prove that, when the nonlinear protocol is strictly increasing, consensus can be achieved if and only if the underlying directed interaction graph has a spanning tree. Numerical examples are taken to show the effectiveness of our theoretical results.
11 citations