Spectral Graph Wavelets for the Classification of Microcalcifications in Mammograms

2017 ◽  
Author(s):  
B. Kiran Bala ◽  
S. Audithan
Keyword(s):  
Spectral Graph ◽  
Spectral Graph Wavelets

scholarly journals Identifying multiscale spatio-temporal patterns in human mobility using manifold learning

2020 ◽  
Vol 6 ◽  
pp. e276 ◽  
Author(s):  
James R. Watson ◽  
Zach Gelbaum ◽  
Mathew Titus ◽  
Grant Zoch ◽  
David Wrathall
Keyword(s):  
Manifold Learning ◽  
Large Scale ◽  
Human Mobility ◽  
Mobile Network ◽  
Human Migration ◽  
Mobility Patterns ◽  
Great Opportunity ◽  
Spectral Graph ◽  
Spectral Graph Wavelets ◽  
Spatio Temporal

When, where and how people move is a fundamental part of how human societies organize around every-day needs as well as how people adapt to risks, such as economic scarcity or instability, and natural disasters. Our ability to characterize and predict the diversity of human mobility patterns has been greatly expanded by the availability of Call Detail Records (CDR) from mobile phone cellular networks. The size and richness of these datasets is at the same time a blessing and a curse: while there is great opportunity to extract useful information from these datasets, it remains a challenge to do so in a meaningful way. In particular, human mobility is multiscale, meaning a diversity of patterns of mobility occur simultaneously, which vary according to timing, magnitude and spatial extent. To identify and characterize the main spatio-temporal scales and patterns of human mobility we examined CDR data from the Orange mobile network in Senegal using a new form of spectral graph wavelets, an approach from manifold learning. This unsupervised analysis reduces the dimensionality of the data to reveal seasonal changes in human mobility, as well as mobility patterns associated with large-scale but short-term religious events. The novel insight into human mobility patterns afforded by manifold learning methods like spectral graph wavelets have clear applications for urban planning, infrastructure design as well as hazard risk management, especially as climate change alters the biophysical landscape on which people work and live, leading to new patterns of human migration around the world.

scholarly journals Spectral clustering of combinatorial fullerene isomers based on their facet graph structure

2020 ◽  
Author(s):  
Artur Bille ◽  
Victor Buchstaber ◽  
Evgeny Spodarev
Keyword(s):  
Main Idea ◽  
Chem Phys ◽  
Spectral Graph Theory ◽  
Topological Descriptors ◽  
Graph Structure ◽  
Schlegel Diagram ◽  
Spectral Graph ◽  
Formal Stability ◽  
Novel Method

AbstractAfter Curl, Kroto and Smalley were awarded 1996 the Nobel Prize in chemistry, fullerenes have been subject of much research. One part of that research is the prediction of a fullerene’s stability using topological descriptors. It was mainly done by considering the distribution of the twelve pentagonal facets on its surface, calculations mostly were performed on all isomers of C40, C60 and C80. This paper suggests a novel method for the classification of combinatorial fullerene isomers using spectral graph theory. The classification presupposes an invariant scheme for the facets based on the Schlegel diagram. The main idea is to find clusters of isomers by analyzing their graph structure of hexagonal facets only. We also show that our classification scheme can serve as a formal stability criterion, which became evident from a comparison of our results with recent quantum chemical calculations (Sure et al. in Phys Chem Chem Phys 19:14296–14305, 2017). We apply our method to classify all isomers of C60 and give an example of two different cospectral isomers of C44. Calculations are done with our own Python scripts available at (Bille et al. in Fullerene database and classification software, https://www.uni-ulm.de/mawi/mawi-stochastik/forschung/fullerene-database/, 2020). The only input for our algorithm is the vector of positions of pentagons in the facet spiral. These vectors and Schlegel diagrams are generated with the software package Fullerene (Schwerdtfeger et al. in J Comput Chem 34:1508–1526, 2013).

Spectral graph features for the classification of graphs and graph sequences

2012 ◽  
Vol 29 (1-2) ◽  
pp. 65-80 ◽  
Author(s):  
Miriam Schmidt ◽  
Günther Palm ◽  
Friedhelm Schwenker
Keyword(s):  
Spectral Graph ◽  
Classification Of Graphs

Almost Tight Spectral Graph Wavelets With Polynomial Filters

2017 ◽  
Vol 11 (6) ◽  
pp. 812-824 ◽  
Author(s):  
David B. H. Tay ◽  
Yuichi Tanaka ◽  
Akie Sakiyama
Keyword(s):  
Spectral Graph ◽  
Polynomial Filters ◽  
Spectral Graph Wavelets

scholarly journals Shape classification using spectral graph wavelets

2017 ◽  
Vol 47 (4) ◽  
pp. 1256-1269 ◽  
Author(s):  
Majid Masoumi ◽  
A. Ben Hamza
Keyword(s):  
Shape Classification ◽  
Spectral Graph ◽  
Spectral Graph Wavelets

scholarly journals Fractional Spectral Graph Wavelets and Their Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Jiasong Wu ◽  
Fuzhi Wu ◽  
Qihan Yang ◽  
Yan Zhang ◽  
Xilin Liu ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Fractional Fourier Transform ◽  
Weighted Graphs ◽  
Extended Version ◽  
Spectral Graph ◽  
Potential Applications ◽  
Fractional Wavelet Transform ◽  
Fourier Series Approximation ◽  
Spectral Graph Wavelets

One of the key challenges in the area of signal processing on graphs is to design transforms and dictionary methods to identify and exploit structure in signals on weighted graphs. In this paper, we first generalize graph Fourier transform (GFT) to spectral graph fractional Fourier transform (SGFRFT), which is then used to define a novel transform named spectral graph fractional wavelet transform (SGFRWT), which is a generalized and extended version of spectral graph wavelet transform (SGWT). A fast algorithm for SGFRWT is also derived and implemented based on Fourier series approximation. Some potential applications of SGFRWT are also presented.

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