683 research outputs found
Characterization of complex networks: A survey of measurements
Each complex network (or class of networks) presents specific topological
features which characterize its connectivity and highly influence the dynamics
of processes executed on the network. The analysis, discrimination, and
synthesis of complex networks therefore rely on the use of measurements capable
of expressing the most relevant topological features. This article presents a
survey of such measurements. It includes general considerations about complex
network characterization, a brief review of the principal models, and the
presentation of the main existing measurements. Important related issues
covered in this work comprise the representation of the evolution of complex
networks in terms of trajectories in several measurement spaces, the analysis
of the correlations between some of the most traditional measurements,
perturbation analysis, as well as the use of multivariate statistics for
feature selection and network classification. Depending on the network and the
analysis task one has in mind, a specific set of features may be chosen. It is
hoped that the present survey will help the proper application and
interpretation of measurements.Comment: A working manuscript with 78 pages, 32 figures. Suggestions of
measurements for inclusion are welcomed by the author
Facilitating Graph Neural Networks with Random Walk on Simplicial Complexes
Node-level random walk has been widely used to improve Graph Neural Networks.
However, there is limited attention to random walk on edge and, more generally,
on -simplices. This paper systematically analyzes how random walk on
different orders of simplicial complexes (SC) facilitates GNNs in their
theoretical expressivity. First, on -simplices or node level, we establish a
connection between existing positional encoding (PE) and structure encoding
(SE) methods through the bridge of random walk. Second, on -simplices or
edge level, we bridge edge-level random walk and Hodge -Laplacians and
design corresponding edge PE respectively. In the spatial domain, we directly
make use of edge level random walk to construct EdgeRWSE. Based on the spectral
analysis of Hodge -Laplcians, we propose Hodge1Lap, a permutation
equivariant and expressive edge-level positional encoding. Third, we generalize
our theory to random walk on higher-order simplices and propose the general
principle to design PE on simplices based on random walk and Hodge Laplacians.
Inter-level random walk is also introduced to unify a wide range of simplicial
networks. Extensive experiments verify the effectiveness of our random
walk-based methods.Comment: Accepted by NeurIPS 202
A Graph Theoretic Approach for Object Shape Representation in Compositional Hierarchies Using a Hybrid Generative-Descriptive Model
A graph theoretic approach is proposed for object shape representation in a
hierarchical compositional architecture called Compositional Hierarchy of Parts
(CHOP). In the proposed approach, vocabulary learning is performed using a
hybrid generative-descriptive model. First, statistical relationships between
parts are learned using a Minimum Conditional Entropy Clustering algorithm.
Then, selection of descriptive parts is defined as a frequent subgraph
discovery problem, and solved using a Minimum Description Length (MDL)
principle. Finally, part compositions are constructed by compressing the
internal data representation with discovered substructures. Shape
representation and computational complexity properties of the proposed approach
and algorithms are examined using six benchmark two-dimensional shape image
datasets. Experiments show that CHOP can employ part shareability and indexing
mechanisms for fast inference of part compositions using learned shape
vocabularies. Additionally, CHOP provides better shape retrieval performance
than the state-of-the-art shape retrieval methods.Comment: Paper : 17 pages. 13th European Conference on Computer Vision (ECCV
2014), Zurich, Switzerland, September 6-12, 2014, Proceedings, Part III, pp
566-581. Supplementary material can be downloaded from
http://link.springer.com/content/esm/chp:10.1007/978-3-319-10578-9_37/file/MediaObjects/978-3-319-10578-9_37_MOESM1_ESM.pd
Network theory approach for data evaluation in the dynamic force spectroscopy of biomolecular interactions
Investigations of molecular bonds between single molecules and molecular
complexes by the dynamic force spectroscopy are subject to large fluctuations
at nanoscale and possible other aspecific binding, which mask the experimental
output. Big efforts are devoted to develop methods for effective selection of
the relevant experimental data, before taking the quantitative analysis of bond
parameters. Here we present a methodology which is based on the application of
graph theory. The force-distance curves corresponding to repeated pulling
events are mapped onto their correlation network (mathematical graph). On these
graphs the groups of similar curves appear as topological modules, which are
identified using the spectral analysis of graphs. We demonstrate the approach
by analyzing a large ensemble of the force-distance curves measured on:
ssDNA-ssDNA, peptide-RNA (system from HIV1), and peptide-Au surface. Within our
data sets the methodology systematically separates subgroups of curves which
are related to different intermolecular interactions and to spatial
arrangements in which the molecules are brought together and/or pulling speeds.
This demonstrates the sensitivity of the method to the spatial degrees of
freedom, suggesting potential applications in the case of large molecular
complexes and situations with multiple binding sites
Graph Classification using Machine Learning Algorithms
In the Graph classification problem, given is a family of graphs and a group of different categories, and we aim to classify all the graphs (of the family) into the given categories. Earlier approaches, such as graph kernels and graph embedding techniques have focused on extracting certain features by processing the entire graph. However, real world graphs are complex and noisy and these traditional approaches are computationally intensive. With the introduction of the deep learning framework, there have been numerous attempts to create more efficient classification approaches.
For this project, we will be focusing on modifying an existing kernel graph convo- lutional neural network approach. Moreover, subgraphs (patches) are extracted from the graph using a community detection algorithm. These patches are provided as input to a graph kernel and max pooling is applied. We will be experimenting with different commu- nity detection algorithms and graph kernels and compare their efficiency and performance. For the experiments, we use eight publicly available real world datasets, ranging from bi- ological to social networks. Additionally, for these datasets we provide results using a baseline algorithm and a spectral decomposition of Laplacian graph for comparison pur- poses
Computing communities in large networks using random walks
Dense subgraphs of sparse graphs (communities), which appear in most
real-world complex networks, play an important role in many contexts. Computing
them however is generally expensive. We propose here a measure of similarities
between vertices based on random walks which has several important advantages:
it captures well the community structure in a network, it can be computed
efficiently, it works at various scales, and it can be used in an agglomerative
algorithm to compute efficiently the community structure of a network. We
propose such an algorithm which runs in time O(mn^2) and space O(n^2) in the
worst case, and in time O(n^2log n) and space O(n^2) in most real-world cases
(n and m are respectively the number of vertices and edges in the input graph).
Experimental evaluation shows that our algorithm surpasses previously proposed
ones concerning the quality of the obtained community structures and that it
stands among the best ones concerning the running time. This is very promising
because our algorithm can be improved in several ways, which we sketch at the
end of the paper.Comment: 15 pages, 4 figure
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