Graph Characterization from Entropy Component Analysis

Ye, Cheng; Wilson, Richard C.; Hancock, Edwin R.

doi:10.1109/icpr.2014.660

Cited by 5 publications

(2 citation statements)

References 14 publications

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“…A first strategy consists in engineering numerical features to be drawn from the structured data at hand, to be concatenated in a vector form. Examples of feature engineering techniques involve entropy measures (Han et al, 2011;Ye et al, 2014;Bai et al, 2012), centrality measures (Mizui et al, 2017;Martino et al, 2018b;Leone Sciabolazza and Riccetti, 2020;Martino et al, 2020a), heat trace (Xiao and Hancock, 2005;Xiao et al, 2009) and modularity (Li, 2013). Whilst this approach is straightforward and allows to move the pattern recognition problem towards the Euclidean space in which any pattern recognition algorithm can be used without alterations, designing the mapping function (i.e., enumerating the set of numerical features to be extracted) requires a deep knowledge of both the problem and the data at hand: indeed, the input spaces being equal, specific subsets of features allow to solve different problems.…”

Section: Current Approaches For Pattern Recognition On the Graph Domainmentioning

confidence: 99%

Complexity vs. Performance in Granular Embedding Spaces for Graph Classification

Baldini

Martino

2020

Proceedings of the 12th International Joint Conference on Computational Intelligence

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The most distinctive trait in structural pattern recognition in graph domain is the ability to deal with the organization and relations between the constituent entities of the pattern. Even if this can be convenient and/or necessary in many contexts, most of the state-of the art classification techniques can not be deployed directly in the graph domain without first embedding graph patterns towards a metric space. Granular Computing is a powerful information processing paradigm that can be employed in order to drive the synthesis of automatic embedding spaces from structured domains. In this paper we investigate several classification techniques starting from Granular Computing-based embedding procedures and provide a thorough overview in terms of model complexity, embedding space complexity and performances on several open-access datasets for graph classification. We witness that certain classification techniques perform poorly both from the point of view of complexity and learning performances as the case of non-linear SVM, suggesting that high dimensionality of the synthesized embedding space can negatively affect the effectiveness of these approaches. On the other hand, linear support vector machines, neuro-fuzzy networks and nearest neighbour classifiers have comparable performances in terms of accuracy, with second being the most competitive in terms of structural complexity and the latter being the most competitive in terms of embedding space dimensionality.

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Section: Current Approaches For Pattern Recognition On the Graph Domainmentioning

confidence: 99%

Complexity vs. Performance in Granular Embedding Spaces for Graph Classification

Baldini

Martino

2020

Proceedings of the 12th International Joint Conference on Computational Intelligence

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“…The goal is to capture the most discriminative features of a graph to enable efficient classification and clustering of graph patterns. The most recent studies in this field proposed descriptors based on different random walk models , spectral graph theory , prototype‐based embedding , substructure embedding , wave kernel trace , and distribution of graph entropy . Those descriptors were primarily applied for graphs representing documents, molecules, or images , which have considerably smaller size than a typical complex network with hundreds of thousands of edges.…”

Section: Complex Network and Graph Comparisonmentioning

confidence: 99%

Distributed computing of distance‐based graph invariants for analysis and visualization of complex networks

Czech

Mielczarek

Dzwinel

2016

Concurrency and Computation

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We present a new framework for analysis and visualization of complex networks based on structural information retrieved from their distance k-graphs and B-matrices. The construction of B-matrices for graphs with more than 1 million edges requires massive Breadth-First Search (BFS) computations and is facilitated using new software prepared for distributed environments. Our framework benefits from data parallelism inherent to all-pair shortest-path problem and extends Cassovary, an open-source in-memory graph processing engine, to enable multinode computation of distance k-graphs and related graph descriptors. We also introduce a new type of B-matrix, constructed using clustering coefficient vertex invariant, which can be generated with a computational effort comparable with the one required for a previously known degree B-matrix, while delivering an additional set of information about graph structure. Our approach enables efficient generation of expressive, multidimensional descriptors useful in graph embedding and graph mining tasks. The experiments showed that the new framework is scalable and for specific all-pair shortest-path task provides better performance than existing generic graph processing frameworks. We further present how the developed tools helped in the analysis and visualization of real-world graphs from Stanford Large Network Dataset Collection. Figure 2. Results of degree B-matrix computation performance tests for the three graphs from SNAP database: Epinions (75,879 vertices, 508,837 edges), Slashdot0902 (82,168 vertices, 948,464 edges), and Web Notre Dame (325,729 vertices, 1,497,134 edges). (a) Dependency of computation time on a number of processors for Epinions and Slashdot0902 graphs, (b) Dependency of computation time on a number of processors for Web Notre Dame graph, (c) Speedup vs. number of processors for Epinions and Slashdot0902 graphs, (d) Speedup vs. number of processors for Web Notre Dame graph.Figure 3. Time of loading and indexing list of edges by Cassovary versus graph size (number of vertices + number of nodes).In this section, we examine discriminating capabilities of B-matrices in the unsupervised learning task. To this end, we constructed feature vectors representing graphs from different groups by coarse graining and row packing of the B-matrices. Next, the dimensionality reduction techniques such as principal component analysis (PCA) and t-distributed stochastic neighbor embedding [48] were used to obtain 2D embedding of graphs for visual comparison of cluster proximity. Let Y stand for V or E symbol, so that B Y;F denotes B V;F or B E;F matrix of a graph G. The set F contains degree or clustering coefficient vertex-domain functions defined for consecutive distance k-graphs. The number of categories n was chosen so that n < jV .G/j. The size of category s b is the same for all categories (bins) in a test setup. The parameter s b reflects granularity of sampling

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