Graph Clustering Using Heat Content Invariants

Xiao, Bai; Hancock, Edwin R.

doi:10.1007/11492542_16

Cited by 3 publications

(3 citation statements)

References 9 publications

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“…Heat Content Invariant From the graph Laplacian and degree matrices (Equations ( A24 ) and ( A23 ), respectively), the normalised Laplacian matrix can be evaluated as:

The spectral decomposition of

reads as:

where

is a diagonal matrix containing the eigenvalues in increasing order and

contains the corresponding unitary-length eigenvectors. The heat equation associated to

is given by [ 124 , 125 ]:

where

is the

heat kernel matrix at time t . The heat content

is given by:

where

is the value related to node

in the k th eigenvector.…”

Section: Appendix A1 Betti Numbersmentioning

confidence: 99%

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Modelling and Recognition of Protein Contact Networks by Multiple Kernel Learning and Dissimilarity Representations

Martino

Santis

Giuliani

2020

Entropy

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Multiple kernel learning is a paradigm which employs a properly constructed chain of kernel functions able to simultaneously analyse different data or different representations of the same data. In this paper, we propose an hybrid classification system based on a linear combination of multiple kernels defined over multiple dissimilarity spaces. The core of the training procedure is the joint optimisation of kernel weights and representatives selection in the dissimilarity spaces. This equips the system with a two-fold knowledge discovery phase: by analysing the weights, it is possible to check which representations are more suitable for solving the classification problem, whereas the pivotal patterns selected as representatives can give further insights on the modelled system, possibly with the help of field-experts. The proposed classification system is tested on real proteomic data in order to predict proteins’ functional role starting from their folded structure: specifically, a set of eight representations are drawn from the graph-based protein folded description. The proposed multiple kernel-based system has also been benchmarked against a clustering-based classification system also able to exploit multiple dissimilarities simultaneously. Computational results show remarkable classification capabilities and the knowledge discovery analysis is in line with current biological knowledge, suggesting the reliability of the proposed system.

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“…Heat Content Invariant From the graph Laplacian and degree matrices (Equations ( A24 ) and ( A23 ), respectively), the normalised Laplacian matrix can be evaluated as:

The spectral decomposition of

reads as:

where

is a diagonal matrix containing the eigenvalues in increasing order and

contains the corresponding unitary-length eigenvectors. The heat equation associated to

is given by [ 124 , 125 ]:

where

is the

heat kernel matrix at time t . The heat content

is given by:

where

is the value related to node

in the k th eigenvector.…”

Section: Appendix A1 Betti Numbersmentioning

confidence: 99%

“…The heat equation associated to

is given by [ 124 , 125 ]:

where

is the

heat kernel matrix at time t . The heat content

is given by:

where

is the value related to node

in the k th eigenvector.…”

Section: Appendix A1 Betti Numbersmentioning

confidence: 99%

Modelling and Recognition of Protein Contact Networks by Multiple Kernel Learning and Dissimilarity Representations

Martino

Santis

Giuliani

2020

Entropy

View full text Add to dashboard Cite

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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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