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(Hyper)Graph Embedding and Classification via Simplicial Complexes

1
Department of Information Engineering, Electronics and Telecommunications, University of Rome “La Sapienza”, Via Eudossiana 18, 00184 Rome, Italy
2
Department of Environment and Health, Istituto Superiore di Sanità, Viale Regina Elena 299, 00161 Rome, Italy
*
Author to whom correspondence should be addressed.
Algorithms 2019, 12(11), 223; https://doi.org/10.3390/a12110223
Received: 26 September 2019 / Revised: 21 October 2019 / Accepted: 24 October 2019 / Published: 25 October 2019
(This article belongs to the Special Issue Granular Computing: From Foundations to Applications)
This paper investigates a novel graph embedding procedure based on simplicial complexes. Inherited from algebraic topology, simplicial complexes are collections of increasing-order simplices (e.g., points, lines, triangles, tetrahedrons) which can be interpreted as possibly meaningful substructures (i.e., information granules) on the top of which an embedding space can be built by means of symbolic histograms. In the embedding space, any Euclidean pattern recognition system can be used, possibly equipped with feature selection capabilities in order to select the most informative symbols. The selected symbols can be analysed by field-experts in order to extract further knowledge about the process to be modelled by the learning system, hence the proposed modelling strategy can be considered as a grey-box. The proposed embedding has been tested on thirty benchmark datasets for graph classification and, further, we propose two real-world applications, namely predicting proteins’ enzymatic function and solubility propensity starting from their 3D structure in order to give an example of the knowledge discovery phase which can be carried out starting from the proposed embedding strategy. View Full-Text
Keywords: granular computing; embedding spaces; graph embedding; topological data analysis; simplicial complexes; computational biology; protein contact networks; complex networks; complex systems granular computing; embedding spaces; graph embedding; topological data analysis; simplicial complexes; computational biology; protein contact networks; complex networks; complex systems
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Martino, A.; Giuliani, A.; Rizzi, A. (Hyper)Graph Embedding and Classification via Simplicial Complexes. Algorithms 2019, 12, 223.

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