(Hyper)Graph Embedding and Classification via Simplicial Complexes

Abstract

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.

A Cooperative Coevolutionary Approach to Discretization-Based Feature Selection for High-Dimensional Data

“…Considering the above issues, we use the [ 32 ] and to guide individual updates. These two objective functions use weight aggregation [ 33 , 34 , 35 ] as the fitness function as shown in ( 6 ), where the smaller the fitness value, the better the individual’s performance. where is a weight coefficient to combine the and .…”

CDE++: Learning Categorical Data Embedding by Enhancing Heterogeneous Feature Value Coupling Relationships

“…Embedding-based representation methods are also used for textual data, and there are several effective embedding methods such as Skim-gram [ 14 ], latent semantic indexing (LSI) [ 15 ], latent Dirichlet allocation (LDA) [ 16 ], as well as some variants of them in [ 17 , 18 , 19 ]. Granular Computing paradigm [ 20 , 21 , 22 ] is an embedding method which is powerful especially when dealing with non-conventional data such as graphs, sequences, text documents. However, the embedding representation for textual data is significantly different from categorical data since categorical data is structured, whereas textual data is unstructured.…”

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

“…In order to deal with such domains, five mainstream approaches can be pursued [ 10 ]: Feature generation and/or feature engineering, where numerical features are extracted ad-hoc from structured patterns (e.g., using their properties or via measurements) and can be further merged according to different strategies (e.g., in a multi-modal way [ 11 ]); Ad-hoc dissimilarities in the input space, where custom dissimilarity measures are designed in order to process structured patterns directly in the input domain without moving towards Euclidean (or metric) spaces. Common—possibly parametric—edit distances include the Levenshtein distance [ 12 ] for sequence domains and graph edit distances [ 13 ] for graphs domains; Embedding via information granulation and granular computing [ 3 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 ]; Dissimilarity representations [ 26 , 27 , 28 ], where structured patterns are embedded in the Euclidean space according to their pairwise dissimilarities; Kernel methods, where the mapping between the original input space and the Euclidean space exploits positive-definite kernel functions [ 29 , 30 , 31 , 32 , 33 ]. …”