* ad-hoc dissimilarities in the input space, where custom dissimilarity measures (e.g., edit distances [19; 20; 21; 22]) are designed in order to directly process patterns in the input space (without moving towards Euclidean spaces)
* dissimilarity representations [18; 23], where each pattern is described by the pairwise distances with other patterns or with respect to a properly chosen subset of pivotal training patterns [23; 24; 25; 26]
* kernel methods, where the mapping between the original input space and the Euclidean space exploits positive-definite kernel functions [27; 28; 29; 30; 31; 32]
* embedding via information granulation. As the latter is concerned, embedding techniques are gaining more and more attention especially since the breakthrough of Granular Computing [33; 34]. In short, Granular Computing is a human-inspired information processing paradigm which aims at the extraction of meaningful entities (_information granules_) arising from both the problem at hand and the data representation. The challenge with Granular Computing-based pattern recognition systems is that there are different levels of granularity according to which a given system can be observed [35; 36; 37]; nonetheless, one shall choose a suitable level of granularity for the problem at hand. These information granules are usually extracted in a data-driven manner and describe data aggregates, namely data which are similar according to structural and/or functional similarity [15; 16; 17]. Data clustering, for example, is a promising tool for extracting information granules [38], especially when clustering algorithms can be equipped with ad-hoc dissimilarity measures in order to deal with structured data [17; 39; 40; 41; 42]. Indeed, several works focused on extracting information granules via motifs clustering (see e.g., Refs. [43; 44; 45; 46; 47]), where a proper granulation module is in charge of extracting and clustering sub-structures (i.e., sub-graphs). The resulting clusters can be considered as information granules and the clusters' representatives form an _alphabet_ on the top of which the embedding procedure is performed thanks to the _symbolic histograms_ approach [46]: let \(M\) be the size of the alphabet, each input pattern is transformed into an \(M\)-length integer-valued feature vector whose \(i\)th element contains the number of occurrences of the \(i\)th alphabet member within the pattern itself. Thanks to the embedding, the problem is moved towards a metric (Euclidean) space and plain pattern recognition algorithms can be used without alterations. The symbols extraction and alphabet synthesis is crucial in granulation-based classifiers: the resulting embedding space must preserve (the vast majority of) the original input space properties (e.g., the more _different_ two objects drawn from the input space are, the more _distant_ they must appear in the embedding space.) [17; 18]. Also, for the sake of modelling complexity, the size of the alphabet must be as small as possible or, specifically, the set of resulting alphabet symbols should be small, yet informative. This aspect is crucial since Granular Computing-based pattern recognition systems aim to be human interpretable: the resulting set of symbols forming the alphabet, hence pivotal for the embedding space, should allow field experts to gather further insights for the problem at hand [17]. The aim of this paper is to investigate a novel procedure for extracting meaningful information granules thanks to simplicial complexes. Conversely to network motifs and graphlets, simplicial complexes are able to capture the multi-scale/higher-order organisation in complex networks [48; 49], overcoming the main limitation offered by 'plain graphs'; that is, they only considers pairwise relations, whereas simplicial complexes (and hypergraphs, in general) also consider multi-way relations. On the top of simplicial complexes, an embedding space is built for pattern recognition purposes.