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

Abstract

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.

(Hyper)graph Kernels over Simplicial Complexes

“…For this reason, graphs are commonly used to model a plethora of real-world, possibly complex, systems [ 1 ]. Notable examples include biological systems and chemistry [ 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 ], social and collaboration networks [ 14 ], computer vision and image processing [ 15 , 16 , 17 , 18 ], natural language processing [ 19 , 20 , 21 , 22 ], and energy distribution networks [ 23 ].…”

“…Building an embedding space consists in moving the pattern recognition problem from the graphs domain towards a possibly metric (Euclidean) space: instead of using the former, one can use the latter which can be equipped with algebraic structures. To this family belongs dissimilarity spaces [ 32 ], where each pattern is described by the pairwise dissimilarities with respect to all training data (or a properly-chosen subset [ 3 , 33 , 34 ]), and embedding via information granulation, where recurrent and meaningful entities called information granules (e.g., network motifs, graphlets, and the like) are extracted by the training data and each pattern is cast into an integer-valued vector ( symbolic histogram ) which counts the number of occurrences of each granule within the pattern itself [ 35 , 36 , 37 , 38 , 39 , 40 ]. …”

“…dissimilarity spaces [ 32 ], where each pattern is described by the pairwise dissimilarities with respect to all training data (or a properly-chosen subset [ 3 , 33 , 34 ]), and…”

(Hyper)Graph Embedding and Classification via Simplicial Complexes

“…• 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.…”

Computation in Complex Networks

“…In the paper “Modelling and Recognition of Protein Contact Networks by Multiple Kernel Learning and Dissimilarity Representations” by Martino et al [ 6 ], the authors focused on predicting the proteins’ functional role, proposing a hybrid classification system based on a linear combination of multiple kernels defined over multiple dissimilarity spaces. Here, the training procedure jointly optimized the kernel weights and the representatives’ selection in the dissimilarity spaces.…”