Dual graph wavelet neural network for graph-based semi-supervised classification

Vertex classification is an important graph mining technique and has important applications in fields such as social recommendation and e-Commerce recommendation. Existing classification methods fail to make full use of the graph topology to improve the classification performance. To alleviate it, we propose a Dual Graph Wavelet neural Network composed of two identical graph wavelet neural networks sharing network parameters. These two networks are integrated with a semi-supervised loss function and carry out supervised learning and unsupervised learning on two matrixes representing the graph topology extracted from the same graph dataset, respectively. One matrix embeds the local consistency information and the other the global consistency information. To reduce the computational complexity of the convolution operation of the graph wavelet neural network, we design an approximate scheme based on the first type Chebyshev polynomial. Experimental results show that the proposed network significantly outperforms the state-of-the-art approaches for vertex classification on all three benchmark datasets and the proposed approximation scheme is validated for datasets with low vertex average degree when the approximation order is small.

Classification in biological networks with hypergraphlet kernels

Motivation Biological and cellular systems are often modeled as graphs in which vertices represent objects of interest (genes, proteins and drugs) and edges represent relational ties between these objects (binds-to, interacts-with and regulates). This approach has been highly successful owing to the theory, methodology and software that support analysis and learning on graphs. Graphs, however, suffer from information loss when modeling physical systems due to their inability to accurately represent multiobject relationships. Hypergraphs, a generalization of graphs, provide a framework to mitigate information loss and unify disparate graph-based methodologies. Results We present a hypergraph-based approach for modeling biological systems and formulate vertex classification, edge classification and link prediction problems on (hyper)graphs as instances of vertex classification on (extended, dual) hypergraphs. We then introduce a novel kernel method on vertex- and edge-labeled (colored) hypergraphs for analysis and learning. The method is based on exact and inexact (via hypergraph edit distances) enumeration of hypergraphlets; i.e. small hypergraphs rooted at a vertex of interest. We empirically evaluate this method on fifteen biological networks and show its potential use in a positive-unlabeled setting to estimate the interactome sizes in various species. Availability and implementation https://github.com/jlugomar/hypergraphlet-kernels Supplementary information Supplementary data are available at Bioinformatics online.

Plithogenic n-Super Hypergraph in Novel Multi-Attribute Decision Making

An optimal decision-making environment demands feasible Multi-Attribute Decision-Making methods. Plithogenic n – Super Hypergraph introduced by Smarandache is a novel concept and it involves many attributes. This article aims to bridge the concept of Plithogenic n-Super Hypergraph in the vicinity of optimal decision making. This research work introduces the novel concepts of enveloping vertex, super enveloping vertex, dominant enveloping vertex, classification of the dominant enveloping vertex (input, intervene, output dominant enveloping vertices), plithogenic connectors. An application of Plithogenic n-super hypergraph in making optimum decisions is discussed under various decision-making scenarios. Several insights are drawn from this research work and will certainly benefit the decision-makers to overcome the challenges in building decisions.