Learning representation on graph plays a crucial role in numerous tasks of pattern recognition. Different from gridshaped images/videos, on which local convolution kernels can be lattices, however, graphs are fully coordinate-free on vertices and edges. In this work, we propose a Gaussianinduced convolution (GIC) framework to conduct local convolution filtering on irregular graphs. Specifically, an edgeinduced Gaussian mixture model is designed to encode variations of subgraph region by integrating edge information into weighted Gaussian models, each of which implicitly characterizes one component of subgraph variations. In order to coarsen a graph, we derive a vertex-induced Gaussian mixture model to cluster vertices dynamically according to the connection of edges, which is approximately equivalent to the weighted graph cut. We conduct our multi-layer graph convolution network on several public datasets of graph classification. The extensive experiments demonstrate that our GIC is effective and can achieve the state-of-the-art results.

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Information retrieval is the important work for Electronic Commerce. Ontology-based semantic retrieval is a hotspot of current research. In order to achieve fuzzy semantic retrieval, this paper applies a fuzzy ontology framework to information retrieval system in E-Commerce. The framework includes three parts: concepts, properties of concepts and values of properties, in which property’s value can be either standard data types or linguistic values of fuzzy concepts. The semantic query expansions are constructed by order relation, equivalence relation, inclusion relation, reversion relation and complement relation between fuzzy concepts defined in linguistic variable ontologies with Resource Description Framework (RDF). The application to retrieve customer, product and supplier information shows that the framework can overcome the localization of other fuzzy ontology models, and this research facilitates the semantic retrieval of information through fuzzy concepts on the Semantic Web.

Graph classification is a fundamental but challenging issue for numerous real-world applications. Despite recent great progress in image/video classification, convolutional neural networks (CNNs) cannot yet cater to graphs well because of graphical non-Euclidean topology. In this work, we propose a walk-steered convolutional (WSC) network to assemble the essential success of standard convolutional neural networks as well as the powerful representation ability of random walk. Instead of deterministic neighbor searching used in previous graphical CNNs, we construct multi-scale walk fields (a.k.a. local receptive fields) with random walk paths to depict subgraph structures and advocate graph scalability. To express the internal variations of a walk field, Gaussian mixture models are introduced to encode principal components of walk paths therein. As an analogy to a standard convolution kernel on image, Gaussian models implicitly coordinate those unordered vertices/nodes and edges in a local receptive field after projecting to the gradient space of Gaussian parameters. We further stack graph coarsening upon Gaussian encoding by using dynamic clustering, such that highlevel semantics of graph can be well learned like the conventional pooling on image. The experimental results on several public datasets demonstrate the superiority of our proposed WSC method over many state-of-the-arts for graph classification.

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