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Graphs are commonly used to represent objects, such as images and text, for pattern classification. In a dynamic world, an object may continuously evolve over time, and so does the graph extracted from the underlying object. These changes in graph structure with respect to the temporal order present a new representation of the graph, in which an object corresponds to a set of time-variant graphs. In this paper, we formulate a novel time-variant graph classification task and propose a new graph feature, called a graph-shapelet pattern, for learning and classifying time-variant graphs. Graph-shapelet patterns are compact and discriminative graph transformation subsequences. A graph-shapelet pattern can be regarded as a graphical extension of a shapelet—a class of discriminative features designed for vector-based temporal data classification. To discover graph-shapelet patterns, we propose to convert a time-variant graph sequence into time-series data and use the discovered shapelets to find graph transformation subsequences as graph-shapelet patterns. By converting each graph-shapelet pattern into a unique tokenized graph transformation sequence, we can measure the similarity between two graph-shapelet patterns and therefore classify time-variant graphs. Experiments on both synthetic and real-world data demonstrate the superior performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]

The latent friend recommendation in online social media is interesting, yet challenging, because the user-item ratings and the user–user relationships are both sparse. In this paper, we propose a new dual implicit mining-based latent friend recommendation model that simultaneously considers the implicit interest topics of users and the implicit link relationships between the users in the local topic cliques. Specifically, we first propose an algorithm called all reviews from a user and all tags from their corresponding items to learn the implicit interest topics of the users and their corresponding topic weights, then compute the user interest topic similarity using a symmetric Jensen–Shannon divergence. After that, we adopt the proposed weighted local random walk with restart algorithm to analyze the implicit link relationships between the users in the local topic cliques and calculate the weighted link relationship similarity between the users. Combining the user interest topic similarity with the weighted link relationship similarity in a unified way, we get the final latent friend recommendation list. The experiments on real-world datasets demonstrate that the proposed method outperforms the state-of-the-art latent friend recommendation methods under four different types of evaluation metrics. [ABSTRACT FROM AUTHOR]

A novel canonical duality theory (CDT) is presented for solving general bilevel mixed integer nonlinear optimization governed by linear and quadratic knapsack problems. It shows that the challenging knapsack problems can be solved analytically in term of their canonical dual solutions. The existence and uniqueness of these analytical solutions are proved. NP-hardness of the knapsack problems is discussed. A powerful CDT algorithm combined with an alternative iteration and a volume reduction method is proposed for solving the NP-hard bilevel knapsack problems. Application is illustrated by benchmark problems in optimal topology design. The performance and novelty of the proposed method are compared with the popular commercial codes. [ABSTRACT FROM AUTHOR]