In this article, we propose a novel routine pattern extraction architecture to analyze the daily behaviors of mobile users. The key component of the proposed architecture is a dynamic programming-based sequence dissimilarity calculation method, which aims to measure the dissimilarity between trajectories and then extract patterns using the clustering method. The method exploits three different information: (1) spatial-temporal information, (2) information in the continuous same location in the sequence and (3) the probabilities of location occurrences in the data. We conduct experiments on a synthetic dataset and two real-world datasets. The obtained results demonstrate that our proposed method is efficient in extracting hidden routine patterns from users’ trajectory data.

Abstract The K‐partitioning problem consists in partitioning the nodes of a complete graph G = (V, E) with weights on the edges in exactly K clusters such that the sum of the weights of the edges inside the clusters is minimized. For this problem, we propose two node‐cluster formulations adapted from the literature on similar problems as well as two edge‐representative formulations. We introduced the first edge‐representative formulation in a previous work while the second is obtained by adding an additional set of edge variables. We compare the structure of the polytopes of the two edge‐representative formulations and identify a new family of facet‐defining inequalities. The quality of the linear relaxation and the resolution times of the four formulations are compared on various data sets. We provide bounds on the relaxation values of the node‐cluster formulations which may account for their low performances. Finally, we propose a branch‐and‐cut strategy, based on the edge‐representative formulations, which performs even better.

In this paper, we tackle the problem of localizing graphical symbols on complex technical document images by using an original approach to solve the subgraph isomorphism problem. In the proposed system, document and symbol images are represented by vector-attributed Region Adjacency Graphs (RAG) which are extracted by a segmentation process and feature extractors. Vertices representing regions are labeled with shape descriptors whereas edges are labeled with feature vector representing topological relations between the regions. Then, in order to search the instances of a model graph describing a particular symbol in a large graph corresponding to a whole document, we model the subgraph isomorphism problem as an Integer Linear Program (ILP) which enables to be error-tolerant on vectorial labels. The problem is then solved using a free efficient solver called SYMPHONY. The whole system is evaluated on a set of synthetic documents.