Capturing Topology in Graph Pattern Matching

Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be conducted in cubic-time. However, they fall short of capturing the topology of data graphs, i.e., graphs may have a structure drastically different from pattern graphs they match, and the matches found are often too large to understand and analyze. To rectify these problems, this paper proposes a notion of strong simulation, a revision of graph simulation, for graph pattern matching. (1) We identify a set of criteria for preserving the topology of graphs matched. We show that strong simulation preserves the topology of data graphs and finds a bounded number of matches. (2) We show that strong simulation retains the same complexity as earlier extensions of simulation, by providing a cubic-time algorithm for computing strong simulation. (3) We present the locality property of strong simulation, which allows us to effectively conduct pattern matching on distributed graphs. (4) We experimentally verify the effectiveness and efficiency of these algorithms, using real-life data and synthetic data.Comment: VLDB201

Three IndicesCalculationof Certain Crown Molecular Graphs

As molecular graph invariant topological indices, harmonic index, zeroth-order general Randic index and Co-PI index have been studied in recent years for prediction of chemicalphenomena. In this paper, we determine the harmonic index, zeroth-order general Randic index andCo-PI indexof certain r-crown molecular graphs

Total Variation Regularized Tensor RPCA for Background Subtraction from Compressive Measurements

Background subtraction has been a fundamental and widely studied task in video analysis, with a wide range of applications in video surveillance, teleconferencing and 3D modeling. Recently, motivated by compressive imaging, background subtraction from compressive measurements (BSCM) is becoming an active research task in video surveillance. In this paper, we propose a novel tensor-based robust PCA (TenRPCA) approach for BSCM by decomposing video frames into backgrounds with spatial-temporal correlations and foregrounds with spatio-temporal continuity in a tensor framework. In this approach, we use 3D total variation (TV) to enhance the spatio-temporal continuity of foregrounds, and Tucker decomposition to model the spatio-temporal correlations of video background. Based on this idea, we design a basic tensor RPCA model over the video frames, dubbed as the holistic TenRPCA model (H-TenRPCA). To characterize the correlations among the groups of similar 3D patches of video background, we further design a patch-group-based tensor RPCA model (PG-TenRPCA) by joint tensor Tucker decompositions of 3D patch groups for modeling the video background. Efficient algorithms using alternating direction method of multipliers (ADMM) are developed to solve the proposed models. Extensive experiments on simulated and real-world videos demonstrate the superiority of the proposed approaches over the existing state-of-the-art approaches.Comment: To appear in IEEE TI

Proposal-Based Multiple Instance Learning for Weakly-Supervised Temporal Action Localization

Weakly-supervised temporal action localization aims to localize and recognize actions in untrimmed videos with only video-level category labels during training. Without instance-level annotations, most existing methods follow the Segment-based Multiple Instance Learning (S-MIL) framework, where the predictions of segments are supervised by the labels of videos. However, the objective for acquiring segment-level scores during training is not consistent with the target for acquiring proposal-level scores during testing, leading to suboptimal results. To deal with this problem, we propose a novel Proposal-based Multiple Instance Learning (P-MIL) framework that directly classifies the candidate proposals in both the training and testing stages, which includes three key designs: 1) a surrounding contrastive feature extraction module to suppress the discriminative short proposals by considering the surrounding contrastive information, 2) a proposal completeness evaluation module to inhibit the low-quality proposals with the guidance of the completeness pseudo labels, and 3) an instance-level rank consistency loss to achieve robust detection by leveraging the complementarity of RGB and FLOW modalities. Extensive experimental results on two challenging benchmarks including THUMOS14 and ActivityNet demonstrate the superior performance of our method.Comment: Accepted by CVPR 2023. Code is available at https://github.com/RenHuan1999/CVPR2023_P-MI