Multi-Level Graph Encoding with Structural-Collaborative Relation Learning for Skeleton-Based Person Re-Identification

Skeleton-based person re-identification (Re-ID) is an emerging open topic providing great value for safety-critical applications. Existing methods typically extract hand-crafted features or model skeleton dynamics from the trajectory of body joints, while they rarely explore valuable relation information contained in body structure or motion. To fully explore body relations, we construct graphs to model human skeletons from different levels, and for the first time propose a Multi-level Graph encoding approach with Structural-Collaborative Relation learning (MG-SCR) to encode discriminative graph features for person Re-ID. Specifically, considering that structurally-connected body components are highly correlated in a skeleton, we first propose a multi-head structural relation layer to learn different relations of neighbor body-component nodes in graphs, which helps aggregate key correlative features for effective node representations. Second, inspired by the fact that body-component collaboration in walking usually carries recognizable patterns, we propose a cross-level collaborative relation layer to infer collaboration between different level components, so as to capture more discriminative skeleton graph features. Finally, to enhance graph dynamics encoding, we propose a novel self-supervised sparse sequential prediction task for model pre-training, which facilitates encoding high-level graph semantics for person Re-ID. MG-SCR outperforms state-of-the-art skeleton-based methods, and it achieves superior performance to many multi-modal methods that utilize extra RGB or depth features. Our codes are available at https://github.com/Kali-Hac/MG-SCR.

Complexes of tournaments, directionality filtrations and persistent homology

Complete digraphs are referred to in the combinatorics literature as tournaments. We consider a family of semi-simplicial complexes, that we refer to as “tournaplexes”, whose simplices are tournaments. In particular, given a digraph $${\mathcal {G}}$$ G , we associate with it a “flag tournaplex” which is a tournaplex containing the directed flag complex of $${\mathcal {G}}$$ G , but also the geometric realisation of cliques that are not directed. We define several types of filtrations on tournaplexes, and exploiting persistent homology, we observe that flag tournaplexes provide finer means of distinguishing graph dynamics than the directed flag complex. We then demonstrate the power of these ideas by applying them to graph data arising from the Blue Brain Project’s digital reconstruction of a rat’s neocortex.

Hierarchical core maintenance on large dynamic graphs

The model of k -core and its decomposition have been applied in various areas, such as social networks, the world wide web, and biology. A graph can be decomposed into an elegant k -core hierarchy to facilitate cohesive subgraph discovery and network analysis. As many real-life graphs are fast evolving, existing works proposed efficient algorithms to maintain the coreness value of every vertex against structure changes. However, the maintenance of the k -core hierarchy in existing studies is not complete because the connections among different k -cores in the hierarchy are not considered. In this paper, we study hierarchical core maintenance which is to compute the k -core hierarchy incrementally against graph dynamics. The problem is challenging because the change of hierarchy may be large and complex even for a slight graph update. In order to precisely locate the area affected by graph dynamics, we conduct in-depth analyses on the structural properties of the hierarchy, and propose well-designed local update techniques. Our algorithms significantly outperform the baselines on runtime by up to 3 orders of magnitude, as demonstrated on 10 real-world large graphs.

Complexes of Tournaments, Directionality Filtrations and Persistent Homology

Complete digraphs are referred to in the combinatorics literature as tournaments. We consider a family of semi-simplicial complexes, that we refer to as ``tournaplexes'', whose simplices are tournaments. In particular, given a digraph G, we associate with it a ``flag tournaplex'' which is a tournaplex containing the directed flag complex of G, but also the geometric realisation of cliques that are not directed. We define several types of filtrations on tournaplexes, and exploiting persistent homology, we observe that flag tournaplexes provide finer means of distinguishing graph dynamics than the directed flag complex. We then demonstrate the power of these ideas by applying them to graph data arising from the Blue Brain Project's digital reconstruction of a rat's neocortex.