Efficient Learning on Large Graphs using a Densifying Regularity Lemma

Learning on large graphs presents significant challenges, with traditional Message Passing Neural Networks suffering from computational and memory costs scaling linearly with the number of edges. We introduce the Intersecting Block Graph (IBG), a low-rank factorization of large directed graphs based on combinations of intersecting bipartite components, each consisting of a pair of communities, for source and target nodes. By giving less weight to non-edges, we show how to efficiently approximate any graph, sparse or dense, by a dense IBG. Specifically, we prove a constructive version of the weak regularity lemma, showing that for any chosen accuracy, every graph, regardless of its size or sparsity, can be approximated by a dense IBG whose rank depends only on the accuracy. This dependence of the rank solely on the accuracy, and not on the sparsity level, is in contrast to previous forms of the weak regularity lemma. We present a graph neural network architecture operating on the IBG representation of the graph and demonstrating competitive performance on node classification, spatio-temporal graph analysis, and knowledge graph completion, while having memory and computational complexity linear in the number of nodes rather than edges.

Depth Over RGB: Automatic Evaluation of Open Surgery Skills Using Depth Camera

Purpose: In this paper, we present a novel approach to the automatic evaluation of open surgery skills using depth cameras. This work is intended to show that depth cameras achieve similar results to RGB cameras, which is the common method in the automatic evaluation of open surgery skills. Moreover, depth cameras offer advantages such as robustness to lighting variations, camera positioning, simplified data compression, and enhanced privacy, making them a promising alternative to RGB cameras. Methods: Experts and novice surgeons completed two simulators of open suturing. We focused on hand and tool detection, and action segmentation in suturing procedures. YOLOv8 was used for tool detection in RGB and depth videos. Furthermore, UVAST and MSTCN++ were used for action segmentation. Our study includes the collection and annotation of a dataset recorded with Azure Kinect. Results: We demonstrated that using depth cameras in object detection and action segmentation achieves comparable results to RGB cameras. Furthermore, we analyzed 3D hand path length, revealing significant differences between experts and novice surgeons, emphasizing the potential of depth cameras in capturing surgical skills. We also investigated the influence of camera angles on measurement accuracy, highlighting the advantages of 3D cameras in providing a more accurate representation of hand movements. Conclusion: Our research contributes to advancing the field of surgical skill assessment by leveraging depth cameras for more reliable and privacy evaluations. The findings suggest that depth cameras can be valuable in assessing surgical skills and provide a foundation for future research in this area.