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This paper introduces ReeSPOT, a novel Reeb graph-based method to model patterns of life in human trajectories (akin to a fingerprint). Human behavior typically follows a pattern of normalcy in day-to-day activities. This is marked by…
We introduce FastGraph, a novel GPU-optimized k-nearest neighbor algorithm specifically designed to accelerate graph construction in low-dimensional spaces (2-10 dimensions), critical for high-performance graph neural networks. Our method…
The watershed is a powerful tool for segmenting objects whose contours appear as crest lines on a gradient image. The watershed transform associates to a topographic surface a partition into catchment basins, defined as attraction zones of…
We present HARP, a novel method for learning low dimensional embeddings of a graph's nodes which preserves higher-order structural features. Our proposed method achieves this by compressing the input graph prior to embedding it, effectively…
We present VMap, a map-like rectangular space-filling visualization, to perform vertex-centric graph exploration. Existing visualizations have limited support for quality optimization among rectangular aspect ratios, vertex-edge…
Graph Convolutional Neural Networks (GCNNs) are generalizations of CNNs to graph-structured data, in which convolution is guided by the graph topology. In many cases where graphs are unavailable, existing methods manually construct graphs…
Graph neural networks (GNNs) are popular machine learning models for graphs with many applications across scientific domains. However, GNNs are considered black box models, and it is challenging to understand how the model makes…
We have developed (1) a graph visualization system that allows users to explore graphs by viewing them as a succession of spanning trees selected interactively, (2) a radial graph layout algorithm, and (3) an animation algorithm that…
Deep neural representations of 3D shapes as implicit functions have been shown to produce high fidelity models surpassing the resolution-memory trade-off faced by the explicit representations using meshes and point clouds. However, most…
Graph representation is a powerful abstraction of real-world objects and relations. Computing the Graph Edit Distance (GED) between graphs is critical in domains such as bioinformatics, machine learning, and pattern recognition. GED…
This paper provides theoretical and computational developments in statistical shape analysis of shape graphs, and demonstrates them using analysis of complex data from retinal blood-vessel (RBV) networks. The shape graphs are represented by…
Recent studies have highlighted significant fairness issues in Graph Transformer (GT) models, particularly against subgroups defined by sensitive features. Additionally, GTs are computationally intensive and memory-demanding, limiting their…
The Mapper algorithm is a popular tool for visualization and data exploration in topological data analysis. We investigate an inverse problem for the Mapper algorithm: Given a dataset $X$ and a graph $G$, does there exist a set of Mapper…
In recent years, there has been a growing trend in computer vision towards exploiting RAW sensor data, which preserves richer information compared to conventional low-bit RGB images. Early studies mainly focused on enhancing visual quality,…
Graph signal processing (GSP) is an emerging field developed for analyzing signals defined on irregular spatial structures modeled as graphs. Given the considerable literature regarding the resilience of infrastructure networks using graph…
Using different methods for laying out a graph can lead to very different visual appearances, with which the viewer perceives different information. Selecting a "good" layout method is thus important for visualizing a graph. The selection…
In this work, we study the computability of topological graphs, which are obtained by gluing arcs and rays together at their endpoints. We prove that every semicomputable graph in a computable metric space can be approximated, with…
Representing a scanned map of the real environment as a topological structure is an important research in robotics. %is currently an important research. Since topological representations of maps save a huge amount of map storage space and…
Distance measures play an important role in shape classification and data analysis problems. Topological distances based on Reeb graphs and persistence diagrams have been employed to obtain effective algorithms in shape matching and scalar…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…