Related papers: G-Mapper: Learning a Cover in the Mapper Construct…

Choosing a suitable filtering function for the Mapper algorithm can be difficult due to its arbitrariness and domain-specific requirements. Finding a general filtering function that can be applied across domains is therefore of interest,…

In a standard cluster analysis, such as k-means, in addition to clusters locations and distances between them, it's important to know if they are connected or well separated from each other. The main focus of this paper is discovering the…

Data clustering with uneven distribution in high level noise is challenging. Currently, HDBSCAN is considered as the SOTA algorithm for this problem. In this paper, we propose a novel clustering algorithm based on what we call graph of…

Objective: The Mapper algorithm is a qualitative method in topological data analysis that constructs graphs from point clouds by combining dimensionality reduction and clustering techniques. The aim of this study is to apply Mapper,…

Pooling operations have shown to be effective on computer vision and natural language processing tasks. One challenge of performing pooling operations on graph data is the lack of locality that is not well-defined on graphs. Previous…

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…

Batch planning is increasingly necessary to quickly produce diverse and quality motion plans for downstream learning applications, such as distillation and imitation learning. This paper presents Global Tensor Motion Planning (GTMP) -- a…

Coverage problems are central in optimization and have a wide range of applications in data mining and machine learning. While several distributed algorithms have been developed for coverage problems, the existing methods suffer from…

In the realm of computer-aided design (CAD) software, the intersection of B-spline surfaces stands as a fundamental operation. Despite the extensive history of surface intersection algorithms, the challenge of handling complex intersection…

This paper deals with the complexity of some natural graph problems when parametrized by {measures that are restrictions of} clique-width, such as modular-width and neighborhood diversity. The main contribution of this paper is to introduce…

Graph learning plays a central role in many data mining and machine learning tasks, such as manifold learning, data representation and analysis, dimensionality reduction, clustering, and visualization. In this work, we propose a highly…

Graph clustering is the problem of identifying sparsely connected dense subgraphs (clusters) in a given graph. Proposed clustering algorithms usually optimize various fitness functions that measure the quality of a cluster within the graph.…

We present ShapeVis, a scalable visualization technique for point cloud data inspired from topological data analysis. Our method captures the underlying geometric and topological structure of the data in a compressed graphical…

Graph pattern mining (GPM) is an important application that identifies structures from graphs. Despite the recent progress, the performance gap between the state-of-the-art GPM systems and an efficient algorithm--pattern decomposition--is…

Motivated by a sampling problem basic to computational statistical inference, we develop a nearly optimal algorithm for a fundamental problem in spectral graph theory and numerical analysis. Given an $n\times n$ SDDM matrix ${\bf…

Sampling is a critical operation in Graph Neural Network (GNN) training that helps reduce the cost. Previous literature has explored improving sampling algorithms via mathematical and statistical methods. However, there is a gap between…

Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…

This paper describes a graph clustering algorithm that aims to minimize the normalized cut criterion and has a model order selection procedure. The performance of the proposed algorithm is comparable to spectral approaches in terms of…

Graph-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the…

Large datasets with interactions between objects are common to numerous scientific fields (i.e. social science, internet, biology...). The interactions naturally define a graph and a common way to explore or summarize such dataset is graph…