Related papers: Discrete Differential Geometry and Cluster Algebra…
Social decisions made by individuals are easily influenced by information from their social neighborhoods. A key predictor of social contagion is the multiplicity of social contexts inside the individual's contact neighborhood, which is…
This paper discusses the construction of local bounded commuting projections for discrete subcomplexes of the gradgrad complexes in two and three dimensions, which play an important role in the finite element theory of elasticity (2D) and…
Clustering mixed data presents numerous challenges inherent to the very heterogeneous nature of the variables. A clustering algorithm should be able, despite of this heterogeneity, to extract discriminant pieces of information from the…
Topological data analysis is an emerging field that applies the study of topological invariants to data. Perhaps the simplest of these invariants is the number of connected components or clusters. In this work, we explore a topological…
Discrete Morse theory emerged as an essential tool for computational geometry and topology. Its core structures are discrete gradient fields, defined as acyclic matchings on a complex $C$, from which topological and geometrical informations…
Given entities and their interactions in the web data, which may have occurred at different time, how can we find communities of entities and track their evolution? In this paper, we approach this important task from graph clustering…
Temporal Graph Clustering (TGC) is a new task with little attention, focusing on node clustering in temporal graphs. Compared with existing static graph clustering, it can find the balance between time requirement and space requirement…
Dimer models (also known as brane tilings) are special bipartite graphs on a torus $\mathbb{T}^2$. They encode the structure of the 4d $\mathcal{N} = 1$ worldvolume theories of D3 branes probing toric affine Calabi-Yau singularities.…
Many complex systems in the real world can be characterized by attributed networks. To mine the potential information in these networks, deep embedded clustering, which obtains node representations and clusters simultaneously, has been paid…
The class of special generic maps contains Morse functions with exactly two singular points, characterizing spheres topologically which are not $4$-dimensional and the $4$-dimensional unit sphere. This class is for higher dimensional…
We describe a robust, fast, and memory-efficient procedure that can cluster millions of structures derived from molecular dynamics simulations. The essence of the method is based on a peak-picking algorithm applied to three- and…
The high dimensionality of hyperspectral images often results in the degradation of clustering performance. Due to the powerful ability of deep feature extraction and non-linear feature representation, the clustering algorithm based on deep…
Deep clustering - joint representation learning and latent space clustering - is a well studied problem especially in computer vision and text processing under the deep learning framework. While the representation learning is generally…
The Distance Geometry Problem (DGP) seeks to find positions for a set of points in geometric space when some distances between pairs of these points are known. The so-called discretization assumptions allow to discretize the search space of…
A new computational algorithm, the discrete singular convolution (DSC), is introduced for computational electromagnetics. The basic philosophy behind the DSC algorithm for the approximation of functions and their derivatives is studied.…
In this work, we study the problem of partitioning a set of graphs into different groups such that the graphs in the same group are similar while the graphs in different groups are dissimilar. This problem was rarely studied previously,…
Discrete conformal mappings based on circle packing, vertex scaling, and related structures has had significant activity since Thurston proposed circle packing as a way to approximate conformal maps in the 1980s. The first convergence…
In this work, we introduce a novel methodology for divisive hierarchical clustering. Our divisive (``top-down'') approach is motivated by the fact that agglomerative hierarchical clustering (``bottom-up''), which is commonly used for…
Active contour models based on partial differential equations have proved successful in image segmentation, yet the study of their geometric formulation on arbitrary geometric graphs is still at an early stage. In this paper, we introduce…
Clustering in dynamic environments is of increasing importance, with broad applications ranging from real-time data analysis and online unsupervised learning to dynamic facility location problems. While meta-heuristics have shown promising…