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High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce.…

Point cloud is an important type of geometric data structure. Due to its irregular format, most researchers transform such data to regular 3D voxel grids or collections of images. This, however, renders data unnecessarily voluminous and…

We establish a connection between tangles, a concept from structural graph theory that plays a central role in Robertson and Seymour's graph minor project, and hierarchical clustering. Tangles cannot only be defined for graphs, but in fact…

Strong evidence suggests that humans perceive the 3D world by parsing visual scenes and objects into part-whole hierarchies. Although deep neural networks have the capability of learning powerful multi-level representations, they can not…

The last decades have not only been characterized by an explosive growth of data, but also an increasing appreciation of data as a valuable resource. Their value comes with the ability to extract meaningful patterns that are of economic,…

Face clustering can provide pseudo-labels to the massive unlabeled face data and improve the performance of different face recognition models. The existing clustering methods generally aggregate the features within subgraphs that are often…

Urban structure detection is a basic task in urban geography. Clustering is a core technology to detect the patterns of urban spatial structure, urban functional region, and so on. In big data era, diverse urban sensing datasets recording…

Dense retrieval methods typically target unstructured text data represented as flat strings. However, e-commerce catalogs often include structured information across multiple fields, such as brand, title, and description, which contain…

For many materials, macroscopic mechanical behavior is determined by an intricate microstructure. Understanding the relation between these two scales helps scientists and engineers design better materials. The relation which maps…

Fully exploring correlation among points in point clouds is essential for their feature modeling. This paper presents a novel end-to-end graph model, named Point2Node, to represent a given point cloud. Point2Node can dynamically explore…

We derive a statistical model for estimation of a dendrogram from single linkage hierarchical clustering (SLHC) that takes account of uncertainty through noise or corruption in the measurements of separation of data. Our focus is on just…

Young massive star clusters spanning $\sim 10^4 - 10^8 M_\odot$ in mass have been observed to have similar surface brightness profiles. Recent hydrodynamical simulations of star cluster formation have also produced star clusters with this…

Clustering is a well-known and studied problem, one of its variants, called contiguity-constrained clustering, accepts as a second input a graph used to encode prior information about cluster structure by means of contiguity constraints…

Instance-level alignment is widely exploited for person re-identification, e.g. spatial alignment, latent semantic alignment and triplet alignment. This paper probes another feature alignment modality, namely cluster-level feature alignment…

High triangle density -- the graph property stating that a constant fraction of two-hop paths belong to a triangle -- is a common signature of social networks. This paper studies triangle-dense graphs from a structural perspective. We prove…

We introduce a graph-theoretic approach to extract clusters and hierarchies in complex data-sets in an unsupervised and deterministic manner, without the use of any prior information. This is achieved by building topologically embedded…

Phase separation mechanisms can produce a variety of complicated and intricate microstructures, which often can be difficult to characterize in a quantitative way. In recent years, a number of novel topological metrics for microstructures…

Cut-based directed graph (digraph) clustering often focuses on finding dense within-cluster or sparse between-cluster connections, similar to cut-based undirected graph clustering methods. In contrast, for flow-based clusterings the edges…

We describe a method for recovering of the substructure, internal dynamics and geometrical shapes of clusters of galaxies. Applying the method to the Virgo cluster, we, first, reveal the substructure of the central 4 arc degree field of the…

A new approach to clustering, based on the physical properties of inhomogeneous coupled chaotic maps, is presented. A chaotic map is assigned to each data-point and short range couplings are introduced. The stationary regime of the system…