Related papers: Non-hierarchical Structures: How to Model and Inde…

The ability to quantify distinctness of a cluster structure is fundamental for certain simulation studies, in particular for those comparing performance of different classification algorithms. The intrinsic integral measure based on the…

Empirical data, on which deep learning relies, has substantial internal structure, yet prevailing theories often disregard this aspect. Recent research has led to the definition of structured data ensembles, aimed at equipping established…

We consider the problem of representing multidimensional data where the domain of each dimension is organized hierarchically, and the queries require summary information at a different node in the hierarchy of each dimension. This is the…

Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical…

Deciding whether there is a single tree -a supertree- that summarizes the evolutionary information in a collection of unrooted trees is a fundamental problem in phylogenetics. We consider two versions of this question: agreement and…

We consider a matrix completion problem that exploits social or item similarity graphs as side information. We develop a universal, parameter-free, and computationally efficient algorithm that starts with hierarchical graph clustering and…

Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…

The described works have been carried out in the framework of a mid-term study initiated by the Centre Electronique de l'Armement and led by ADERSA, a French company of research under contract. The aim was to study the techniques of regular…

Topological deep learning (TDL) has emerged as a powerful tool for modeling higher-order interactions in relational data. However, phenomena such as oversquashing in topological message-passing remain understudied and lack theoretical…

Detecting the components common or correlated across multiple data sets is challenging due to a large number of possible correlation structures among the components. Even more challenging is to determine the precise structure of these…

The global Information and Communications Technology (ICT) supply chain is a complex network consisting of all types of participants. It is often formulated as a Social Network to discuss the supply chain network's relations, properties,…

This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are…

Data aggregation in Geographic Information Systems (GIS) is only marginally present in commercial systems nowadays, mostly through ad-hoc solutions. In this paper, we first present a formal model for representing spatial data. This model…

Large tree structures are ubiquitous and real-world relational datasets often have information associated with nodes (e.g., labels or other attributes) and edges (e.g., weights or distances) that need to be communicated to the viewers. Yet,…

Hierarchical clustering is an effective, interpretable method for analyzing structure in data. It reveals insights at multiple scales without requiring a predefined number of clusters and captures nested patterns and subtle relationships,…

Recently, the emergence of large language models (LLMs) has motivated integrating language descriptions into graphs, forming text-attributed graphs (TAGs) that enhance model encoding capabilities from a data-centric perspective. A review of…

Originally designed to model text, topic modeling has become a powerful tool for uncovering latent structure in domains including medicine, finance, and vision. The goals for the model vary depending on the application: in some cases, the…

We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…

Cartesian tree matching is a form of generalized pattern matching where a substring of the text matches with the pattern if they share the same Cartesian tree. This form of matching finds application for time series of stock prices and can…

We show that in the hierarchical tile assembly model, if there is a producible assembly that overlaps a nontrivial translation of itself consistently (i.e., the pattern of tile types in the overlap region is identical in both translations),…