Related papers: Geometric Data Analysis, From Correspondence Analy…
We review the theory and practice of determining what parts of a data set are ultrametric. It is assumed that the data set, to begin with, is endowed with a metric, and we include discussion of how this can be brought about if a…
Widespread use of the Internet and social networks invokes the generation of big data, which is proving to be useful in a number of applications. To deal with explosively growing amounts of data, data analytics has emerged as a critical…
We present a robust method to find region-level correspondences between shapes, which are invariant to changes in geometry and applicable across multiple shape representations. We generate simplified shape graphs by jointly decomposing the…
Graph matching pairs corresponding nodes across two or more graphs. The problem is difficult as it is hard to capture the structural similarity across graphs, especially on large graphs. We propose to incorporate high-order information for…
Riemannian metric learning is an emerging field in machine learning, unlocking new ways to encode complex data structures beyond traditional distance metric learning. While classical approaches rely on global distances in Euclidean space,…
Structured sentiment analysis attempts to extract full opinion tuples from a text, but over time this task has been subdivided into smaller and smaller sub-tasks, e,g,, target extraction or targeted polarity classification. We argue that…
We propose a novel framework for combining datasets via alignment of their intrinsic geometry. This alignment can be used to fuse data originating from disparate modalities, or to correct batch effects while preserving intrinsic data…
The purpose of this note is to study the complex structures orthogonal to a given Riemannian metric. For another paper on this topic, we highly recommend the work of Salamon. His work describes in great detail the role that curvature plays…
Many neural nets appear to represent data as linear combinations of "feature vectors." Algorithms for discovering these vectors have seen impressive recent success. However, we argue that this success is incomplete without an understanding…
Recently, there has been growing interest in developing learning-based methods to detect and utilize salient semi-global or global structures, such as junctions, lines, planes, cuboids, smooth surfaces, and all types of symmetries, for 3D…
We survey the model merging literature through the lens of loss landscape geometry to connect observations from empirical studies on model merging and loss landscape analysis to phenomena that govern neural network training and the…
A large amount of information is stored in data tables. Users can search for data tables using a keyword-based query. A table is composed primarily of data values that are organized in rows and columns providing implicit structural…
Graph Neural Networks (GNNs) have emerged as a promising tool to handle data exhibiting an irregular structure. However, most GNN architectures perform well on homophilic datasets, where the labels of neighboring nodes are likely to be the…
This is the introduction I wrote for the multi-authored book "From Riemann to differential geometry and relativity", edited by L. Ji, A. Papadopoulos and S. Yamada (Berlin, Springer verlag, 2017). The book consists of twenty chapters,…
Review of the book "Thermal Convection: Patterns, Evolution and Stability" by M. Lappa. Invited by the journal Geophysical and Astrophysical Fluid Dynamics.
Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity…
This paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or positioning of the vision sensors. It concentrates on the problem where images are encoded with compressed linear…
While many good textbooks are available on Protein Structure, Molecular Simulations, Thermodynamics and Bioinformatics methods in general, there is no good introductory level book for the field of Structural Bioinformatics. This book aims…
Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional…
The evolution of AI systems toward agentic operation and context-aware retrieval necessitates transforming unstructured text into structured formats like tables, knowledge graphs, and charts. While such conversions enable critical…