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In this article, we present a novel box-covering algorithm for analyzing the fractal properties of complex networks. Unlike traditional algorithms that impose a predetermined box size, our approach assigns nodes to boxes identified by their…
Graphs are widely used to represent complex information and signal domains with irregular support. Typically, the underlying graph topology is unknown and must be estimated from the available data. Common approaches assume pairwise node…
This paper proposes convolutional filtering for data whose structure can be modeled by a simplicial complex (SC). SCs are mathematical tools that not only capture pairwise relationships as graphs but account also for higher-order network…
Tree-based models are often robust to uninformative features and can accurately capture non-smooth, complex decision boundaries. Consequently, they often outperform neural network-based models on tabular datasets at a significantly lower…
In this paper, we propose a simple but effective method for fast image segmentation. We re-examine the locality-preserving character of spectral clustering by constructing a graph over image regions with both global and local connections.…
We discuss our new implementation of the Real-space Electronic Structure method for studying the atomic and electronic structure of infinite periodic as well as finite systems, based on density functional theory. This improved version which…
Time series forecasting is a long-standing problem in statistics and machine learning. One of the key challenges is processing sequences with long-range dependencies. To that end, a recent line of work applied the short-time Fourier…
The morphological structure of left ventricle segmented from cardiac magnetic resonance images can be used to calculate key clinical parameters, and it is of great significance to the accurate and efficient diagnosis of cardiovascular…
We introduce a novel fully convolutional neural network (FCN) architecture for predicting the secondary structure of ribonucleic acid (RNA) molecules. Interpreting RNA structures as weighted graphs, we employ deep learning to estimate the…
Ricci curvature and its associated flow offer powerful geometric methods for analyzing complex networks. While existing research heavily focuses on applications for undirected graphs such as community detection and core extraction, there…
Hypergraphs, describing networks where interactions take place among any number of units, are a natural tool to model many real-world social and biological systems. In this work we propose a principled framework to model the organization of…
Federated Clustering (FC) is an emerging and promising solution in exploring data distribution patterns from distributed and privacy-protected data in an unsupervised manner. Existing FC methods implicitly rely on the assumption that…
In today's data-driven digital era, the amount as well as complexity, such as multi-view, non-Euclidean, and multi-relational, of the collected data are growing exponentially or even faster. Clustering, which unsupervisely extracts valid…
Collaborative Representation Classification (CRC) for face recognition attracts a lot attention recently due to its good recognition performance and fast speed. Compared to Sparse Representation Classification (SRC), CRC achieves a…
Similarity notions between vertices in a graph, such as structural and regular equivalence, are one of the main ingredients in clustering tools in complex network science. We generalise structural and regular equivalences for undirected…
The mathematical representation of uncertainty has led to a proliferation of preference structures, such as interval-valued fuzzy sets, intuitionistic fuzzy sets, and various granular models. While these extensions are often studied…
Formal Concept Analysis (FCA) is a mathematical framework for knowledge representation and discovery. It performs a hierarchical clustering over a set of objects described by attributes, resulting in conceptual structures in which objects…
We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through the \texttt{Questionnaire} algorithm, an iterative…
Geometric deep learning extends deep learning to incorporate information about the geometry and topology data, especially in complex domains like graphs. Despite the popularity of message passing in this field, it has limitations such as…
Our work is concerned with simplicial complexes that describe higher-order interactions in real complex systems. This description allows to go beyond the pairwise node-to-node representation that simple networks provide and to capture a…