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This article examines the application of a popular measure of sparsity, Gini Index, on network graphs. A wide variety of network graphs happen to be sparse. But the index with which sparsity is commonly measured in network graphs is edge…
Structural Entropy (SE) measures the structural information contained in a graph. Minimizing or maximizing SE helps to reveal or obscure the intrinsic structural patterns underlying graphs in an interpretable manner, finding applications in…
In signal analysis and synthesis, linear approximation theory considers a linear decomposition of any given signal in a set of atoms, collected into a so-called dictionary. Relevant sparse representations are obtained by relaxing the…
Visual summarization of clinical data collected on patients contained within the electronic health record (EHR) may enable precise and rapid triage at the time of patient presentation to an emergency department (ED). The triage process is…
In this paper, we developed a novel method of nonparametric relative entropy (RlEn) for modelling loss of complexity in intermittent time series. The method consists of two steps. We first fit a nonlinear autoregressive model to each…
The complexity of a signal can be measured by the Recurrence period density entropy (RPDE) from the reconstructed phase space. We have chosen a window based RPDE method for the classification of signals, as RPDE is an average entropic…
Privacy policy documents are often lengthy, complex, and difficult for non-expert users to interpret, leading to a lack of transparency regarding the collection, processing, and sharing of personal data. As concerns over online privacy…
We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of…
This paper presents a command-line tool, called Entropia, that implements a family of conformance checking measures for process mining founded on the notion of entropy from information theory. The measures allow quantifying classical…
We have developed PyTIE (Python Topological Indices Expressions) which is defined as the collections of Python packages such as PyTIE D, PyTIE DS, PyTIE SMS DE, and PyTIE SMS DSE, which are open-source software packages and cross-platform…
The estimation of a precision matrix is a crucial problem in various research fields, particularly when working with high dimensional data. In such settings, the most common approach is to use the penalized maximum likelihood. The…
Traditional measures of entropy, like the Von Neumann entropy, while fundamental in quantum information theory, are insufficient when interpreted as thermodynamic entropy due to their invariance under unitary transformations, which…
The use of correntropy as a similarity measure has been increasing in different scenarios due to the well-known ability to extract high-order statistic information from data. Recently, a new similarity measure between complex random…
The Straightness is a measure designed to characterize a pair of vertices in a spatial graph. It is defined as the ratio of the Euclidean distance to the graph distance between these vertices. It is often used as an average, for instance to…
We give a scheme to geometrize the partial entanglement entropy (PEE) for holographic CFT in the context of AdS/CFT. More explicitly, given a point $\textbf{x}$ we geometrize the two-point PEEs between $\textbf{x}$ and any other points in…
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
Visual attention plays a critical role when our visual system executes active visual tasks by interacting with the physical scene. However, how to encode the visual object relationship in the psychological world of our brain deserves to be…
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…
We investigate the perceived visual complexity (VC) in data visualizations using objective image-based metrics. We collected VC scores through a large-scale crowdsourcing experiment involving 349 participants and 1,800 visualization images.…
Explainable AI (XAI) in medical histopathology is essential for enhancing the interpretability and clinical trustworthiness of deep learning models in cancer diagnosis. However, the black-box nature of these models often limits their…