Related papers: Topological Information Data Analysis
The complex and dynamic crosstalk between tumour and immune cells results in tumours that can exhibit distinct qualitative behaviours - elimination, equilibrium, and escape - and intricate spatial patterns, yet share similar cell…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
Battiston et al. (arXiv:2110.06023) provide a comprehensive overview of how investigations of complex systems should take into account interactions between more than two elements, which can be modelled by hypergraphs and studied via…
We demonstrate that the algorithmic information content of a system is deeply connected to its potential dynamics, thus affording an avenue for moving systems in the information-theoretic space and controlling them in the phase space. To…
Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must…
Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must…
Assessing the synergistic high-order behaviors (HOBs) that emerge from underlying structural mechanisms is crucial to characterize complex systems. This work leverages the combined use of predictability and information measures to detect…
Topological data analysis, as a tool for extracting topological features and characterizing geometric shapes, has experienced significant development across diverse fields. Its key mathematical techniques include persistent homology and the…
An important problem in the field of bioinformatics is to identify interactive effects among profiled variables for outcome prediction. In this paper, a logistic regression model with pairwise interactions among a set of binary covariates…
Interaction information is one of the multivariate generalizations of mutual information, which expresses the amount information shared among a set of variables, beyond the information, which is shared in any proper subset of those…
A wide range of data that appear in scientific experiments and simulations are multivariate or multifield in nature, consisting of multiple scalar fields. Topological feature search of such data aims to reveal important properties useful to…
Mutual information (MI) is a general measure of statistical dependence with widespread application across the sciences. However, estimating MI between multi-dimensional variables is challenging because the number of samples necessary to…
Topological data analysis (TDA) is an active field of mathematics for quantifying shape in complex data. Standard methods in TDA such as persistent homology (PH) are typically focused on the analysis of data consisting of a single entity…
Topological methods are very rarely used in structural health monitoring (SHM), or indeed in structural dynamics generally, especially when considering the structure and topology of observed data. Topological methods can provide a way of…
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…
We introduce the category of information structures, whose objects are suitable diagrams of measurable sets that encode the possible outputs of a given family of observables and their mutual relationships of refinement; they serve as…
Total correlation (TC) is a fundamental concept in information theory that measures statistical dependency among multiple random variables. Recently, TC has shown noticeable effectiveness as a regularizer in many learning tasks, where the…
Statistical hypothesis testing is the central method to demarcate scientific theories in both exploratory and inferential analyses. However, whether this method befits such purpose remains a matter of debate. Established approaches to…
Integrated population models (IPMs) combine multiple ecological data types such as capture-mark-recapture histories, reproduction surveys, and population counts into a single statistical framework. In such models, each data type is…
The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data…