Related papers: Consistent, multidimensional differential histogra…
Persistence diagrams are one of the main tools in the field of Topological Data Analysis (TDA). They contain fruitful information about the shape of data. The use of machine learning algorithms on the space of persistence diagrams proves to…
Multimodal data modeling has emerged as a powerful approach in clinical research, enabling the integration of diverse data types such as imaging, genomics, wearable sensors, and electronic health records. Despite its potential to improve…
A major challenge in nuclear fusion research is the coherent combination of data from heterogeneous diagnostics and modelling codes for machine control and safety as well as physics studies. Measured data from different diagnostics often…
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…
This book introduces the new research area of Geometric Data Science, where data can represent any real objects through geometric measurements. The first part of the book focuses on finite point sets. The most important result is a complete…
Heterogeneous data pose serious challenges to data analysis tasks, including exploration and visualization. Current techniques often utilize dimensionality reductions, aggregation, or conversion to numerical values to analyze heterogeneous…
Using the gauge-gravity duality, we argue that for a certain class of out-of-equilibrium steady-state systems in contact with a thermal background at a given temperature, the macroscopic physics can be captured by an effective thermodynamic…
Using a time series model to mimic an observed time series has a long history. However, with regard to this objective, conventional estimation methods for discrete-time dynamical models are frequently found to be wanting. In fact, they are…
In the analysis of large/big data sets, aggregation (replacing values of a variable over a group by a single value) is a standard way of reducing the size (complexity) of the data. Data analysis programs provide different aggregation…
A novel method for common and individual feature analysis from exceedingly large-scale data is proposed, in order to ensure the tractability of both the computation and storage and thus mitigate the curse of dimensionality, a major…
The approaches taken to describe and develop spatial discretisations of the domains required for geophysical simulation models are commonly ad hoc, model or application specific and under-documented. This is particularly acute for…
Symbolic data analysis (SDA) is an emerging area of statistics concerned with understanding and modelling data that takes distributional form (i.e. symbols), such as random lists, intervals and histograms. It was developed under the premise…
In real-world applications, machine learning models often become obsolete due to shifts in the joint distribution arising from underlying temporal trends, a phenomenon known as the "concept drift". Existing works propose model-specific…
Over the past two decades, the field of high-dimensional statistics has experienced substantial progress, driven largely by technological advances that have dramatically reduced the cost and effort for data collection and storage across a…
Data-driven approaches to modeling physical systems fail to generalize to unseen systems that share the same general dynamics with the learning domain, but correspond to different physical contexts. We propose a new framework for this key…
The standard model of cosmology has provided a good phenomenological description of a wide range of observations both at astrophysical and cosmological scales for several decades. This concordance model is constructed by a universal…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
Simulated high-dimensional data is useful for testing, validating, and improving algorithms used in dimension reduction, supervised and unsupervised learning. High-dimensional data is characterized by multiple variables that are dependent…
A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems…
In category theory, the use of string diagrams is well known to aid in the intuitive understanding of certain concepts, particularly when dealing with adjunctions and monoidal categories. We show that string diagrams are also useful in…