Related papers: Scalable Topological Data Analysis and Visualizati…

Leveraging hypergraph structures to model advanced processes has gained much attention over the last few years in many areas, ranging from protein-interaction in computational biology to image retrieval using machine learning. Hypergraph…

We consider the observability model in networks with arbitrary topologies. We introduce a system of coupled nonlinear equations, valid under the locally tree-like ansatz, to describe the size of the largest observable cluster as a function…

It plays a fundamental role to compactly represent the visual information towards the optimization of the ultimate utility in myriad visual data centered applications. With numerous approaches proposed to efficiently compress the texture…

Topological Data Analysis (TDA) has been praised by researchers for its ability to capture intricate shapes and structures within data. TDA is considered robust in handling noisy and high-dimensional datasets, and its interpretability is…

As large-scale social data explode and machine-learning methods evolve, scholars of entrepreneurship and innovation face new research opportunities but also unique challenges. This chapter discusses the difficulties of leveraging…

The design of periodic nanostructures allows to tailor the transport of photons, phonons, and matter waves for specific applications. Recent years have seen a further expansion of this field by engineering topological properties. However,…

The importance of explainability in machine learning continues to grow, as both neural-network architectures and the data they model become increasingly complex. Unique challenges arise when a model's input features become high dimensional:…

Deep learning (DL) models have achieved paradigm-changing performance in many fields with high dimensional data, such as images, audio, and text. However, the black-box nature of deep neural networks is a barrier not just to adoption in…

Topological materials are at the forefront of quantum materials research, offering tremendous potential for next-generation energy and information devices. However, current investigation of these materials remains largely focused on…

This survey provides a comprehensive exploration of applications of Topological Data Analysis (TDA) within neural network analysis. Using TDA tools such as persistent homology and Mapper, we delve into the intricate structures and behaviors…

As the rate of data collection continues to grow rapidly, developing visualization tools that scale to immense data sets is a serious and ever-increasing challenge. Existing approaches generally seek to decouple storage and visualization…

Complex network topologies and hyperbolic geometry seem specularly connected, and one of the most fascinating and challenging problems of recent complex network theory is to map a given network to its hyperbolic space. The Popularity…

We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…

The rapid development of tools for acquisition and storage of information has lead to the formation of enormous medical databases. The large quantity of data definitely surpasses the abilities of humans for efficient usage without…

Microscopic examination of slides prepared from tissue samples is the primary tool for detecting and classifying cancerous lesions, a process that is time-consuming and requires the expertise of experienced pathologists. Recent advances in…

Contour trees describe the topology of level sets in scalar fields and are widely used in topological data analysis and visualization. A main challenge of utilizing contour trees for large-scale scientific data is their computation at scale…

The study of irreducible higher-order interactions has become a core topic of study in complex systems. Two of the most well-developed frameworks, topological data analysis and multivariate information theory, aim to provide formal tools…

Recently, we have been witnessing huge advancements in the scale of data we routinely generate and collect in pretty much everything we do, as well as our ability to exploit modern technologies to process, analyze and understand this data.…

Monitoring and Managing High Performance Computing (HPC) systems and environments generate an ever growing amount of data. Making sense of this data and generating a platform where the data can be visualized for system administrators and…

Parallel coordinate plots (PCPs) are among the most useful techniques for the visualization and exploration of high-dimensional data spaces. They are especially useful for the representation of correlations among the dimensions, which…