Related papers: A Comprehensive Review of the Mapper Algorithm, a …
We study the use of the Euler characteristic for multiparameter topological data analysis. Euler characteristic is a classical, well-understood topological invariant that has appeared in numerous applications, including in the context of…
Communication and networking research introduces new protocols and standards with an increasing number of researchers relying on real experiments rather than simulations to evaluate the performance of their new protocols. A number of…
Uniform Manifold Approximation and Projection (UMAP) is a widely used manifold learning technique for dimensionality reduction. This paper studies UMAP, supervised UMAP, and several competing dimensionality reduction methods, including…
The exponential growth of data in current times and the demand to gain information and knowledge from the data present new challenges for database researchers. Known database systems and algorithms are no longer capable of effectively…
This work seeks to tackle the inherent complexity of dataspaces by introducing a novel data structure that can represent datasets across multiple levels of abstraction, ranging from local to global. We propose the concept of a multilevel…
In this paper we evaluate the performance of topological features for generalizable and robust classification of firn image data, with the broader goal of understanding the advantages, pitfalls, and trade-offs in topological featurization.…
Processing large complex networks recently attracted considerable interest. Complex graphs are useful in a wide range of applications from technological networks to biological systems like the human brain. Sometimes these networks are…
Tabular data learning has extensive applications in deep learning but its existing embedding techniques are limited in numerical and categorical features such as the inability to capture complex relationships and engineering. This paper…
Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…
The rules in a shape grammar apply in terms of embedding to take advantage of the parts that emerge visually in the appearance of shapes. While the shapes are kept unanalyzed as a computation moves forward, part-structures for shapes can be…
Mathematical morphology is a theory and technique to collect features like geometric and topological structures in digital images. Given a target image, determining suitable morphological operations and structuring elements is a cumbersome…
Graph-related applications have experienced significant growth in academia and industry, driven by the powerful representation capabilities of graph. However, efficiently executing these applications faces various challenges, such as load…
Topological analysis of the magnetic field in simulated plasmas allows the study of various physical phenomena in a wide range of settings. One such application is magnetic reconnection, a phenomenon related to the dynamics of the magnetic…
In this article, we show how the recent statistical techniques developed in Topological Data Analysis for the Mapper algorithm can be extended and leveraged to formally define and statistically quantify the presence of topological…
Complex systems are difficult to study not only because they are nonlinear, multiscale, and often nonstationary, but because their scientifically relevant organization is often invisible at the level of individual components, pairwise…
Despite the remarkable accuracies attained by machine learning classifiers to separate complex datasets in a supervised fashion, most of their operation falls short to provide an informed intuition about the structure of data, and, what is…
Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…
Persistent homology is a widely-used tool in topological data analysis (TDA) for understanding the underlying shape of complex data. By constructing a filtration of simplicial complexes from data points, it captures topological features…
The classification of high-dimensional data defined on graphs is particularly difficult when the graph geometry is unknown. We introduce a Haar scattering transform on graphs, which computes invariant signal descriptors. It is implemented…
Big data analytics is one of the most promising areas of new research and development in computer science, enterprises, e-commerce, and defense. For many organizations, big data is considered one of their most important strategic assets.…