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Graph vertex ordering is widely employed in spatial data analysis, especially in urban analytics, where street graphs serve as spatial discretization for modeling and simulation. It is also crucial for visualization, as many methods require…
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…
Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be…
Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a…
We propose a series of methods to represent the evolution of a field of science at different levels: namely micro, meso and macro levels. We use a previously introduced asymmetric measure of paradigmatic proximity between terms that enables…
Visualizations of tabular data are widely used; understanding their effectiveness in different task and data contexts is fundamental to scaling their impact. However, little is known about how basic tabular data visualizations perform…
In many scenarios, especially biomedical applications, the correct delineation of complex fine-scaled structures such as neurons, tissues, and vessels is critical for downstream analysis. Despite the strong predictive power of deep learning…
Graph sampling is a technique to pick a subset of vertices and/ or edges from original graph. It has a wide spectrum of applications, e.g. survey hidden population in sociology [54], visualize social graph [29], scale down Internet AS graph…
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
We study the topological construction called Mapper in the context of simply connected domains, in particular on images. The Mapper construction can be considered as a generalization for contour, split, and joint trees on simply connected…
Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…
Many computer vision tasks address the problem of scene understanding and are naturally interrelated e.g. object classification, detection, scene segmentation, depth estimation, etc. We show that we can leverage the inherent relationships…
The classification of shapes is of great interest in diverse areas ranging from medical imaging to computer vision and beyond. While many statistical frameworks have been developed for the classification problem, most are strongly tied to…
Persistent homology is a widely used tool in Topological Data Analysis that encodes multiscale topological information as a multi-set of points in the plane called a persistence diagram. It is difficult to apply statistical theory directly…
The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables,…
Multivariate spatial data plays an important role in computational science and engineering simulations. The potential features and hidden relationships in multivariate data can assist scientists to gain an in-depth understanding of a…
Dimensionality reduction is often used as an initial step in data exploration, either as preprocessing for classification or regression or for visualization. Most dimensionality reduction techniques to date are unsupervised; they do not…
One of the essential tasks in connectomics is the morphology analysis of neurons and organelles like mitochondria to shed light on their biological properties. However, these biological objects often have tangled parts or complex branching…
We propose a flexible and multi-scale method for organizing, visualizing, and understanding datasets sampled from or near stratified spaces. The first part of the algorithm produces a cover tree using adaptive thresholds based on a…
Nervous systems are characterized by neurons displaying a diversity of morphological shapes. Traditionally, different shapes have been qualitatively described based on visual inspection and quantitatively described based on morphometric…