Related papers: Baby Morse Theory in Data Analysis

The problem of finding groups in data (cluster analysis) has been extensively studied by researchers from the fields of Statistics and Computer Science, among others. However, despite its popularity it is widely recognized that the…

While branching network structures abound in nature, their objective analysis is more difficult than expected because existing quantitative methods often rely on the subjective judgment of branch structures. This problem is particularly…

Non-trivial spatial topology of the Universe may give rise to potentially measurable signatures in the cosmic microwave background. We explore different machine learning approaches to classify harmonic-space realizations of the microwave…

In this paper, I outline several conceptual and methodological issues related to modeling individual and group processes embedded in clustered/hierarchical data structures. We position multilevel modeling techniques within a broader set of…

Accurate delineation of fine-scale structures is a very important yet challenging problem. Existing methods use topological information as an additional training loss, but are ultimately making pixel-wise predictions. In this paper, we…

We show that geometric inference of a point cloud can be calculated by examining its kernel density estimate with a Gaussian kernel. This allows one to consider kernel density estimates, which are robust to spatial noise, subsampling, and…

Segmentation of curvilinear structures such as vasculature and road networks is challenging due to relatively weak signals and complex geometry/topology. To facilitate and accelerate large scale annotation, one has to adopt semi-automatic…

A fundamental problem in computer vision is boundary estimation, where the goal is to delineate the boundary of objects in an image. In this paper, we propose a method which jointly incorporates geometric and topological information within…

This paper introduces a new approach to analyzing spatial point data clustered along or around a system of curves or "fibres." Such data arise in catalogues of galaxy locations, recorded locations of earthquakes, aerial images of minefields…

The concept of $typed$ $topology$ is introduced. In a typed topological space, some open sets are assigned "types", and topological concepts such as closure, connectedness can be defined using types. A finite data set in $R^2$ is a…

We present a self-supervised task on point clouds, in order to learn meaningful point-wise features that encode local structure around each point. Our self-supervised network, named MortonNet, operates directly on unstructured/unordered…

In many applications, the two-dimensional trajectories of fluid particles are available, but little is known about the underlying flow. Oceanic floats are a clear example. To extract quantitative information from such data, one can measure…

In this paper, we present a new approach for analyzing gene expression data that builds on topological characteristics of time series. Our goal is to identify cell cycle regulated genes in micro array dataset. We construct a point cloud out…

Faces-classes of grains, often referred to as topological features, largely dictate the evolution of polycrystalline microstructures during grain growth. Realising these topological features is generally an arduous task, often demanding…

Recently, the advancement of 3D point clouds in deep learning has attracted intensive research in different application domains such as computer vision and robotic tasks. However, creating feature representation of robust, discriminative…

This paper presents a new interaction point process that integrates geological knowledge for the purpose of automatic sources detection of multiple sources in groundwaters from hydrochemical data. The observations are considered as spatial…

A short survey on applications of algebraic geometry in topological data analysis.

Complex prediction models such as deep learning are the output from fitting machine learning, neural networks, or AI models to a set of training data. These are now standard tools in science. A key challenge with the current generation of…

Scientists use a mathematical subject called 'topology' to study the shapes of objects. An important part of topology is counting the numbers of pieces and holes in objects, and people use this information to group objects into different…

Morse complexes are gradient-based topological descriptors with close connections to Morse theory. They are widely applicable in scientific visualization as they serve as important abstractions for gaining insights into the topology of…