Related papers: Decorated Merge Trees for Persistent Topology
Although there is no doubt that multi-parameter persistent homology is a useful tool to analyse multi-variate data, efficient ways to compute these modules are still lacking in the available topological data analysis toolboxes. Other issues…
The present lack of a stable method to compare persistent homology groups with torsion is a relevant problem in current research about Persistent Homology and its applications in Pattern Recognition. In this paper we introduce a…
Neural networks (NNs) and decision trees (DTs) are both popular models of machine learning, yet coming with mutually exclusive advantages and limitations. To bring the best of the two worlds, a variety of approaches are proposed to…
Tabular datasets play a crucial role in various applications. Thus, developing efficient, effective, and widely compatible prediction algorithms for tabular data is important. Currently, two prominent model types, Gradient Boosted Decision…
Long lived topological features are distinguished from short lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and…
Consider the space of continuous functions on a geometric tree $X$ whose persistent homology gives rise to a finite generic barcode $D$. We show that there are exactly as many path connected components in this space as there are merge trees…
A novel fusion python application of data mining techniques (DMT) was designed and implemented to locate, identify, and delineate the subsurface structural pattern (SSP) of source rocks for the features of interest underlain the study area.…
Mixtures of truncated exponentials (MTE) potentials are an alternative to discretization for representing continuous chance variables in influence diagrams. Also, MTE potentials can be used to approximate utility functions. This paper…
Succinct trees, such as wavelet trees and those based on, for instance, range Min-Max trees (RMMTs), are a family of practical data structures that store information close to their information-theoretic space lower bound. These structures…
Mapping and localization, preferably from a small number of observations, are fundamental tasks in robotics. We address these tasks by combining spatial structure (differentiable mapping) and end-to-end learning in a novel neural network…
This work incorporates topological features via persistence diagrams to classify point cloud data arising from materials science. Persistence diagrams are multisets summarizing the connectedness and holes of given data. A new distance on…
In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA,…
Persistence diagrams have been widely used to quantify the underlying features of filtered topological spaces in data visualization. In many applications, computing distances between diagrams is essential; however, computing these distances…
Gradient boosted decision trees (GBDT) is the leading algorithm for many commercial and academic data applications. We give a deep analysis of this algorithm, especially the histogram technique, which is a basis for the regulized…
Persistent Homology (PH) allows tracking homology features like loops, holes and their higher-dimensional analogs, along with a single-parameter family of nested spaces. Currently, computing descriptors for complex data characterized by…
Work presented in this paper describes a general algorithm and its finite element implementation for performing concurrent multiple sub-domain simulations in linear structural dynamics. Using this approach one can solve problems in which…
Persistence diagrams, combining geometry and topology for an effective shape description used in pattern recognition, have already proven to be an effective tool for shape representation with respect to a certainfiltering function.…
Using the wedge sum of metric spaces, for all compact metrizable spaces, we construct a topological embedding of the compact metrizable space into the set of all metric trees in the Gromov--Hausdorff space with finite prescribed values. As…
In this paper, we study merge trees induced by a discrete Morse function on a tree. Given a discrete Morse function, we provide a method to constructing an induced merge tree and define a new notion of equivalence of discrete Morse…
We give the first non-trivial fully dynamic probabilistic tree embedding algorithm for weighted graphs undergoing edge insertions and deletions. We obtain a trade-off between amortized update time and expected stretch against an oblivious…