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Topological Data Analysis (TDA) has emerged as a powerful framework for extracting robust and interpretable features from noisy high-dimensional data. In the context of Social Choice Theory, where preference profiles and collective…
At present, the vast majority of human subjects with neurological disease are still diagnosed through in-person assessments and qualitative analysis of patient data. In this paper, we propose to use Topological Data Analysis (TDA) together…
In this article, we introduce a Topological Data Analysis (TDA) pipeline for neural spike train data. Understanding how the brain transforms sensory information into perception and behavior requires analyzing coordinated neural population…
The Mapper algorithm, a technique within topological data analysis (TDA), constructs a simplified graphical representation of high-dimensional data to uncover its underlying shape and structural patterns. The algorithm has attracted…
Topological Data Analysis (TDA) involves techniques of analyzing the underlying structure and connectivity of data. However, traditional methods like persistent homology can be computationally demanding, motivating the development of neural…
Topological data analysis (TDA) is an active field of mathematics for quantifying shape in complex data. Standard methods in TDA such as persistent homology (PH) are typically focused on the analysis of data consisting of a single entity…
Topological Data Analysis (TDA) is an approach to handle with big data by studying its shape. A main tool of TDA is the persistence diagram, and one can use it to compare data sets. One approach to learn on the similarity between two…
We present a way to use Topological Data Analysis (TDA) for machine learning tasks on grayscale images. We apply persistent homology to generate a wide range of topological features using a point cloud obtained from an image, its natural…
Recently, there has been an explosion in statistical learning literature to represent data using topological principles to capture structure and relationships. We propose a topological data analysis (TDA)-based framework, named Topological…
In this chapter, we discuss applications of topological data analysis (TDA) to spatial systems. We briefly review the recently proposed level-set construction of filtered simplicial complexes, and we then examine persistent homology in two…
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,…
Topological Data Analysis (TDA) has been successfully used for various tasks in signal/image processing, from visualization to supervised/unsupervised classification. Often, topological characteristics are obtained from persistent homology…
Software libraries for Topological Data Analysis (TDA) offer limited support for interactive visualization. Most libraries only allow to visualize topological descriptors (e.g., persistence diagrams), and lose the connection with the…
Topological Data Analysis (TDA) is a recent and growing branch of statistics devoted to the study of the shape of the data. In this work we investigate the predictive power of TDA in the context of supervised learning. Since topological…
In machine learning, ensembles are important tools for improving the model performance. In natural language processing specifically, ensembles boost the performance of a method due to multiple large models available in open source. However,…
Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…
Topological data analysis (TDA) is a rising branch in modern applied mathematics. It extracts topological structures as features of a given space and uses these features to analyze digital data. Persistent homology, one of the central tools…
In topological data analysis (TDA), one often studies the shape of data by constructing a filtered topological space, whose structure is then examined using persistent homology. However, a single filtered space often does not adequately…
Persistent homology (PH) is a method used in topological data analysis (TDA) to study qualitative features of data that persist across multiple scales. It is robust to perturbations of input data, independent of dimensions and coordinates,…
Topological Data Analysis (TDA) provides tools to describe the shape of data, but integrating topological features into deep learning pipelines remains challenging, especially when preserving local geometric structure rather than…