Related papers: Improved Modeling of Persistence Diagram
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…
In topological data analysis (TDA), persistence diagrams have been a succesful tool. To compare them, Wasserstein and Bottleneck distances are commonly used. We address the shortcomings of these metrics and show a way to investigate them in…
Topological Data Analysis (TDA), an emerging field in investment sciences, harnesses mathematical methods to extract data features based on shape, offering a promising alternative to classical portfolio selection methodologies. We utilize…
This work is dedicated to the topological analysis of complex transitional networks for dynamic state detection. Transitional networks are formed from time series data and they leverage graph theory tools to reveal information about the…
We present the application of topological data analysis (TDA) to study unweighted complex networks via their persistent homology. By endowing appropriate weights that capture the inherent topological characteristics of such a network, we…
While the strength of Topological Data Analysis has been explored in many studies on high dimensional numeric data, it is still a challenging task to apply it to text. As the primary goal in topological data analysis is to define and…
We consider the problem of robustifying high-dimensional structured estimation. Robust techniques are key in real-world applications which often involve outliers and data corruption. We focus on trimmed versions of structurally regularized…
In urgent decision making applications, ensemble simulations are an important way to determine different outcome scenarios based on currently available data. In this paper, we will analyze the output of ensemble simulations by considering…
By their nature it is difficult to differentiate chaotic dynamical systems through measurement. In recent years, work has begun on using methods of Topological Data Analysis (TDA) to qualitatively type dynamical data by approximating the…
Deep neural networks are known to be vulnerable to unseen data: they may wrongly assign high confidence stcores to out-distribuion samples. Recent works try to solve the problem using representation learning methods and specific metrics. In…
This paper introduces a new data analysis method for big data using a newly defined regression model named multiple model linear regression(MMLR), which separates input datasets into subsets and construct local linear regression models of…
This paper introduces a simple principle for robust high-dimensional statistical inference via an appropriate shrinkage on the data. This widens the scope of high-dimensional techniques, reducing the moment conditions from sub-exponential…
Dimensionality reduction is a crucial first step for many unsupervised learning tasks including anomaly detection and clustering. Autoencoder is a popular mechanism to accomplish dimensionality reduction. In order to make dimensionality…
Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely…
Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…
Unsupervised data representation and visualization using tools from topology is an active and growing field of Topological Data Analysis (TDA) and data science. Its most prominent line of work is based on the so-called Mapper graph, which…
A novel topological-data-analytical (TDA) method is proposed to distinguish, from noise, small holes surrounded by high-density regions of a probability density function. The proposed method is robust against additive noise and outliers.…
Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding…
This paper presents a robust and efficient method for tracking topological features in time-varying scalar data. Structures are tracked based on the optimal matching between persistence diagrams with respect to the Wasserstein metric. This…
We propose a novel algorithm for supervised dimensionality reduction named Manifold Partition Discriminant Analysis (MPDA). It aims to find a linear embedding space where the within-class similarity is achieved along the direction that is…