Related papers: Same But Different: Distance Correlations Between …
Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…
Information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, and biological networks. The primary challenge in this domain is measuring…
We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…
Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging. A high resolution means longer image acquisition and larger…
Single-parameter persistent homology, a key tool in topological data analysis, has been widely applied to data problems along with statistical techniques that quantify the significance of the results. In contrast, statistical techniques for…
This paper brings together three distinct theories with the goal of quantifying shape textures with complex morphologies. Distance fields are central objects in shape representation, while topological data analysis uses algebraic topology…
Comparing document semantics is one of the toughest tasks in both Natural Language Processing and Information Retrieval. To date, on one hand, the tools for this task are still rare. On the other hand, most relevant methods are devised from…
Hypergraphs are useful mathematical models for describing complex relationships among members of a structured graph, while hyperdigraphs serve as a generalization that can encode asymmetric relationships in the data. However, obtaining…
Topological data analysis combines machine learning with methods from algebraic topology. Persistent homology, a method to characterize topological features occurring in data at multiple scales is of particular interest. A major obstacle to…
We propose a novel method to determine the dissimilarity between subjects for functional data clustering. Spline smoothing or interpolation is common to deal with data of such type. Instead of estimating the best-representing curve for each…
Comparison between multidimensional persistent Betti numbers is often based on the multidimensional matching distance. While this metric is rather simple to define and compute by considering a suitable family of filtering functions…
The machinery of topological data analysis becomes increasingly popular in a broad range of machine learning tasks, ranging from anomaly detection and manifold learning to graph classification. Persistent homology is one of the key…
In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…
Merge trees, a type of topological descriptor, serve to identify and summarize the topological characteristics associated with scalar fields. They present a great potential for the analysis and visualization of time-varying data. First,…
Within the context of topological data analysis, the problems of identifying topological significance and matching signals across datasets are important and useful inferential tasks in many applications. The limitation of existing solutions…
The accurate classification of galaxies in large-sample astrophysical databases of galaxy clusters depends sensitively on the ability to distinguish between morphological types, especially at higher redshifts. This capability can be…
The interleaving distance is arguably the most prominent distance measure in topological data analysis. In this paper, we provide bounds on the computational complexity of determining the interleaving distance in several settings. We show…
The study of the topological structure of complex networks has fascinated researchers for several decades, and today we have a fairly good understanding of the types and reoccurring characteristics of many different complex networks.…
Similarity distance measure between two trajectories is an essential tool to understand patterns in motion, for example, in Human-Robot Interaction or Imitation Learning. The problem has been faced in many fields, from Signal Processing,…