Related papers: A topological analysis of the space of recipes
We use methods from topological data analysis to study the topological features of certain distributions of string vacua. Topological data analysis is a multi-scale approach used to analyze the topological features of a dataset by…
TDA (topological data analysis) is a relatively new area of research related to importing classical ideas from topology into the realm of data analysis. Under the umbrella term TDA, there falls, in particular, the notion of persistent…
The application of network techniques to the analysis of neural data has greatly improved our ability to quantify and describe these rich interacting systems. Among many important contributions, networks have proven useful in identifying…
In materials science and many other application domains, 3D information can often only be extrapolated by taking 2D slices. In topological data analysis, persistence vineyards have emerged as a powerful tool to take into account topological…
Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not…
Topological Data Analysis (TDA) is the collection of mathematical tools that capture the structure of shapes in data. Despite computational topology and computational geometry, the utilization of TDA in time series and signal processing is…
We combine standard persistent homology with image persistent homology to define a novel way of characterizing shapes and interactions between them. In particular, we introduce: (1) a mixup barcode, which captures geometric-topological…
A central challenge in topological data analysis is the interpretation of barcodes. The classical algebraic-topological approach to interpreting homology classes is to build maps to spaces whose homology carries semantics we understand and…
Topological data analysis has been recently applied to investigate stylistic signatures and trends in musical compositions. A useful tool in this area is Persistent Homology. In this paper, we develop a novel method to represent a weighted…
We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of…
Solving optimization tasks based on functions and losses with a topological flavor is a very active, growing field of research in data science and Topological Data Analysis, with applications in non-convex optimization, statistics and…
In topological data analysis, we want to discern topological and geometric structure of data, and to understand whether or not certain features of data are significant as opposed to simply random noise. While progress has been made on…
A central problem in data-driven scientific inquiry is how to interpret structure in noisy, high-dimensional data. Topological data analysis (TDA) provides a solution via persistent homology, which encodes features of interest as…
The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with…
While topological data analysis has emerged as a powerful paradigm for structural inference, its foundational tools, notably persistent homology and the persistent Laplacian, are frequently insensitive to localized structural fluctuations…
Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…
Persistent homology computes the multiscale topology of a data set by using a sequence of discrete complexes. In this paper, we propose that persistent homology may be a useful tool for studying the structure of the landscape of string…
Multiplexed imaging allows multiple cell types to be simultaneously visualised in a single tissue sample, generating unprecedented amounts of spatially-resolved, biological data. In topological data analysis, persistent homology provides…
The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data…
Topological data analysis (TDA) aims to extract noise-robust features from a data set by examining the number and persistence of holes in its topology. We show that a computational problem closely related to a core task in TDA --…