Topological data analysis
L Wasserman - Annual Review of Statistics and Its Application, 2018 - annualreviews.org
Topological data analysis (TDA) can broadly be described as a collection of data analysis
methods that find structure in data. These methods include clustering, manifold estimation …
methods that find structure in data. These methods include clustering, manifold estimation …
Two's company, three (or more) is a simplex: Algebraic-topological tools for understanding higher-order structure in neural data
The language of graph theory, or network science, has proven to be an exceptional tool for
addressing myriad problems in neuroscience. Yet, the use of networks is predicated on a …
addressing myriad problems in neuroscience. Yet, the use of networks is predicated on a …
Persistence images: A stable vector representation of persistent homology
Many data sets can be viewed as a noisy sampling of an underlying space, and tools from
topological data analysis can characterize this structure for the purpose of knowledge …
topological data analysis can characterize this structure for the purpose of knowledge …
[PDF][PDF] A roadmap for the computation of persistent homology
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 …
qualitative features of data that persist across multiple scales. It is robust to perturbations of …
[PDF][PDF] Statistical topological data analysis using persistence landscapes.
P Bubenik - J. Mach. Learn. Res., 2015 - jmlr.org
We define a new topological summary for data that we call the persistence landscape. Since
this summary lies in a vector space, it is easy to combine with tools from statistics and …
this summary lies in a vector space, it is easy to combine with tools from statistics and …
A stable multi-scale kernel for topological machine learning
Topological data analysis offers a rich source of valuable information to study vision
problems. Yet, so far we lack a theoretically sound connection to popular kernel-based …
problems. Yet, so far we lack a theoretically sound connection to popular kernel-based …
A review on cognitive and brain endophenotypes that may be common in autism spectrum disorder and attention-deficit/hyperactivity disorder and facilitate the search …
We propose to bring together the hitherto rather separate research fields of autism spectrum
disorder (ASD) and attention-deficit/hyperactivity disorder (ADHD), and argue that by …
disorder (ASD) and attention-deficit/hyperactivity disorder (ADHD), and argue that by …
Persistent brain network homology from the perspective of dendrogram
The brain network is usually constructed by estimating the connectivity matrix and
thresholding it at an arbitrary level. The problem with this standard method is that we do not …
thresholding it at an arbitrary level. The problem with this standard method is that we do not …
A persistence landscapes toolbox for topological statistics
Topological data analysis provides a multiscale description of the geometry and topology of
quantitative data. The persistence landscape is a topological summary that can be easily …
quantitative data. The persistence landscape is a topological summary that can be easily …
[图书][B] Nonparametric statistics on manifolds and their applications to object data analysis
V Patrangenaru, L Ellingson - 2016 - api.taylorfrancis.com
The main objective of this book is to introduce the reader to a new way of analyzing object
data, that primarily takes into account the geometry of the spaces of objects measured on the …
data, that primarily takes into account the geometry of the spaces of objects measured on the …