Abstract
Many and varied methods currently exist for featurization, which is the process of mapping persistence diagrams to Euclidean space, with the goal of maximally preserving structure. However, and to our knowledge, there are presently no methodical comparisons of existing approaches, nor a standardized collection of test data sets. This paper provides a comparative study of several such methods. In particular, we review, evaluate, and compare the stable multi-scale kernel, persistence landscapes, persistence images, the ring of algebraic functions, template functions, and adaptive template systems. Using these approaches for feature extraction, we apply and compare popular machine learning methods on five data sets: MNIST, Shape retrieval of non-rigid 3D Human Models (SHREC14), extracts from the Protein Classification Benchmark Collection (Protein), MPEG7 shape matching, and HAM10000 skin lesion data set. These data sets are commonly used in the above methods for featurization, and we use them to evaluate predictive utility in real-world applications.
Highlights
Persistence diagrams are an increasingly useful shape descriptor from Topological Data Analysis
To compute Multi-Scale Kernel as given by Eq 6 we require pairs of persistent diagrams. Since this multi-scale kernel provides a notion of similarity between persistent diagrams (Reininghaus et al, 2015) we require it to be computed between diagrams corresponding to the same dimension homology and method type
The kernel matrix that corresponds to the 0-dimensional homology of a data set is computed using the persistence scale space kernel between two sets of persistence diagrams that represent the 0-dimensional homology
Summary
Persistence diagrams are an increasingly useful shape descriptor from Topological Data Analysis. One of their more popular uses to date has been as features for machine learning tasks, with success in several applications to science and engineering. We provide the necessary background and mathematical justification for six different methods (in chronological order): the Multi-Scale Kernel, Persistence Landscapes, Persistence Images, Adcock-Carlsson Coordinates, Template Systems, and Adaptive Template Systems. To thoroughly evaluate these methods, we have researched five different data sets and the relevant methods to compute persistence diagrams from them. Both S2 and M are connected, while S2 is orientable but
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
