29 research outputs found
Delay Parameter Selection in Permutation Entropy Using Topological Data Analysis
Permutation Entropy (PE) is a powerful tool for quantifying the
predictability of a sequence which includes measuring the regularity of a time
series. Despite its successful application in a variety of scientific domains,
PE requires a judicious choice of the delay parameter . While another
parameter of interest in PE is the motif dimension , Typically is
selected between and with or giving optimal results for the
majority of systems. Therefore, in this work we focus solely on choosing the
delay parameter. Selecting is often accomplished using trial and error
guided by the expertise of domain scientists. However, in this paper, we show
that persistent homology, the flag ship tool from Topological Data Analysis
(TDA) toolset, provides an approach for the automatic selection of . We
evaluate the successful identification of a suitable from our TDA-based
approach by comparing our results to a variety of examples in published
literature
Adaptive Partitioning for Template Functions on Persistence Diagrams
As the field of Topological Data Analysis continues to show success in theory
and in applications, there has been increasing interest in using tools from
this field with methods for machine learning. Using persistent homology,
specifically persistence diagrams, as inputs to machine learning techniques
requires some mathematical creativity. The space of persistence diagrams does
not have the desirable properties for machine learning, thus methods such as
kernel methods and vectorization methods have been developed. One such
featurization of persistence diagrams by Perea, Munch and Khasawneh uses
continuous, compactly supported functions, referred to as "template functions,"
which results in a stable vector representation of the persistence diagram. In
this paper, we provide a method of adaptively partitioning persistence diagrams
to improve these featurizations based on localized information in the diagrams.
Additionally, we provide a framework to adaptively select parameters required
for the template functions in order to best utilize the partitioning method. We
present results for application to example data sets comparing classification
results between template function featurizations with and without partitioning,
in addition to other methods from the literature.Comment: To appear in proceedings of IEEE ICMLA 201