A Topological Machine Learning Pipeline for Classification

被引:6
|
作者
Conti, Francesco [1 ,2 ]
Moroni, Davide [2 ]
Pascali, Maria Antonietta [2 ]
机构
[1] Univ Pisa, Dept Math, I-56126 Pisa, Italy
[2] Natl Res Council Italy CNR, Inst Informat Sci & Technol A Faedo, I-56124 Pisa, Italy
关键词
topological machine learning; persistent homology; classification; vectorization; SIZE FUNCTIONS; REGRESSION; SELECTION;
D O I
10.3390/math10173086
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this work, we develop a pipeline that associates Persistence Diagrams to digital data via the most appropriate filtration for the type of data considered. Using a grid search approach, this pipeline determines optimal representation methods and parameters. The development of such a topological pipeline for Machine Learning involves two crucial steps that strongly affect its performance: firstly, digital data must be represented as an algebraic object with a proper associated filtration in order to compute its topological summary, the Persistence Diagram. Secondly, the persistence diagram must be transformed with suitable representation methods in order to be introduced in a Machine Learning algorithm. We assess the performance of our pipeline, and in parallel, we compare the different representation methods on popular benchmark datasets. This work is a first step toward both an easy and ready-to-use pipeline for data classification using persistent homology and Machine Learning, and to understand the theoretical reasons why, given a dataset and a task to be performed, a pair (filtration, topological representation) is better than another.
引用
收藏
页数:33
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