Vectorization of persistence barcode with applications in pattern classification of porous structures

Abstract

Persistence barcode is a topological summary for persistent homology to exhibit topological features with different persistence. Persistence rank function (PRF), derived from persistence barcode, organizes persistence Betti numbers in the form of an integer-valued function. To obtain topological patterns of objects such as point clouds represented by finite-dimensional vectors for machine learning classification tasks, the vectorizing representations of barcodes is generated via decomposing PRF on a system of Haar basis. Theoretically, the generated vectorizing representation is proved to have 1-Wasserstein stability. In practice, to reduce training time and achieve better results, a technique of dimensionality reduction through out-of-sample mapping in supervised manifold learning is used to generate a low-dimensional vector. Experiments demonstrate that the representation is effective for capturing the topological patterns of data sets. Moreover, the classification of porous structures has become an essential problem in the fields such as material science in recent decades. The proposed method is successfully applied to distinguish porous structures on a novel data set of porous models.