A Comparative Study of Machine Learning Methods for Persistence Diagrams.
A Comparative Study of Machine Learning Methods for Persistence Diagrams.
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DOI：
10.3389/frai.2021.681174
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发表时间：
2021
影响因子：
4
通讯作者：
Perea JA
中科院分区：
文献类型：
--
作者：
Barnes D;Polanco L;Perea JA
目前存在许多不同的特征化方法，即将持久性图映射到欧几里得空间的过程，其目标是最大限度地保留结构。然而，据我们所知，目前还没有对现有方法进行系统比较，也没有标准化的测试数据集集合。本文对几种此类方法进行了比较研究。特别是，我们回顾、评估和比较了稳定的多尺度内核、持久性景观、持久性图像、代数函数环、模板函数和自适应模板系统。使用这些特征提取方法，我们在五个数据集上应用和比较流行的机器学习方法：MNIST、非刚性 3D 人体模型的形状检索 (SHREC14)、蛋白质分类基准集合（蛋白质）中的提取、MPEG7 形状匹配和 HAM10000 皮肤病变数据集。这些数据集通常用于上述特征化方法中，我们使用它们来评估实际应用中的预测效用。
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.