An important problem in computational topology is to calculate the homology of a space from samples. In this work, we develop a statistical approach to this problem by calculating the expected rank of an induced map on homology from a sub-sample to the full space. We develop a greedy matroid algorithm for finding an optimal basis for the image of the induced map, and investigate the relationship between this algorithm and the probability of sampling vectors in the image of the induced map.

翻译：计算拓扑学中的一个重要问题是从样本中计算空间的同调。在本文中，我们通过计算从子样本到全空间的诱导同调映射的期望秩，发展了一种统计方法来处理该问题。我们提出了一种贪婪拟阵算法，用于寻找诱导映射像的最优基，并研究了该算法与采样向量落入诱导映射像的概率之间的关系。