Persistent topology of decision boundaries
Persistent topology of decision boundaries
复制标题
决策边界的持久拓扑
DOI：
10.1109/icassp.2015.7178708
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
K. Ramamurthy
中科院分区：
文献类型：
--
作者：
Kush R. Varshney;K. Ramamurthy
拓扑信号处理，特别是持久同调，是一个不断发展的研究领域，用于分析迄今为止应用于未标记数据的数据点集合。在这项工作中，我们考虑了标签数据的情况，并检查了分隔不同标签类的决策边界的拓扑。具体地说，我们提出了一种新的方法来构造决策边界的单纯复形，该复形可以用于理解决策边界的拓扑。此外，我们还举例说明了监督分类问题中核选择的这一理论工作的一个用例。
Topological signal processing, especially persistent homology, is a growing field of study for analyzing sets of data points that has been heretofore applied to unlabeled data. In this work, we consider the case of labeled data and examine the topology of the decision boundary separating different labeled classes. Specifically, we propose a novel approach to construct simplicial complexes of decision boundaries, which can be used to understand their topology. Furthermore, we illustrate one use case for this line of theoretical work in kernel selection for supervised classification problems.