论文标题
使用增强持久图的有效图形重建和表示
Efficient Graph Reconstruction and Representation Using Augmented Persistence Diagrams
论文作者
论文摘要
持续的同源性是可以通过量化同源特征来总结数据形状的工具。当数据是$ \ mathbb {r}^d $中的对象时，（增强）持续的差异转换（（a）pht）是一个持久图的家族，通过周围空间中的方向进行了参数。在理解PHT的最新进步中，使用重建框架，以找到有限的一组忠实代表形状的方向，这既具有理论和实际利益。在本文中，我们改进了这一结果，并提出了图形的改进算法 - 并且更通常是单骨骼的重建。改进是在重建边缘，我们使用径向二进制（多）搜索。所采用的二进制搜索可以利用以下事实：边缘可以相对于参考平面径向排序，这是图形所独有的特征。
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of persistence diagrams, parameterized by directions in the ambient space. A recent advance in understanding the PHT used the framework of reconstruction in order to find finite a set of directions to faithfully represent the shape, a result that is of both theoretical and practical interest. In this paper, we improve upon this result and present an improved algorithm for graph -- and, more generally one-skeleton -- reconstruction. The improvement comes in reconstructing the edges, where we use a radial binary (multi-)search. The binary search employed takes advantage of the fact that the edges can be ordered radially with respect to a reference plane, a feature unique to graphs.
