  Techniques from computational topology, in particular persistent homology,
are becoming increasingly relevant for data analysis. Their stable metrics
permit the use of many distance-based data analysis methods, such as
multidimensional scaling, while providing a firm theoretical ground. Many
modern machine learning algorithms, however, are based on kernels. This paper
presents persistence indicator functions (PIFs), which summarize persistence
diagrams, i.e., feature descriptors in topological data analysis. PIFs can be
calculated and compared in linear time and have many beneficial properties,
such as the availability of a kernel-based similarity measure. We demonstrate
their usage in common data analysis scenarios, such as confidence set
estimation and classification of complex structured data.
