Supervised Learning with Indefinite Topological Kernels
This work addresses the problem of integrating complex topological summaries into machine learning for researchers in data analysis, though it appears incremental as it builds on existing kernel methods.
The paper tackled the challenge of using topological data analysis (TDA) in supervised learning by defining a topological exponential kernel that works despite not being positive semi-definite, and demonstrated its effectiveness in regression and classification tasks.
Topological Data Analysis (TDA) is a recent and growing branch of statistics devoted to the study of the shape of the data. In this work we investigate the predictive power of TDA in the context of supervised learning. Since topological summaries, most noticeably the Persistence Diagram, are typically defined in complex spaces, we adopt a kernel approach to translate them into more familiar vector spaces. We define a topological exponential kernel, we characterize it, and we show that, despite not being positive semi-definite, it can be successfully used in regression and classification tasks.