Persistence Codebooks for Topological Data Analysis

Understand

Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs) which are 2D multisets of points.

• Their variable size makes them, however, difficult to combine with typical machine learning workflows.
• In this paper we introduce persistence codebooks, a novel expressive and discriminative fixed-size vectorized representation of PDs.
• To this end, we adapt bag-of-words (BoW), vectors of locally aggregated descriptors (VLAD) and Fischer vectors (FV) for the quantization of PDs.