Topological data analysis, such as persistent homology has shown beneficial properties for machine learning in many tasks. Topological representations, such as the persistence diagram (PD), however, have a complex structure (multiset of intervals) which makes it difficult to combine with typical machine learning workflows. We present novel compact fixed-size vectorial representations of PDs based on clustering and bag of words encodings that cope well with the inherent sparsity of PDs. Our novel representations outperform state-of-the-art approaches from topological data analysis and are computationally more efficient.
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