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Part 4: MAKE-Topology; International audience; This is the report of a preliminary study, in which a new coding of persistence diagrams and two relevance feedback methods, designed for use with persistent homology, are combined. The coding consists in substituting persistence diagrams with complex polynomials; these are “shortened”, in the sense that only the first few coefficients are used. The relevance feedback methods play on the user’s feedback for changing the impact of the different filtering functions in determining the output.

Part 4: MAKE-Topology; International audience; The use of group equivariant operators is becoming more and more important in machine learning and topological data analysis. In this paper we introduce a new method to build G-equivariant non-expansive operators from a set $$\varPhi $$ of bounded and continuous functions $$\varphi :X\rightarrow \mathbb {R}$$ to $$\varPhi $$ itself, where X is a topological space and G is a subgroup of the group of all self-homeomorphisms of X.