Computing multiparameter persistent homology through a discrete Morse-based approach

摘要: Abstract Persistent homology allows for tracking topological features, like loops, holes and their higher-dimensional analogues, along a single-parameter family of nested shapes. Computing descriptors complex data characterized by multiple parameters is becoming major challenging task in several applications, including physics, chemistry, medicine, geography. Multiparameter persistent generalizes to allow the exploration analysis shapes endowed with filtering functions. Still, computational constraints prevent multiparameter be feasible tool analyzing large size sets. We consider discrete Morse theory as strategy reduce computation working on reduced dataset. propose new preprocessing algorithm, well suited parallel distributed implementations, we provide first evaluation impact computations.