Tools of Topological Data Analysis provide stable summaries encapsulating the
shape of the considered data. Persistent homology, the most standard and well
studied data summary, suffers a number of limitations; its computations are
hard to distribute, it is hard to generalize to multifiltrations and is
computationally prohibitive for big data-sets. In this paper we study the
concept of Euler Characteristics Curves, for one parameter filtrations and
Euler Characteristic Profiles, for multi-parameter filtrations. While being a
weaker invariant in one dimension, we show that Euler Characteristic based
approaches do not possess some handicaps of persistent homology; we show
efficient algorithms to compute them in a distributed way, their generalization
to multifiltrations and practical applicability for big data problems. In
addition we show that the Euler Curves and Profiles enjoys certain type of
stability which makes them robust tool in data analysis. Lastly, to show their
practical applicability, multiple use-cases are considered.Comment: 32 pages, 19 figures. Added remark on multicritical filtrations in
section 4, typos correcte