  Persistent homology (PH) provides topological descriptors for geometric data,
such as weighted graphs, which are interpretable, stable to perturbations, and
invariant under, e.g., relabeling. Most applications of PH focus on the
one-parameter case -- where the descriptors summarize the changes in topology
of data as it is filtered by a single quantity of interest -- and there is now
a wide array of methods enabling the use of one-parameter PH descriptors in
data science, which rely on the stable vectorization of these descriptors as
elements of a Hilbert space. Although the multiparameter PH (MPH) of data that
is filtered by several quantities of interest encodes much richer information
than its one-parameter counterpart, the scarceness of stability results for MPH
descriptors has so far limited the available options for the stable
vectorization of MPH. In this paper, we aim to bring together the best of both
worlds by showing how the interpretation of signed barcodes -- a recent family
of MPH descriptors -- as signed measures leads to natural extensions of
vectorization strategies from one parameter to multiple parameters. The
resulting feature vectors are easy to define and to compute, and provably
stable. While, as a proof of concept, we focus on simple choices of signed
barcodes and vectorizations, we already see notable performance improvements
when comparing our feature vectors to state-of-the-art topology-based methods
on various types of data.
