  In Topological Data Analysis, a common way of quantifying the shape of data
is to use a persistence diagram (PD). PDs are multisets of points in
$\mathbb{R}^2$ computed using tools of algebraic topology. However, this
multi-set structure limits the utility of PDs in applications. Therefore, in
recent years efforts have been directed towards extracting informative and
efficient summaries from PDs to broaden the scope of their use for machine
learning tasks. We propose a computationally efficient framework to convert a
PD into a vector in $\mathbb{R}^n$, called a vectorized persistence block
(VPB). We show that our representation possesses many of the desired properties
of vector-based summaries such as stability with respect to input noise, low
computational cost and flexibility. Through simulation studies, we demonstrate
the effectiveness of VPBs in terms of performance and computational cost within
various learning tasks, namely clustering, classification and change point
detection.
