  A relatively new set of transport-based transforms (CDT, R-CDT, LOT) have
shown their strength and great potential in various image and data processing
tasks such as parametric signal estimation, classification, cancer detection
among many others. It is hence worthwhile to elucidate some of the mathematical
properties that explain the successes of these transforms when they are used as
tools in data analysis, signal processing or data classification. In
particular, we give conditions under which classes of signals that are created
by algebraic generative models are transformed into convex sets by the
transport transforms. Such convexification of the classes simplify the
classification and other data analysis and processing problems when viewed in
the transform domain. More specifically, we study the extent and limitation of
the convexification ability of these transforms under an algebraic generative
modeling framework. We hope that this paper will serve as an introduction to
these transforms and will encourage mathematicians and other researchers to
further explore the theoretical underpinnings and algorithmic tools that will
help understand the successes of these transforms and lay the groundwork for
further successful applications.

Machine Learning;Signal Processing;Machine Learning