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A relatively new set of transport-based transforms (CDT, R-CDT, LOT) haveshown their strength and great potential in various image and data processingtasks such as parametric signal estimation, classification, cancer detectionamong many others. It is hence worthwhile to elucidate some of the mathematicalproperties that explain the successes of these transforms when they are used astools in data analysis, signal processing or data classification. Inparticular, we give conditions under which classes of signals that are createdby algebraic generative models are transformed into convex sets by thetransport transforms. Such convexification of the classes simplify theclassification and other data analysis and processing problems when viewed inthe transform domain. More specifically, we study the extent and limitation ofthe convexification ability of these transforms under an algebraic generativemodeling framework. We hope that this paper will serve as an introduction tothese transforms and will encourage mathematicians and other researchers tofurther explore the theoretical underpinnings and algorithmic tools that willhelp understand the successes of these transforms and lay the groundwork forfurther successful applications.

Partitioning signal classes using transport transforms for data analysis and machine learning