Matthew Thorpe

Optimal Mass Transport: Signal processing and machine-learning applications

Transport-based techniques for signal and data analysis have recently received increased interest. Given their ability to provide accurate generative models for signal intensities and other data distributions, they have been used in a variety of applications, including content-based retrieval, cancer detection, image superresolution, and statistical machine learning, to name a few, and they have been shown to produce state-of-the-art results. Moreover, the geometric characteristics of transport-related metrics have inspired new kinds of algorithms for interpreting the meaning of data distributions. Here, we provide a practical overview of the mathematical underpinnings of mass transport-related methods, including numerical implementation, as well as a review, with demonstrations, of several applications. Software accompanying this article is available from [43].

Convergence of the

The

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-Means Minimization Problem using

-means method is an iterative clustering algorithm which associates each observation with one of

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-Convergence

clusters. It traditionally employs cluster centers in the same space as the observed data. By relaxing this requirement, it is possible to apply the

A Transportation L^p Distance for Signal Analysis

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Convergence and rates for fixed-interval multiple-track smoothing using

-means method to infinite dimensional problems, for example, multiple target tracking and smoothing problems in the presence of unknown data association. Via a

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-means type optimization

-convergence argument, the associated optimization problem is shown to converge in the sense that both the