Transport-based techniques for signal and data analysis have received increased attention recently. 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 super-resolution, and statistical machine learning, to name a few, and shown to produce state of the art results in several applications. 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 tutorial is available at [43].

Discriminating data classes emanating from sensors is an important problem with many applications in science and technology. We describe a new transform for pattern identification that interprets patterns as probability density functions, and has special properties with regards to classification. The transform, which we denote as the Cumulative Distribution Transform (CDT) is invertible, with well defined forward and inverse operations. We show that it can be useful in 'parsing out' variations (confounds) that are 'Lagrangian' (displacement and intensity variations) by converting these to 'Eulerian' (intensity variations) in transform space. This conversion is the basis for our main result that describes when the CDT can allow for linear classification to be possible in transform space. We also describe several properties of the transform and show, with computational experiments that used both real and simulated data, that the CDT can help render a variety of real world problems simpler to solve.

Invertible image representation methods (transforms) are routinely employed as low-level image processing operations based on which feature extraction and recognition algorithms are developed. Most transforms in current use (e.g. Fourier, Wavelet, etc.) are linear transforms, and, by themselves, are unable to substantially simplify the representation of image classes for classification. Here we describe a nonlinear, invertible, low-level image processing transform based on combining the well known Radon transform for image data, and the 1D Cumulative Distribution Transform proposed earlier. We describe a few of the properties of this new transform, and with both theoretical and experimental results show that it can often render certain problems linearly separable in transform space.

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Free space optical communications utilizing orbital angular momentum beams have recently emerged as a new technique for communications with potential for increased channel capacity. Turbulence due to changes in the index of refraction emanating from temperature, humidity, and air flow patterns, however, add nonlinear effects to the received patterns, thus making the demultiplexing task more difficult. Deep learning techniques have been previously been applied to solve the demultiplexing problem as an image classification task. Here we make use of a newly developed theory suggesting a link between image turbulence and photon transport through the continuity equation to describe a method that utilizes a "shallow" learning method instead. The decoding technique is tested and compared against previous approaches using deep convolutional neural networks. Results show that the new method can obtain similar classification accuracies (bit error ratio) at a small fraction (1/90) of the computational cost, thus enabling higher bit rates.

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We present our HABERTOR model for detecting hatespeech in large scale user-generated content. Inspired by the recent success of the BERT model, we propose several modifications to BERT to enhance the performance on the downstream hatespeech classification task. HABERTOR inherits BERT's architecture, but is different in four aspects: (i) it generates its own vocabularies and is pre-trained from the scratch using the largest scale hatespeech dataset; (ii) it consists of Quaternionbased factorized components, resulting in a much smaller number of parameters, faster training and inferencing, as well as less memory usage; (iii) it uses our proposed multisource ensemble heads with a pooling layer for separate input sources, to further enhance its effectiveness; and (iv) it uses a regularized adversarial training with our proposed finegrained and adaptive noise magnitude to enhance its robustness. Through experiments on the large-scale real-world hatespeech dataset with 1.4M annotated comments, we show that HABERTOR works better than 15 state-ofthe-art hatespeech detection methods, including fine-tuning Language Models. In particular, comparing with BERT, our HABERTOR is 4∼5 times faster in the training/inferencing phase, uses less than 1/3 of the memory, and has better performance, even though we pretrain it by using less than 1% of the number of words. Our generalizability analysis shows that HABERTOR transfers well to other unseen hatespeech datasets and is a more efficient and effective alternative to BERT for the hatespeech classification.