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Title: A unified framework and fast computation for large-margin tensor classifiers Authors:  Boxiang Wang - University of Iowa (United States) [presenting]
Qing Mai - Florida State University (United States)
Abstract: Tensor data, also known as higher-order arrays, are increasingly common in econometrics, image processing, social network analysis, digital marketing, among many other applications. We focus on binary classification and we formulate a unified framework for tensor large-margin classifiers. The framework includes some popular classifiers such as support vector machine (SVM), Huberized SVM, distance-weighted discrimination, and logistic regression. Despite the success of these classifiers in classifying the vector-valued data, the computation is actually highly intensive. Although it seems natural to extend these methods to the tensor data analysis by applying an alternating minimization-type algorithm, this approach is rather computationally prohibitive. To over such computational burdens, we develop a computationally efficient accelerated proximal gradient descent algorithm to solve the smooth tensor large-margin classifiers and show the convergence. We also develop a novel smoothing algorithm to solve the tensor SVM. In addition, we reveal some connections between our unified framework and the tensor single index model. We use simulations and real applications to demonstrate the performance and efficiency of our proposal.