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Abstract:
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Tensor classification problem has become very popular in modern applications such as image recognition and high dimensional spatio-temporal data analysis. Support Tensor Machine classifier, which is extended from support vector machine, takes tensor type data as input and predict the labels of data. The distribution-free property of STM highlights its potential in handling wide varieties of data applications. Training a support tensor machine classifier with compressed tensor can be computational efficient while retaining high classification accuracy. In this work, we develop a STM model with single random projection on tensors balancing between prediction accuracy and computational cost, which we name as Random-Projection based Support Tensor Machine (RPSTM). Both theoretical and numerical results demonstrate the decent performance of RPSTM in high-dimensional tensor classification problems. An upper bound has been constructed within statistical framework to control the generalisation error of RPSTM classifier, which also highlights the trade-off between computational cost and its statistical consistency. The method has been validated by extensivsimulation and real data examples.
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