Tensor classification methods are widely utilized across various research fields, such as pharmaceuticals and computer vision. However, practical scenarios, such as toxicity prediction, may exhibit asymmetric costs stemming from type I and type II errors. Moreover, tensor classification methods frequently involve a greater number of parameters, which, regrettably, are highly prone to capturing imbalances in the sample sizes across different classes within the training dataset. Addressing these concerns, we have developed new tensor classification algorithms under the Neyman-Pearson (NP) paradigm, utilizing the base classifiers Tensor Neural Network (NN) and Tensor Linear Discriminant Analysis (LDA); and we name them T-NN-NP and T-LDA-NP respectively. Extensive numerical studies have val...[ Read more ]

Tensor classification methods are widely utilized across various research fields, such as pharmaceuticals and computer vision. However, practical scenarios, such as toxicity prediction, may exhibit asymmetric costs stemming from type I and type II errors. Moreover, tensor classification methods frequently involve a greater number of parameters, which, regrettably, are highly prone to capturing imbalances in the sample sizes across different classes within the training dataset. Addressing these concerns, we have developed new tensor classification algorithms under the Neyman-Pearson (NP) paradigm, utilizing the base classifiers Tensor Neural Network (NN) and Tensor Linear Discriminant Analysis (LDA); and we name them T-NN-NP and T-LDA-NP respectively. Extensive numerical studies have validated the efficacy of these new classifiers. On the theoretical front, we have derived the NP oracle classifier under the Tensor LDA model, demonstrated the fulfillment of conditional detection conditions under mild assumptions, and established NP oracle inequalities with the type I error bounded at the target and the excess type II error diminishing to 0 as sample size diverges.