Universal Consistency of Support Tensor Machine

Peide Li, T. Maiti
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引用次数: 5

Abstract

Tensor (multidimensional array) classification problem has become popular in modern applications such as computer vision and spatial-temporal data analysis. The Support Tensor Machine (STM) classifier, which is extended from support vector machine, takes tensor type data as predictors to predict the labels of the data. The distribution-free property of STM highlights its potential in handling different types of data applications. In this work, we provide a theoretical result for the universal consistency of STM. This result guarantees the solid generalization ability of STM with universal tensor based kernel functions. In addition, we give out a way of constructing universal kernel functions for tensor data, which may be helpful for other types of tensor based kernel methods.
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支持张量机的通用一致性
张量(多维数组)分类问题在计算机视觉和时空数据分析等现代应用中得到广泛应用。支持张量机(Support Tensor Machine, STM)分类器是在支持向量机的基础上扩展而来的,它以张量型数据作为预测器来预测数据的标签。STM的无分布特性突出了它在处理不同类型数据应用程序方面的潜力。在这项工作中,我们为STM的普遍一致性提供了一个理论结果。这一结果保证了基于泛张量核函数的STM具有可靠的泛化能力。此外,我们还给出了一种构造张量数据通用核函数的方法,这对其他类型的基于张量的核方法也有一定的借鉴意义。
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