带有错误标签的张量数据的稳健多分类模型

Robust Multiclass Models for Mislabeled Tensor Data

摘要: 传统机器学习方法大多都是基于正确标签的训练数据进行监督学习，但实际观测到的训练数据标签极可能受到污染，而错误标签的存在会导致传统模型产生有偏估计。现存的关于错误标签的稳健模型往往基于向量数据进行分类，面对存在错误标签的高阶张量数据时只能将其转化为低阶格式，由此产生过拟合问题且破坏张量结构。针对上述问题提出一种稳健的张量多分类模型(RMLTMLR)，基于最小γ-散度估计、张量管道秩及相应的核范数来处理带有错误标签的低秩张量，在利用张量结构特点的同时使模型对污染标签具有稳健性，提高多分类准确率。进行的大量实验表明RMLTMLR模型在不同类别和污染程度的张量数据上有着优良的分类效果，与非稳健的模型相比，分类准确率显著提升。

Abstract: Most of the traditional machine learning methods perform supervised learning based on training data with correct labels. However, the actual observed training data labels are likely to be contaminated, and the existence of wrong labels will lead to biased estimates of the traditional model. The existing robust models for mislabel classification are often based on vector data. When facing high-order tensor data with mislabels, they have to transform it into low-order format, resulting in overfitting problem and damage to the tensor structure. Aiming at the above problems, a robust tensor multi-classification model (RMLTMLR) is proposed, which is based on minimum γ-divergence estimation, tensor tubal rank and the corresponding nuclear norm to deal with low-rank tensors with wrong labels. The model is robust to contaminated labels while taking advantage of the structural characteristics of tensors, and improves the accuracy of multi-classification. A large number of experiments show that the RMLTMLR model has excellent classification effects on tensor data with different categories and pollution levels, and the classification accuracy is significantly improved compared with the non-robust model.