基于张量低管道秩的图像多分类模型
Image Multi-Classification Model Based on Tensor Low Tubal Rank
摘要: 传统机器学习方法在对高阶张量数据进行分类时，往往将其转化为低阶格式，由此会产生过拟合问题并且破坏张量的结构。针对上述问题提出一种基于张量低管道秩的多分类模型(LRTMLR)。该模型可以直接对张量格式的图像进行分类，使用由张量–张量积诱导的张量管道秩及相应的张量核范数来处理低秩张量，更好地利用张量结构特点，提高张量格式图像的多分类准确性。在三分类仿真数据集上，LRTMLR的分类准确率较无结构信息(MLR)、带矩阵结构信息(LRMLR)的方法均提升9.6个百分点，在五分类仿真数据集上则分别提升23.2和25.2个百分点。在加州理工大学的101类彩色图像识别数据集的三分类、五分类和十四分类子集上，LRTMLR的分类准确率较MLR分别提升了10.01、25.61和40.78个百分点，较LRMLR分别提升了10.68、25.61和40.78个百分点，与基于CP分解的方法(MCPLR)相比提高了6.47、13.37和27.73个百分点，与基于Tucker分解的方法(MTuLR)相比提高了1.79、12.38和13.71个百分点。并在消融实验中证明了创新的有效性。
Abstract: Traditional machine learning methods often convert high-order tensor data into a lower-order format for classification purposes. However, this approach can result in overfitting and the loss of tensor structure. To address these issues, this paper proposes a multi-classification model based on tensor low-tubal-rank (LRTMLR). The LRTMLR model directly classifies images in tensor format and utilizes the tensor pipe rank induced by tensor-tensor product and corresponding tensor kernel norm to handle low-rank tensors. This enables better utilization of the characteristics of the tensor structure and improves the accuracy of multi-classification for images in tensor format. The classification accuracy of LRTMLR was 9.6 percentage points higher than that of the methods without structure information (MLR) and with matrix structure information (LRMLR) on the three-class simulation data set, and 23.2 and 25.2 percentage points higher on the five-class simulation data set, respectively. On the three-class, five-class and 14-class subsets of the 101-class color image recognition dataset of Caltech University, the classification accuracy of LRTMLR was 10.01, 25.61 and 40.78 percentage points higher than that of MLR, and 10.68, 25.61 and 40.78 percentage points higher than that of LRMLR. Compared with the method based on CP decomposition (MCPLR), it is 6.47, 13.37 and 27.73 percentage points higher, and compared with the method based on Tucker decomposition (MTuLR), it is 1.79, 12.38 and 13.71 percentage points higher. The effectiveness of the innovation is demonstrated in ablation experiments.
文章引用：张家瑞, 胡毓榆, 唐开煜, 樊亚莉. 基于张量低管道秩的图像多分类模型[J]. 建模与仿真, 2024, 13(3): 3980-3997. https://doi.org/10.12677/mos.2024.133362

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