There has been growing interest in developing more effective algorithms for matrix data classification. At present, most of the existing vector-based classifications involve vectorization process, which results in two main problems. First, the underlying structural information is disregarded. Second, the vectorization of a matrix incurs the creation of a vector with potentially very high dimensionality, which may lead to overfitting when the number of training data is small. To avoid such problems, we propose a new matrix-based regression algorithm for classification, in which the input matrices to be classified are directly used to learn two regression matrices for each order of the input matrix. To further explore the discrimination information, we add a joint _ 2,1 -norm on two regression matrices, which endows the algorithm optimized regression rank by uncovering common sparse columns in the two regression matrices. To further boost the classification performance, we incorporate a semisupervised learning process, which leverages both labeled and unlabeled data to enhance the training process. Experiments on public benchmark datasets show that our method outperforms a number of the existing state-of-the-art classification methods even when only few labeled training samples are provided.

中文翻译：

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矩阵数据分类的优化排名的半监督回归


人们对开发更有效的矩阵数据分类算法越来越感兴趣。目前，现有的基于向量的分类大多涉及向量化过程，这导致两个主要问题。首先，忽略了底层的结构信息。其次，矩阵的矢量化会导致创建维度可能非常高的向量，当训练数据数量较小时，这可能会导致过度拟合。为了避免此类问题，我们提出了一种新的基于矩阵的回归算法进行分类，其中直接使用待分类的输入矩阵来学习输入矩阵的每个阶的两个回归矩阵。为了进一步探索判别信息，我们在两个回归矩阵上添加联合 _ 2,1 -范数，通过发现两个回归矩阵中的公共稀疏列来赋予算法优化回归排名。为了进一步提高分类性能，我们采用了半监督学习过程，该过程利用标记和未标记数据来增强训练过程。对公共基准数据集的实验表明，即使只提供很少的标记训练样本，我们的方法也优于许多现有的最先进的分类方法。