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 over-fitting 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 ${\ell _{2,1}}$ -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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具有矩阵优化的排序的半监督回归

对开发用于矩阵数据分类的更有效算法的兴趣日益增长。当前，大多数现有的基于向量的分类都涉及向量化过程，这导致两个主要问题。首先，基础结构信息被忽略。其次，矩阵的向量化会导致创建具有潜在非常高维数的向量，当训练数据的数量较少时，这可能导致过度拟合。为避免此类问题，我们提出了一种新的基于矩阵的分类回归算法，该算法将要分类的输入矩阵直接用于为输入矩阵的每个阶学习两个回归矩阵。为了进一步探索歧视信息，我们在两个回归矩阵上添加了一个联合{{\ ell _ {2,1}} $-范数，通过揭示两个回归矩阵中的公共稀疏列，赋予算法优化的回归等级。为了进一步提高分类性能，我们引入了半监督学习过程，该过程利用标记和未标记的数据来增强训练过程。在公共基准数据集上进行的实验表明，即使仅提供了很少的带标签的训练样本，我们的方法也比许多现有的最新分类方法要好。