Linear regression is a supervised method that has been widely used in classification tasks. In order to apply linear regression to classification tasks, a technique for relaxing regression targets was proposed. However, methods based on this technique ignore the pressure on a single transformation matrix due to the complex information contained in the data. A single transformation matrix in this case is too strict to provide a flexible projection, thus it is necessary to adopt relaxation on transformation matrix. This paper proposes a double transformation matrices learning method based on latent low-rank feature extraction. The core idea is to use double transformation matrices for relaxation, and jointly projecting the learned principal and salient features from two directions into the label space, which can share the pressure of a single transformation matrix. Firstly, the low-rank features are learned by the latent low rank representation (LatLRR) method which processes the original data from two directions. In this process, sparse noise is also separated, which alleviates its interference on projection learning to some extent. Then, two transformation matrices are introduced to process the two features separately, and the information useful for the classification is extracted. Finally, the two transformation matrices can be easily obtained by alternate optimization methods. Through such processing, even when a large amount of redundant information is contained in samples, our method can also obtain projection results that are easy to classify. Experiments on multiple data sets demonstrate the effectiveness of our approach for classification, especially for complex scenarios.

本文提出了一种基于隐含低秩特征提取的双重转换矩阵学习方法，通过在两个方向上将学习的主要和显著特征共同投影到标签空间中，从而避免了单个转换矩阵在处理数据时太过严格所限制的灵活性。实验表明，我们的方法对于处理分类任务特别是在复杂情景下的样本降维有着良好的效果。

基于低秩特征的双变换矩阵学习用于图像分类