As the cornerstone for joint dimension reduction and feature extraction, extensive linear projection algorithms were proposed to fit various requirements. When being applied to image data, however, existing methods suffer from representation deficiency since the multi-way structure of the data is (partially) neglected. To solve this problem, we propose a novel Low-Rank Preserving t-Linear Projection (LRP-tP) model that preserves the intrinsic structure of the image data using t-product-based operations. The proposed model advances in four aspects: 1) LRP-tP learns the t-linear projection directly from the tensorial dataset so as to exploit the correlation among the multi-way data structure simultaneously; 2) to cope with the widely spread data errors, e.g., noise and corruptions, the robustness of LRP-tP is enhanced via self-representation learning; 3) LRP-tP is endowed with good discriminative ability by integrating the empirical classification error into the learning procedure; 4) an adaptive graph considering the similarity and locality of the data is jointly learned to precisely portray the data affinity. We devise an efficient algorithm to solve the proposed LRP-tP model using the alternating direction method of multipliers. Extensive experiments on image feature extraction have demonstrated the superiority of LRP-tP compared to the state-of-the-arts.

中文翻译：

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低秩保留t线性投影以实现鲁棒的图像特征提取

作为减少关节尺寸和提取特征的基础，提出了广泛的线性投影算法以适应各种要求。然而，当应用于图像数据时，由于（部分地）忽略了数据的多路结构，因此现有方法存在表示缺陷。为解决此问题，我们提出了一种新颖的低秩保留t线性投影（LRP-tP）模型，该模型使用基于t乘积的运算来保留图像数据的固有结构。提出的模型在四个方面进行了改进：1）LRP-tP直接从张量数据集中学习t线性投影，以便同时利用多路数据结构之间的相关性。2）为应对广泛传播的数据错误，例如噪声和损坏，通过自我表征学习增强了LRP-tP的鲁棒性；3）通过将经验分类误差纳入学习过程，使LRP-tP具有很好的判别能力。4）共同学习考虑数据相似性和局部性的自适应图，以精确地描绘数据亲和力。我们设计了一种有效的算法，使用乘法器的交替方向方法来求解所提出的LRP-tP模型。图像特征提取方面的大量实验表明，与最新技术相比，LRP-tP具有优越性。我们设计了一种有效的算法，使用乘法器的交替方向方法来求解所提出的LRP-tP模型。图像特征提取方面的大量实验表明，与最新技术相比，LRP-tP具有优越性。我们设计了一种有效的算法，使用乘法器的交替方向方法来求解所提出的LRP-tP模型。图像特征提取方面的大量实验表明，与最新技术相比，LRP-tP具有优越性。