基于张量分解的鲁棒核低秩表示算法研究

低秩表示算法，如低秩表示（Low-Rank Representation, LRR），鲁棒核低秩表示（Robust Kernel Low-Rank Representation, LRRRKLRR），在处理高维数据方面展现了广阔的应用前景，然而这些方法并不适合高阶数据，传统的低秩表示算法通常只对数据的某一特征属性进行降维。在本文中，我们提出了基于张量分解的鲁棒核低秩表示算法（Kernel Low-Rank Representation by Robust Tensor Decomposition, RTDKLRR），该算法能够处理高阶非线性的张量数据，对噪声更加鲁棒。本文首先对RTDKLRR算法设计目标函数并给出约束条件，其次，设计迭代规则对目标函数进行优化。在合成数据集和真实数据集上的实验结果表明，我们的算法优于同类算法。

Robust Kernel Low-Rank Representation by Tensor Decomposition

Low-rank representation, e.g., low-rank representation (LRR), robust kernel low-rank representation (RKLRR), has shown promising performance in handling high-dimensional data. However, these methods are not applicable to high-order data since the traditional low-rank representation has been usually used to reduce the dimension of data with only one type of feature. In this paper, a kernel low-rank representation by robust tensor decomposition (RTDKLRR) algorithm is proposed, the algorithm could handle high order nonlinear tensor data and more robust to noise. Firstly, the paper designed an objective function for the algorithm with constraint. Then, the iterative rules of the algorithm are derived by optimizing the objective function. Experimental results on synthetic and real-world data sets demonstrate that the proposed algorithm outperforms the compared algorithms on a series of high-order data sets.