High-dimensional small sample size problems exist in the real world, which significantly increases the difficulty of data processing. In this paper, we propose a kernel-based within class collaborative preserving discriminant projection method to reduce data dimensionality. In order to deal with nonlinear problems and improve the discrimination of the projection subspace, the proposed method preserves the collaborative reconstruction relationship of the same class samples in the kernel space, and pursuits maximizing the between class scatter. A two-step eigenvalue decomposition method is used to stably obtain the optimal discriminant projection matrix. Moreover, simulation experiments show that, even in low dimensions and small sample size, the proposed method can achieve high recognition accuracy.

中文翻译：

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一种有前途的非线性降维方法：基于内核的类内协同保留判别投影

现实世界中存在高维小样本问题，大大增加了数据处理的难度。在本文中，我们提出了一种基于内核的类内协同保留判别投影方法来降低数据维度。为了处理非线性问题，提高投影子空间的判别能力，该方法在核空间中保留了同类样本的协同重建关系，追求类间散布度的最大化。采用两步特征值分解方法稳定得到最优判别投影矩阵。此外，仿真实验表明，即使在低维度和小样本量的情况下，所提出的方法也能达到较高的识别精度。