有监督核化邻域投影分析算法

Kernel-based Supervised Neighborhood Projection Analysis Algorithm

通过将鉴别邻域嵌入分析算法扩展到非线性场景,提出了一种有监督核化邻域投影分析算法。该算法在目标函数中引入类别标签和线性投影矩阵,并利用核函数处理非线性数据。通过两种不同策略优化目标函数,可将该算法进一步细分为有监督核化邻域投影分析算法一及有监督核化邻域投影分析算法二。其中,在有监督核化邻域投影分析算法一中应用拉普拉斯搜索方向达到了较快的收敛速度并降低了计算复杂度。实验结果表明,所提算法对于复杂的数据流形具有较高的识别率,且与鉴别邻域嵌入分析等相关算法相比在有效性和鲁棒性方面的表现更为出色。

A new algorithm called KSNPA which exhibits a nonlinear form of discriminative elastic embedding （DEE） was proposed. KSNPA integrates class labels and linear projection matrix into the final objective function, as well as uses kernel function to deal with nonlinear embedding situation. According to two different strategies for optimizing the objective function, the algorithm is divided into kernel-based supervised neighborhood projection analysis algorithm 1 （KSNPA1） and supervised neighborhood projection analysis algorithm 2 （KSNPA2）. Furthermore, a deliberately selected search direction, termed as Laplacian Direction, is applied in KSNPA1 for achieving faster convergence rate and lower computational complexit. Experimental results on several databases demonstrate that the proposed algorithm achieves powerful pattern revealing capability for complex manifold data. Moreover, the algorithm is more efficient and robust than DEE and related dimensionality reduction algorithms.