基于核函数的稳健线性嵌入方法

LLE算法是一种新的非监督学习方法，主要针对非线性降维问题。针对该算法存在的缺点，提出了一种基于核函数的稳健线性嵌入方法，该方法通过引进核函数来优化算法邻域点的求解；在特征空间中，修正权值矩阵W，进行降噪处理，经过推导，最终将实际的子空间计算归结为标准的特征值分解问题。采用最小近邻分类器估算识别率。在Yale人脸库以及AT&T人脸库的测试结果表明，在姿态、光照、表情、训练样本数目变化的情况下，改进的算法都具有较好的识别率。

Robust Linear Embeding Based on a Kernel Function

As a new unsupervised learning method, Local Linear Embedding algorithm(LLE)aims at reducing the nonlinear dimensionality.Since the local linear embedding method has many disadvantages, a new method, namely robust linear embedding method based on a kernel function, is presented to solve this problem. Firstly, the kernel function is utilized to adjust the Euclidean distance between data points, so the new method can improve the performance and the range of application of LLE. Secondly, the new method using the improved W is selected because it is insensitive to noise. It is shown that the actual computation of the subspace is reduced to a standard eigenvalue problem. The proposed method was tested and evaluated in the Yale face database and AT&T face database. Nearest neighborhood (NN)algorithm was used to construct classifiers. The experimental results showed that the improved algorithm has good performance when pose, lighting condition, face expression and train sample number change.