一种基于数值逼近的KPCA改进算法

核方法广泛应用于模式识别等领域,但其存在着特征抽取效率和样本集的大小成反比的瓶颈问题.因此提出一种基于数值逼近的方法确定虚拟样本矢量,以此代替训练样本,提高KPCA(Kernel Principle Component Analysis)特征抽取效率.在确定虚拟样本矢量时,只需将样本矢量的初值设定为随机变量,算法实现简单、高效.在基准数据集上的实验结果显示该算法优于同类算法.

Improved KPCA algorithm based on numerical approximation

Though kernel methods have been widely used for pattern recognition,they suffer from the problem that the extraction efficiency is in inverse proportion to the size of the training sample set.To solve it,we propose a novel improvement to Kernel Principle Component Analysis (KPCA) based on numerical approximation.The method is on the base of the assumption that the discriminant vector in the feature space can be approximately expressed by a certain linear combination of some constructed virtual sample vectors.We determine these virtual sample vectors one by one by using a very simple and computationally efficient iterative algorithm.When they are dissimilar to each other,this set is able to well replace the role of the whole training sample set in expressing the discriminant vector in the feature space.It is remarkable that the determined virtual sample vectors lead to a good improvement to KPCA,which allows an efficient feature extraction procedure to be obtained.Also,we need only to set the initial values of the virtual sample vectors to random values.The experiments on two benchmark datasets show that our method can achieve the goal of efficient feature extraction as well as good and stable classification accuracy.