Like The Original Issue Of The Kernel Principal Component Analysis

Kernel methods have been commonly employed in the field of pattern recognition and machine learning which transform training data from the low-dimensional input space to high-dimensional feature space by a nonlinear mapping and take advantage of linear method for feature extraction and pattern classification in feature space. The kernel techniques are employed skillfully in order to avoid complex computation as well as the curse of dimensionality. Image de-noising based on KPCA actually is a kind of reconstruction process from high-dimensional feature space to low-dimensional space which is mainly related to two stages, the first one is sample reconstruction in high-dimensional feature space, second is the problem of approximately finding pre-image of sample in low-dimensional space.For non-isomorphic problem between feature space and input space, in other words, among samples have close proximity in high dimensional space don’t necessarily have preimage in low dimensional space. In this paper, K-nearest neighbor and Iterative technique will be fused into the process of pre-image computation, which is called KNN-Preimage method. Pre-image reconstruction selects the training samples according to K-nearest neighbor in the input space, fusing iterative technique could effectively avoid the non-isomorphic problem between the input space and feature space. Experimental analysis and comparison on the USPS dataset demonstrates the feasibility and effectiveness of the proposed method.The Preimage reconstruction process based on Newton iterative optimization for the random initialization is easy to fall into local optimal value and numerical characteristics of instability. To tackle this problem, the integration of the inner product of algebraic methods is proposed, which selects the average of some sample points as a initialization point. Finally, the experimental results show that the pre-image reconstruction fusing the inner product is not only able to produce a lower number of iterations, but also superior to the original method and has higher stability.