An Adaptive Robust Kernel Principal Component Analysis Algorithm

In pattern recognition fields, as a key process in pattern recognition system, character selection and extraction transform the origin data in order to find its essential character for pattern recognition.Principal Component Analysis (PCA), as a rudimental method of character selection and extraction, is widely used in statistic data analysis, communication theory, pattern recognition and image processing. Kernel PCA, which is an improved method from PCA, is easier to extract nonlinear character from sample set. However, outliers in the sample set will take much effect on the extracted principal component, even though the proportion of them is small. In pattern recognition fields, inaccurate principal component will affect final recognition outcome. So, it is need to discuss the robust of Kernel PCA.At first, because only the sample set's second order statistic character is considered by PCA, Independent Component Analysis (ICA) can process high order statistic character of sample set. In view of characteristic of small moving targets in infrared image, the sequence images with complicated background and moving small targets are regarded as mixed-signals.Then the Fast Independent Component Analysis (Fast ICA) method is proposed and applied to separate the independent components from the mixed-signals. Experimental results show that FastICA method is of quickness, robustness and strong applicability.Secondly, error between origin samples and reconstruction samples in feature space is discussed, and then minimization of the square representation error is proved as another equivalent definition of kernel PCA.Based on above discussion, gradient descent method is used to find the minimum of square error function and iterative form's Kernel PCA algorithm is developed. We can also change square error function and analysis each step's reconstruction error, then the algorithm can change the learning parameter adaptively according to reconstruction error. Thus robust Kernel PCA algorithm is developed.Experiment results approve that this algorithm can reduce the effect of outliers on principal component effectively.