| Because of its huge amount of original data and the mixed useless noises, pattern recognition problems that exist in many research areas are difficult to be solved satisfactorily both in precision and in efficiency by using classical algorithms. With the precondition that the geometrical relationship and the distance measurement among data be kept unchanged, we can map manifold corresponding to the original data in high dimension space into that in low dimension space so that not only is the data quantity reduced in future relative calculation, but also disturbance of the noise is removed, which highly improved the precision and efficiency of pattern recognition. We will focus on this manifold-learning algorithm in this paper.The manifold-learning algorithm can be divided into two classes– linear and nonlinear. The linear manifold-learning algorithms represented by PCA, with their substantial mathematical foundation and simple implementation, but they are not able to show complex nonlinear manifold structure with their linear essence, which gives rise to nonlinear manifold-learning algorithms such as Isomap, SIE etc. Experiments show that adding manifold-learning to the process of pattern recognition does not cause loss in precision, indeed its precision is better than those without manifold-learning and its efficiency is remarkably improved.Classical manifold-learning algorithms can not choose right neighborhood set when dealing with data set with high variation in local manifold. Therefore, by using Locally Principal Direction Reconstruction (LPDR) to intensify recognition of the neighborhood set and mingling with the uniform goal of the manifold-learning algorithms such as Laplacian Eigenmaps, we get Supervised Locally Principal Direction preservation Kernel construction (SLPDK). Experiments show that SLPDK is always more precise than other algorithms in data classification, especially data set with high variation in local manifold, and its relative performance and standard deviation is better than others'. |
