With the development of science and technology, more and more data are collected.The data volume booming can be reflected in two ways,the increase of the number and the dimension of observations.Traditional statistical methods can deal well with the former problem.However, these methods suffer from the later problem, which can be termed as the curse of dimensionality.It is essential to provide an effective method to deal with this problem. Subspace learning methods are effective tools to deal with the curse of dimensionality.A subspace learning algorithm projects the original high dimensional data space to a low dimensional subspace, wherein specific statistical properties can be well preserved. Subspace learning sheds light both on classification and regression problems. This paper focuses on some subspace learning methods, the main contributions are as follows: 1.This thesis first introduces the classical linear and nonlinear subspace learning methods, such as principal component analysis(PCA), Fisher's linear discriminant analysis (LDA), multi-dimension scaling and locally linear embedding algorithms and so on, then analysis its advantages and disadvantages. 2.Two dimensional discriminant analysis (2DLDA) extends the traditional linear discriminant analysis to matrix data representation. However, this method suffers from the non-convergent issue that the training stage is not convergent. This greatly limits the practical application of 2DLDA. In order to solve this problem, this thesis proposes a novel method to solve this problem. We employ evolutionary computation methods to provide a convergent training stage for 2DLDA. Based on mutation and combination operators, the evolutionary computation method can iteratively search the local optimal or global optimal solutions from randomly generated projection matrixes. Experiments on ORL and extended YaleB face databases prove the effectiveness of our method. 3.Augmented reality is one of the most important applications of computer vision, its purpose is to combine the virtual computer-generated imagery and the real-world environment to give people a sense of immersive. The augmented reality system includes feature detection module, feature matching module and camera calibration module and so on. Feature matching module plays a very important role in AR system. Subspace learning methods can be used for feature matching. PCA can be used for interest point descriptor. The neighbor region of the inter...
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