Study On Feature Extraction Based On Manifold Learning

Feature extraction is one of the most basic problems in pattern recognition.For image recognition tasks,extracting the effective image features is a crucial step.The essence of feature extraction is to reduce a high-dimensional original sample space to a low-dimensional feature subspace that is benefit to classification.In the passed decade years,many correlated algorithms have been proposed to solve this problem,for example,Principle Component Analysis(PCA),Linear Discriminant Analysis(LDA) and manifold learning.However,the classical linear models may fail to discover nonlinear data structures;manifold learning algorithms might not be suitable for real world applications,because they yield maps that are defined only on the training data points,and are also complex to compute.Along this direction,there is considerable interest in using linear methods,inspired by the geometric intuition of manifold learning,to fred the nonlinear structure of data set,called linear manifold learning.In this paper,classical linear methods,linear and nonlinear manifold learning algorithms are all deeply analyzed.Furthermore,we develop a supervised dimensionality reduction method,Lorentzian Discriminant Projection(LDP),for discriminant analysis and classification.Our method represents the structures of sample data by a manifold,which is furnished with a Lorentzian metric tensor.Different from classic feature extraction techniques, LDP uses distances from points to their within-class neighbors and global geometric centroid to model a new manifold to detect the intrinsic local and global geometric structures of data set.In this way,both the geometry of group of classes and global data structures can be learnt from the Lorentzian metric tensor.Thus feature extraction in original sample space reduces to metric learning on Lorentzian manifold.We give the experimental results on real world face recognition and handwriting digital data analysis,which demonstrate the effectiveness of our proposed method.