Study Of Manifold Learning Based Dimension Reduction Methods And Applications

Nowadays,more and more data show the property of high dimensionality in information world,which will result in "curse of dimensionality" when classifying them directly.In order to overcome the problem,dimensionality reduction methods are always adopted to deal with the high dimensional data.In this thesis,on the basis of manifold learning methods,two supervised dimensionality reduction methods are presented for high dimensional data feature extraction and classification,where class labels are taken into account.Experimental results validates that the proposed methods can gain comparatively well classification performance.The main works of the thesis are listed below:(1)A manifold learning method based on sparse reconstruction Fisher criterion is brought forward.In the proposed method,for any point,all intra-class data and some nearest inter-class data are selected,by which it can be reconstructed sparsely.Moreover,the intra-class scatter and the inter-class scatter,which individually characterize intra-class data clustering and inter-class data separability,can be reasoned.At last an objective function with Fisher formation can be modeled to explore a low dimensional subspace,where intra-class data will be more closely located and inter-class will be more apart.(2)A constrained neighborhood discriminant embedding(CDNE)method is proposed.On the one hand,class information is introduced to constructed an intra-class neighborhood graph and an inter-class neighborhood graph,from which a marginal metric is defined to quantify the apartness between different labeled data;on the other hand,a local statistical uncorrelation using locally linear reconstruction technique is modeled as constraint.Finally,an objective function can be constructed to explore a low dimensional subspace with local statistical uncorrelation,where the marginal metric will be maximized.