Study Of Feature Extraction And Classification Based On Manifold Margin

At present,machine learning is a process of prediction according to data information,and the key step is dimensionality reduction.Compared with other dimensionality reduction methods,feature extraction is more capable of mining the essential information of the data.Because many actual data cannot be linearly separated,the method of nonlinear feature extraction is more worthy of study.Among them,manifold learning has become a research hotspot because of its local characteristic of Euclidean space.However,some manifold learning methods show some shortcomings,such as not using the category information of the data and not selecting the appropriate distance measure.In order to overcome these shortcomings,this thesis mainly proposes two feature extraction methods.The main work of this thesis is summarized as following two aspects:(1)To solve the problem of missing category information,this thesis proposes a locally linear representation manifold margin(LLRMM)method.Firstly,the category information is used to construct the within-manifold graph,the between-manifold graph,and the total-manifold graph,then the corresponding three scatters and manifold margin are calculated.Finally,the optimization problems of maximizing manifold margin and minimizing global representation errors are solved.(2)To solve the problem of inappropriate distance measure.,this thesis proposes a Log-Euclidean distance metric learning(LEDML)method.Firstly,the scatter of each category manifold is calculated,then the sum of the distances between manifolds is calculated.The measure of distance is the Log-Euclidean distance.Finally,the optimization problems of maximizing distance between manifolds and minimizing global representation errors are solved.Experimental results on several widely used face datasets indicate that LLRMM method performs better than other nonlinear feature extraction methods.At the same time,LEDML method also performs well compared with other metric distances.