Research On Feature Learning Based On Sparse Representation And Locality Preserving Projection

Locality preserving projection is a classical graph based feature extraction method.It firstly construct a graph that describes the data relationship,and then extracts important features based on the learned graph.These two-step feature learning methods have the following defects:One is that the graph construction depends on parameter selection and distance measurement,and it is sensitive to parameter values and noises,making it difficult to obtain a graph depicting real data relationship;The other is that separating graph learning and feature learning as two independent stages ignores the relationship between two related steps,i.e.,during the process of graph construction,it does not consider the necessity of feature learning,so the constructed graph may not be the optimal for feature learning.Considering about this,this paper avoids the parameter influence on graph construction,and considers the potential link between graph learning and feature learning.So we improve the way of learning graph structure,and further improve the feature learning framework of locality preserving projection.The improved method can simultaneously perform graph learning and feature learning,and the graph construction is not affected by artificial or global parameters.On the contrary,it adaptively learns the graph structure that can reflect the data relationship.Moreover,this improved method can also acquire recognitive features,thus makes the extracted features be capable of better recognition results.On the basis of the classical locality preserving projection feature learning method,this paper combines the learning of graph and projection matrix to the same frame,and establishes a model of jointly learning graph and feature extraction.Applying the idea of sparse representation,we treat the whole training set as a data dictionary,and reconstruct every training sample in a way of regression,then minimize the reconstruction error.Besides,the l₁ norm constraint is adopted to the reconstruction matrix,which can induce the training samples competing to represent each other,so the samples of the same class are more likely to obtain higher representation weight,and the reconstruction coefficient matrix is learnt.Furthermore,we require the coefficient matrix nonnegative so that it can be directly seen as a graph for analysis,and we can achieve an adaptive-learning graph.Based on the above ideas,in this paper we propose the joint sparse representation and locality preserving projection for feature extraction.We also transform the above non-convex optimization problem into a convex optimization problem,and the alternating direction method of multiplier is used for alternately solving each variable,which is the proposed optimization algorithm by alternately and iteratively solving the problem.To testify the effectiveness of the proposed model and the convergence of the algorithm,we conduct the feature extraction method of joint sparse representation and locality preserving projection on three public face image data sets,the extended Yale B,AR and ORL,and one public object image data set of COIL20.Experiments show that the algorithm can achieve convergence within five iterations,and the recognition accuracy has reached a higher stability.In addition,the recognition accuracy results compared with several existing traditional methods indicate that the recognition rate of this proposal is improved by different degrees than that of other algorithms in different data sets,specifically by 8%-20%in the case of comparing with the accuracy rate of the original locality preserving projection method.Moreover,the change of the visualized graph structure during the optimization process shows that the graph learned from the unified framework presents data relationship more clearly than the graph initialized by original method.Therefore the improved algorithm has good convergence,and it is more capable to show data structure,suit for feature extraction,and improve the recognition accuracy.