Sparse Coding Based Image Classification

Feature representation is a basic topic in machine learning.As a method for feature representation,sparse coding can represent data features in an efficient manner.Most existing sparse constraint approaches used in sparse coding is L1 norm.However,the object function of the model cannot capture the details in the gradient direction during the parameter optimization process.The reason comes from the differential characteristic of L1 norm,which has unfavorable effect on the codes' representation ability,for instance,the accuracy of classification.Hypersphere constraint based sparse filtering adopts row and column constraint which need two stage differential operations when the error back-propagated to the L1 layer.Doubled computation is required to conduct the training process.In addition,the L1 norm used in sparse filtering shares the same differential property with classical L1 sparse coding.Much more than that,sparse filtering is not able to recover the original signal since it is not a typical code method.In this work,an innovative method called GHC(G Hypersphere Constraint)sparse coding is proposed to constraint the sparse distribution of the codes.The global correlation property of G gradient ensures the optimization process capturing the variation of parameter values in the gradient direction with fine grit.And the geometry property of hypersphere ensures local sparsity which is useful to counteract the global over correlation result from the G function.Tight relationships between G and L1 norm has been proved in mathematics as well as L infinity norm.Convergence property has been proved by analyzing the positive definiteness of G function's hessian matrix.As exploratory work,tight relationship between sparsity and AF features is discussed to obtain the figures of different image datasets.Classification accuracy in image verified the boosted performance of GHC comparing with L1 constraint sparse coding and hypersphere constraint sparse filtering as well as other indexes such as sparsity,MSE and PSNR.