基于L_(2,p)矩阵范数稀疏表示的图像分类方法  

Sparse representation via L_(2,p) norm for image classification

作　　者：时中荣 王胜[2] 刘传才[1] 

机构地区：[1]南京理工大学计算机科学与工程学院,江苏南京210094 [2]河南大学图像处理与模式识别研究所,河南开封475004

出　　处：《南京理工大学学报》2017年第1期80-89,共10页Journal of Nanjing University of Science and Technology

基　　金：国家自然科学基金(61373063)

摘　　要：为了提高基于稀疏表示分类算法的分类精度,该文充分利用同类样本的非零系数高度集中的特点,提出一种用l2,p矩阵范数进行稀疏约束的基于稀疏表示的分类方法。该算法的训练阶段,构造的目标函数主要包括三个部分:重构误差、稀疏矩阵类内一致性约束、稀疏矩阵类间不一致性约束,其中的稀疏矩阵类内一致性约束用l2,p矩阵范数实现。该算法的测试阶段,计算新样本的稀疏重构系数以用于分类。和传统的基于稀疏表示的分类方法比较,该方法求稀疏重构系数时对样本不再单个处理,而是对同类样本整体处理,且充分利用同类样本的相似性和不同类样本的相异性,提高了基于稀疏表示的图像分类方法的分类精度。实验结果表明:该方法进一步提高了图像分类的准确率,在AR、Extended Yale B和Fifteen Scene Category数据库上和基于稀疏表示的分类方法(Sparse representation based classification,SRC)相比较,识别率分别提高了20.11%、20.88%和2.13%。For the sparse representation-based classification method,since the non-zero elements of sparse coefficients with the same class are concentrated in a few rows,we propose to regularize thecoefficient matrix using an l2,pmatrix norm.In the training phase of the algorithm,the objective function consists of three parts：reconstruction error,sparse regularization,and inconsistency of reconstruction coefficients between different classes.The sparse regularization term is implemented by an l2,pmatrix norm.In the test phase,the sparse reconstruction coefficient of a new sample is found using the dictionary learned in the training phase.Finally,the new sample is classified according to the sparse reconstruction coefficient.Compared with the traditional classification method based on sparse representation,the proposed method does not process a single sample to find its sparse reconstruction coefficient,but the whole sample matrix can be processed,this takes full advantage of the similarity among the same class.The experimental results show that this method can improve the accuracies of image classification 20.11%,20.88%,and 2.13% compared with a baseline SRC（Sparse representation based classification） method in AR,Extended Yale B,and Fifteen Scene Category databases,respectively.This method makes full use of the similarity of the same class and improves the accuracy of the image classification based on sparse representation.

关 键 词：图像分类 稀疏表示 稀疏分类 矩阵范数 稀疏编码 字典学习 稀疏正则项 稀疏诱导范数 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]