徐涛 王晓明

摘 要：在提高字典鉴别能力的过程中，最大间隔字典学习忽视了利用重新获得的数据构建分类器的泛化性能，不仅与最大间隔原理有关，还与包含数据的最小包含球（MEB）半径有关。针对这一事实，提出泛化误差界指导的鉴别字典学习算法GEBGDL。首先，利用支持向量机（SVM）的泛化误差上界理论对支持向量引导的字典学习算法（SVGDL）的鉴别条件进行改进;然后，利用SVM大间隔分类原理和MEB半径作为鉴别约束项，促使不同类编码向量间的间隔最大化，并减小包含所有编码向量的MEB半径;最后，为了更充分考虑分类器的泛化性能，采用交替优化策略分别更新字典、编码系数和分类器，进而获得编码向量相对间隔更大的分类器，从而促使字典更好地学习，提升字典鉴别能力。在USPS手写数字数据集，Extended Yale B、AR、ORL三个人脸集， Caltech101、COIL20、COIL100物体数据集中进行实驗，讨论了超参数和数据维度对识别率的影响。实验结果表明，在七个图像数据集中，多数情况下所提算法的识别率优于类标签一致K奇异值分解（LC-KSVD）、局部特征和类标嵌入约束字典学习（LCLE-DL）算法、Fisher鉴别字典学习（FDDL）和SVGDL等算法;且在七个数据集中，该算法也取得了比基于稀疏表示的分类（SRC）、基于协作表示的分类（CRC）和SVM更高的识别率。

关键词：字典学习;泛化误差界;支持向量机;最小包含球;数字图像分类

中图分类号：TP391.41

文献标志码：A

文章编号：1001-9081（2019）04-0940-09

Abstract： In the process of improving discriminant ability of dictionary， max-margin dictionary learning methods ignore that the generalization of classifiers constructed by reacquired data is not only in relation to the principle of maximum margin， but also related to the radius of Minimum Enclosing Ball （MEB） containing all the data. Aiming at the fact above， Generalization Error Bound Guided discriminative Dictionary Learning （GEBGDL） algorithm was proposed. Firstly， the discriminant condition of Support Vector Guided Dictionary Learning （SVGDL） algorithm was improved based on the upper bound theory of about the generalization error of Support Vector Machine （SVM）. Then， the SVM large margin classification principle and MEB radius were used as constraint terms to maximize the margin between different classes of coding vectors， and to minimum the MEB radius containing all coding vectors. Finally， as the generalization of classifier being better considered， the dictionary， coding coefficients and classifiers were updated respectively by alternate optimization strategy， obtaining the classifiers with larger margin between the coding vectors， making the dictionary learn better to improve dictionary discriminant ability. The experiments were carried out on a handwritten digital dataset USPS， face datasets Extended Yale B， AR and ORL， object dataset Caltech 101， COIL20 and COIL100 to discuss the influence of hyperparameters and data dimension on recognition rate. The experimental results show that in most cases， the recognition rate of GEBGDL is higher than that of Label Consistent K-means-based Singular Value Decomposition （LC-KSVD）， Locality Constrained and Label Embedding Dictionary Learning （LCLE-DL）， Fisher Discriminative Dictionary Learning （FDDL） and SVGDL algorithm， and is also higher than that of Sparse Representation based Classifier （SRC）， Collaborative Representation based Classifier （CRC） and SVM.

Key words： dictionary learning; generalization error bound; Support Vector Machine （SVM）; Minimum Enclosing Ball （MEB）; digital image classification

0 引言

由于自然图像可以表示为字典原子稀疏的线性组合，字典在稀疏表示应用中起着非常重要的作用。……