基于原子Fisher判别准则约束字典学习算法

为了提高字典的判别性能，提出基于原子Fisher判别准则约束的字典学习算法AFDDL。首先，利用特定类字典学习算法为每个原子分配一个类标，计算同类原子和不同类原子间的散度矩阵。然后，利用类内散度矩阵和类间散度矩阵的迹的差作为判别式约束项，促使不同类原子间的差异最大化，并在最小化同类原子间差异的同时减少原子间的自相关性，使得同类原子尽可能地重构某一类样本，提高字典的判别性能。在AR、FERET和LFW三个人脸数据库和USPS手写字体数据库中进行实验，实验结果表明，在四个图像数据库中，所提算法在识别率和训练时间方面均优于类标一致的K奇异值分解（LC-KSVD）算法、局部特征和类标嵌入约束的字典学习（LCLE-DL）算法、支持矢量指导的字典学习（SVGDL）算法和Fisher判别字典学习算法；且在四个数据库中，该算法也比稀疏表示分类（SRC）和协同表示分类（CRC）取得更高的识别率。

Dictionary learning algorithm based on Fisher discriminative criterion constraint of atoms

In order to improve the discriminative ability of dictionary, a dictionary learning algorithm based on Fisher discriminative criterion constraint of the atoms was proposed, which was called Fisher Discriminative Dictionary Learning of Atoms (AFDDL). Firstly, the specific class dictionary learning algorithm was used to assign a class label to each atom, and the scatter matrices of within-class atoms and between-class atoms were calculated. Then, the difference between within-class scatter matrix and between-class scatter matrix was taken as the Fisher discriminative criterion constraint to maximize the differences of between-class atoms. The difference between the same class atoms was minimized when the autocorrelation was reduced, which made the same class atoms reconstruct one type of samples as much as possible and improved the discriminative ability of dictionary. The experiments were carried out on the AR face database, FERET face database, LFW face database and the USPS handwriting database. The experimental results show that, on the four image databases, the proposed algorithm has higher recognition rate and less training time compared with the Label Consistent K-means-based Singular Value Decomposition (LC-KSVD) algorithm, Locality Constrained and Label Embedding Dictionary Learning (LCLE-DL) algorithm, Support Vector Guided Dictionary Learning (SVGDL) algorithm, and Fisher Discriminative Dictionary Learning (FDDL) algorithm. And on the four image databases, the proposed algorithm has higher recognition rate compared with Sparse Representation based Classification (SRC) and Collaborative Representation based Classification (CRC).