基于Profiles的Fisher判别约束字典学习算法

为了增强编码系数的判别性能，提出编码系数矩阵行向量（Profiles）的Fisher判别字典（Profiles of fisher discriminative dictionary learning，PFDDL）学习算法。首先，根据Profiles能反映原子在字典学习中的使用情况，提出一种自适应的原子类标构造方法。然后，利用Profiles与原子间的一一对应关系，设计Profiles的Fisher判别准则作为判别式项，使得同类原子对应Profiles的类内散度尽可能小，不同类原子对应Profiles的类间散度尽可能大，促使字典中的同类原子尽量表示同类训练样本，提高编码系数的判别性能。在3个人脸和1个手写字体数据库上的实验结果表明，提出的算法比其他稀疏编码和字典学习算法能取得更高的分类性能。

Fisher Discriminative Constraint Dictionary Learning Algorithm Based on Profiles

To improve the discriminative ability of the coding coefficients, the Profiles (the line vectors of coding coefficients matrix) of Fisher discriminative dictionary learning (PFDDL) is proposed. Firstly, the Profiles can indicate the corresponding atoms which are used by the training samples to encode in the dictionary learning, and an adaptive method is proposed to construct the labels of atoms. Since there are one-to-one correspondences between the Profiles and atoms, then the Fisher discriminative criterion is imposed on the Profiles so that they have small within-class compactness but large between-class separability. Thus, it can encourage the atoms of the same class to reconstruct the training sample of the same class, and enhance the discriminative ability of the coding coefficients, then improve the performance of dictionary learning. Experimental results show that the PFDDL algorithm can achieve better classification performance than other sparse coding and dictionary learning algorithms on the three face and one handwriting databases.