L_(2,1)范数正则化的不相关判别分析及其在人脸识别中的应用

对高维数据降维并选取有效特征对分类起着关键作用。针对人脸识别中存在的高维和小样本问题,从特征选取和子空间学习入手,提出了一种L_(2,1)范数正则化的不相关判别分析算法。该算法首先对训练样本矩阵进行奇异值分解;然后通过一系列变换,将原非线性的Fisher鉴别准则函数转化为线性模型;最后加入L_(2,1)范数惩罚项进行求解,得到一组最佳鉴别矢量。将训练样本和测试样本投影到该低维子空间中,利用最近欧氏距离分类器进行分类。由于加入了L_(2,1)范数惩罚项,该算法能使特征选取和子空间学习同时进行,有效改善识别性能。在ORL、YaleB及PIE人脸库上的实验结果表明,算法在有效降维的同时能进一步提高鉴别能力。

Uncorrelated linear discriminant analysis with L2,1-norm regularization and its application in face recognition

For high-dimensional data reduction, selection of effective features is important for classification. In order to solve the high-dimensional and small sample size problem in face recognition, starting with the feature selection and subspace learning, we propose a new method of uncorrelated linear discriminant analysis based on L2,1-norm regularization. To add L2,1-norm penalty term to the objective function, this algorithm firstly decomposes the sample matrix by the SVD. Then it presents a series of transformation, transforming its nonlinear Fisher criterion into linear type. Finally, it adds the L2,1-norm penalty term to the linear model, and solves the regularization problem to get a set of optimal discriminant vectors. We project training samples and testing samples onto low-dimensional subspace respectively, and use the nearest Euclidean distance classifier to classify the testing samples. Due to the characteristic of L2,1-norm, which can perform feature selection and subspace learning simultaneously, the recognition performance is greatly improved. Experiments on three standard face databases (ORL, YaleB and PIE) verify the performance of the algorithm, and show the efficiency of dimensionality reduction and the improvement of discriminant ability.