三角稀疏回归分类器及其在稳健人脸识别中的应用

Triangle sparse regression and its application in robust face recognition

以稀疏表示为代表的回归分类方法对于高斯噪声具有较好的鲁棒性,但容易受到训练样本中离群点数据的影响导致欠拟合或过拟合.通过探索余弦函数对离群数据呈现的周期不敏感特性,使用余弦函数来刻画回归残差,并在复数域空间进行稀疏回归,提出了三角稀疏回归分类器(TSRC)模型.考虑到模型的非凸特性,普通的迭代算法难以获得全局最优解.因此,通过三角函数演算与核函数技巧将TSRC转化为一个凸优化问题,使用交替方向乘子法(ADMM)对模型进行求解,核函数的计算过程从核空间角度解释了模型对离群点鲁棒的本质原因,通过欧拉公式能够完全避开复数域的计算过程,从而起到加速的作用.在AR,Extend-YaleB及NUST-RF带有遮挡和光照变化的人脸识别数据集上进行了识别率与速度的实验,验证了所提出模型的有效性,在Extend-YaleB数据集上测试了所提出方法在不同尺度的训练样本下的运行效率,并与现阶段先进方法进行了对比.

Regression-based classifiers（e.g.Sparse Representation Classifier）have shown the promising performances in several classification tasks with Gaussian noise.However,they are sensitive to the impacts from outlier points in the training data,and lead to underfitting or overfitting results.Exploring the insensitivity of trigonometry functions in one period,the cosine function is employed to measure the fitting residuals of regressions.Considering the non-convexity of the cosine function,directly optimizations are not able to achieve the global minimizer.Therefore,the proposed Triangle Sparse Regression Classifier（TSRC）is transformed to a convex problem by trigonometry and kernel tricks.Subsequently,Alternating Direction Method of Multipliers（ADMM）method is used to solve the proposed model.The provided calculations reveal the robustness of TSRC,and eliminate the complex numbers in optimizations,by virtue of the Euler-Equation.Hence the optimization is only operated in the real numbers field,and thus obtain the efficiency algorithm.Finally,experiments on AR,Extend-YaleB and NUST-RF datasets（with variousocclusions and illumination changes）validate the accuracy of the proposed methods,and the running time is illustrated on the variations of samples size of Extend-YaleB dataset,compared with the state-of-the-art regression methods.