目的 本文针对基于最小均方差准则的主成分分析算法(如2DPCA-L₂(two-dimensional PCA with L₂-norm)算法和2DPCA-L₁(two-dimensional PCA with L₁-norm)算法)对外点敏感、识别率低的问题,结合信息论中的最大相关熵准则,提出了一种基于最大相关熵准则的2DPCA(2DPCA-MCC)。方法 2DPCA-MCC算法采用最大相关熵表示目标函数,通过半二次优化技术解决相关熵问题,降低了外点在目标函数评价中的贡献,从而提高了算法的鲁棒性和识别精度。结果 通过对比2DPCA-MCC算法和2DPCA-L₂、2DPCA-L₁在ORL人脸数据库上的识别效果,表明了2DPCA-MCC算法的识别率比2维主成分分析算法的识别率最低提高了近10%,最高提高了近30%。结论 提出了一种基于最大相关熵的2DPCA算法,通过半二次优化技术解决非线性优化问题,实验结果表明,本算法能够较好地解决外点问题,显著提高识别精度,适用于解决人脸识别中的外点问题。

Objective Principal component analysis (PCA) plays an important role in image processing and machine learning because of its simplicity and effectiveness. In the image analysis domain, a 2D image is usually reshaped into a 1D vector, thus leading to high dimensionality and damage to intrinsic spatial information. Two-dimensional PCA (2DPCA) successfully solves the high-dimensional problem caused by vector-based methods and can significantly preserve spatial information. However, 2DPCA minimizes the minimum mean square error (MSE) and is sensitive to outliers. In this paper, a robust 2DPCA algorithm based on the maximum correntropy criterion (MCC) is proposed for face recognition. The proposed method can reduce the effect of outliers and improve recognition accuracy remarkably. Method In 2DPCA-MCC, the objective function is computed on the basis of the MCC, which is a useful measurement to handle non-zero-mean data. Given that the correntropy objective is a nonlinear optimization problem, which can be efficiently solved by the half-quadratic (HQ) optimization framework in an iterative manner, this study derives the algorithm to solve the correntropy objective on the basis of MCC. At each iteration, the complex nonlinear optimization problem is reduced to a weighed PCA problem and the correntropy objective is increased systematically. Thus, this new 2DPCA algorithm can handle non-centered data and can naturally estimate the data mean. Result Face recognition experiments have been implemented on ORL databases. In the experiment, 5 training images are randomly selected from all 10 face images for each individual and the data is not zero-centered. To test the robustness to outliers of the proposed method, 20, 40, and 60 percent of the 5 training images are occluded with random location and random size dots. The proposed algorithm can separately improve the recognition accuracy by nearly 10, 19, and 30 percent compared to the original two-dimensional PCA algorithms at 20, 40, and 60 percent images with outliers of all training images for each individual. Conclusion The minimum MSE is a simple measurement to compute the objective function. However, the MSE-based algorithm can only handle zero-mean data. To address this problem, this study proposes a new robust 2DPCA algorithm based on the MCC, which is a useful measurement for handling non-centered data. The algorithm uses the HQ optimization framework to solve the correntropy objective, which is a complicated nonlinear optimization problem. The experimental results on the ORL database prove that the proposed 2DPCA-MCC algorithm is more robust to outliers and can achieve better recognition results than the original MSE-based 2DPCA algorithms without the limitation of zero-mean data.