基于最大相关熵的KPCA异常检测方法

KPCA Based Novelty Detection Method Using Maximum Correntropy Criterion

异常检测是机器学习中一个重要的研究内容,目前已存在大量的异常检测方法。作为一种常用的核方法,核主成分分析(Kernel Principal Component Analysis,KPCA)已被成功地用于解决异常检测问题。然而,传统的KPCA异常检测方法对噪声非常敏感,若训练样本中存在噪声,则会降低KPCA异常检测方法的检测性能。为了提高KPCA异常检测方法的抗噪声能力,提出了一种基于最大相关熵(Maximum Correntropy Criterion,MCC)的KPCA异常检测方法。利用信息理论学习中的相关熵代替KPCA异常检测方法中基于l_(2)范数的度量,通过调节相关熵函数中的宽度参数,可以有效抑制噪声带来的不利影响;利用半二次优化技术对所提方法的优化问题进行求解,仅需较少的迭代次数即可取得局部最优解。此外,给出了所提方法的算法描述,并分析了算法的计算复杂度。在16个UCI基准数据集上的实验结果表明,与其他4种相关方法相比,所提方法取得了更优的抗噪声能力和泛化性能。

Novelty detection is an important research issue in the field of machine learning.Till now,there exist lots of novelty detection approaches.As a commonly used kernel method,kernel principal component analysis(KPCA)has been successfully applied to deal with the problem of novelty detection.However,the traditional KPCA based novelty detection method is very sensitive to noise.If there exist noise in the given training samples,the detection performance of KPCA based novelty detection method may be decreased.To enhance the anti-noise ability of KPCA based novelty detection method,a maximum correntropy criterion(MCC)based novelty detection method is proposed.Correntropy in information theoretic learning is utilized to substitute the l_(2)-norm based measure in KPCA based novelty detection method.By adjusting the width parameter of the correntropy function,the adverse effect of noise can be alleviated.The half-quadratic optimization technique is used to solve the optimization problem of the proposed method.The local optimal solution can thus be obtained after a few iterations.Moreover,the algorithmic description of the proposed method is provided,and the computational complexity of the corresponding algorithm is analyzed.Experimental results on the 16 UCI benchmark data sets demonstrate that the proposed method obtains better anti-noise and generalization performance in comparison with the other four related approaches.