密度敏感鲁棒模糊核主成分分析算法

针对传统核主成分分析算法(Kernel principal component analysis, KPCA)对野性样本点敏感等缺陷, 提出一种密度敏感鲁棒模糊核主成分分析算法(Density-Sensitive robust fuzzy kernel principal component analysis, DRF-KPCA).该算法首先通过引入相对密度确定样本初始隶属度, 并构建出基于重构误差的隶属度确定方法, 同时采用最优梯度下降法实现隶属度的更新, 有效解决了传统核主成分分析算法对野性样本点敏感导致的主成分偏移等问题.最后, 通过简化重构误差的计算公式, 大大降低了算法的计算复杂度和运行时间.实验部分, 利用有野性样本点和无野性样本点的数据集对本文算法、KPCA及其他改进算法的主成分分析性能进行测试, 结果表明DRF-KPCA能有效消除野性样本点对主元分布的影响.此外, 试验通过分析参数对算法性能的影响给出了合理的参数取值建议.最后将本文算法与其他算法应用到分类问题中进行对比, 实验表明本文算法的分类性能较其他算法有显著提高.

Density-sensitive Robust Fuzzy Kernel Principal Component Analysis Algorithm

In order to address the problem that the traditional kernel principal component analysis (KPCA) is sensitive to the sample points with large deviation and has higher computational complexity, a novel algorithm based on the density-sensitive robust fuzzy kernel principal component analysis algorithm (DRF-KPCA) is proposed. Firstly, the initial membership degree of the sample is determined by introducing the relative density. Secondly, the membership degree based on the reconstruction error is formulated and updated by the optimal gradient descent method, which can effectively solve the problem of the principal component skewing that is caused by the sensitivity of the traditional kernel principal component analysis algorithm to the data with outliers. Finally, the computational complexity and running time of the algorithm are significantly reduced by simplifying the calculation formula of the reconstruction error. In the experiments, compared with KPCA and other modified algorithms on both the datasets with large deviation samples and the datasets without large deviation samples, the DRF-KPCA is evaluated to effectively eliminate the impacts of the large deviation samples. In addition, the influence of parameters on the performance of the algorithm is analyzed and the suggestions of determination on the optimal parameters are given. Finally, the comparison results with other algorithms on classification problems demonstrate that the performance of the proposed algorithm is significantly improved.