基于密度峰值聚类的正则化LFDA算法

Regularized LFDA algorithm based on density peak clustering

考虑到现有费舍尔判别分析(FDA)及其改进算法无法同时有效利用有标签数据和无标签数据进行学习,提出一种基于密度峰值聚类的正则化局部费舍尔判别分析(DPC-RLFDA)算法。该算法首先利用密度峰值聚类算法得到的伪标签构造两个正则化项来规范局部FDA的类间散度矩阵和类内散度矩阵;然后通过求解目标函数得到最优投影向量。此外,为适用于非线性非高斯分布数据集,提出了基于核的DPC-RLFDA。在人工数据集和UCI数据集上的实验结果表明,与FDA及其改进算法相比,所提算法的判别性能得到了显著提升。

Considering that the existing Fisher Discriminant Analysis(FDA)and its improved algorithms cannot effectively use both labeled and unlabeled data for learning,a Regularized LFDA algorithm based on Density Peak Clustering(DPC-RLFDA)was proposed.Two regularization terms were constructed using pseudo-labels derived from the density peak clustering technique to regularize the within-class scatter matrix and between-class scatter matrix of local FDA,and then the optimal projection vector was obtained by solving the objective function.In addition,to accommodate for non-linear and non-Gaussian distributed datasets,a kernel-based DPC-RLFDA was proposed.The experimental results on artificial datasets and UCI datasets showed that compared with the FDA and its improved algorithm,the discriminant performance of the proposed algorithm was significantly improved.