融合多个核函数提升聚类稳定性与效果
Multiple kernel concept factorization algorithm based on global fusion
- 基于全局线性融合，同时学习多个核函数
- 在多个真实数据集上优于KMeans、谱聚类等算法
- 适合需要自动选择核函数的无监督聚类场景
非负矩阵分解（NMF）仅能对非负数据进行低秩逼近，而概念因子分解（CF）将矩阵分解拓展至单个非线性核空间，增强了学习能力与适应性。在无监督环境下，为解决特定数据集的核函数设计或选择难题，提出一种全局化多核概念因子分解（GMKCF）算法。该算法同时输入多个候选核函数，在CF框架下通过全局线性融合进行联合学习，获得高质量且稳定的聚类结果，有效解决了CF面临的核心函数选择问题。通过交替迭代求解模型，验证了算法的收敛性。在多个真实数据库上的实验表明，所提算法在数据聚类性能上优于核K均值（KKM）、谱聚类（SC）、核CF（KCF）、协同正则化多视图谱聚类（Coreg）以及鲁棒多核K均值（RMKKM）。
原文摘要 · Abstract (English)
Non-negative Matrix Factorization(NMF) algorithm can only be used to find low rank approximation of original non-negative data while Concept Factorization(CF) algorithm extends matrix factorization to single non-linear kernel space, improving learning ability and adaptability of matrix factorization. In unsupervised environment, to design or select proper kernel function for specific dataset, a new algorithm called Globalized Multiple Kernel CF(GMKCF)was proposed. Multiple candidate kernel functions were input in the same time and learned in the CF framework based on global linear fusion, obtaining a clustering result with high quality and stability and solving the problem of kernel function selection that the CF faced. The convergence of the proposed algorithm was verified by solving the model with alternate iteration. The experimental results on several real databases show that the proposed algorithm outperforms comparison algorithms in data clustering, such as Kernel K-Means(KKM), Spectral Clustering(SC), Kernel CF(KCF), Co-regularized multi-view spectral clustering(Coreg), and Robust Multiple KKM(RMKKM).
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