Application of Kernel Trick to Fuzzy c-Means with Regularization by K-L Information
Application of Kernel Trick to Fuzzy c-Means with Regularization by K-L Information
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DOI：
10.20965/jaciii.2004.p0566
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发表时间：
2004-11
期刊：
影响因子：
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通讯作者：
H. Ichihashi;Katsuhiro Honda
中科院分区：
文献类型：
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作者：
H. Ichihashi;Katsuhiro Honda
支持向量机（SVM），核主成分分析（KPCA）和核Fisher判别分析（KFD）是成功的基于核的学习方法的例子。通过在高斯混合密度模型（GMM）的模糊映射中加入正则化算子和核技巧，提出了一种扩展高维特征空间的聚类算法。与全局非线性方法不同，GMM或其模糊对应物是用PCA的局部线性子模型的集合或混合来建模非线性结构。当特征向量和聚类数分别为n和C时，该核方法可以找到C × n个非零特征值。采用概率主成分分析（PPCA）中控制混合模型参数个数的方法，减少参数个数。我们将核技巧应用到高维特征空间的聚类方法中。该算法在原始输入数据空间中提供了一种具有灵活形状的聚类划分。
Support vector machines (SVM), kernel principal component analysis (KPCA), and kernel Fisher discriminant analysis (KFD), are examples of successful kernel-based learning methods. By the addition of a regularizer and the kernel trick to a fuzzy counterpart of Gaussian mixture density models (GMM), this paper proposes a clustering algorithm in an extended high dimensional feature space. Unlike the global nonlinear approaches, GMM or its fuzzy counterpart is to model nonlinear structure with a collection, or mixture, of local linear sub-models of PCA. When the number of fearture vectors and clusters are n and C respectively, this kernel approach can find up to C × n nonzero eigenvalues. A way to control the number of parameters in the mixture of probabilistic principal component analysis (PPCA) is adopted to reduce the number of parameters. We apply the kernel trick to the clustering method in a high dimensional feature space. The algorithm provides a partitioning with flexible shape of clusters in the original input data space.