Subset kernel principal component analysis
Subset kernel principal component analysis
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DOI：
10.1109/mlsp.2009.5306221
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发表时间：
2009-10
期刊：
影响因子：
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通讯作者：
Y. Washizawa
中科院分区：
文献类型：
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作者：
Y. Washizawa
核主成分分析（KPCA或KPCA）已被广泛用于非线性特征提取，降维和分类问题。然而，已知KPCA具有高计算复杂度，即其大小等于样本数目n的特征值分解。此外，为了计算向量到由KPCA获得的子空间上的投影，我们必须存储所有n个样本并对核函数求值n次。为了克服这些问题，我们提出了子集KPCA，最大限度地减少了所有样本使用有限数量的残差，我们提供了它的解决方案。实验结果表明，即使问题的规模是KPCA的十分之一，该方法也能给出与KPCA几乎相同的结果。
Kernel principal component analysis (kernel PCA or KPCA) has been used widely for non-linear feature extraction, dimensionally reduction, and classification problems. However, KPCA is known to have high computational complexity, that is the eigenvalue decomposition of which size equals to the number of samples n. Moreover, in order to calculate projection of vector onto the subspace obtained by KPCA, we have to store all n samples and evaluate the kernel function n times. In order to overcome these problems, we propose subset KPCA that minimizes a residual error for all samples using limited number of them, and we provide its solution. Experimental results using synthetic and real data show that the proposed method gives almost the same result as KPCA even if the size of the problem is one-tenth of KPCA.