Chin Tat-Jun, Suter David
Department of Electrical and Computer Systems Engineering, Monash University, Victoria, Australia.
IEEE Trans Image Process. 2007 Jun;16(6):1662-74. doi: 10.1109/tip.2007.896668.
The kernel principal component analysis (KPCA) has been applied in numerous image-related machine learning applications and it has exhibited superior performance over previous approaches, such as PCA. However, the standard implementation of KPCA scales badly with the problem size, making computations for large problems infeasible. Also, the "batch" nature of the standard KPCA computation method does not allow for applications that require online processing. This has somewhat restricted the domains in which KPCA can potentially be applied. This paper introduces an incremental computation algorithm for KPCA to address these two problems. The basis of the proposed solution lies in computing incremental linear PCA in the kernel induced feature space, and constructing reduced-set expansions to maintain constant update speed and memory usage. We also provide experimental results which demonstrate the effectiveness of the approach.
核主成分分析（KPCA）已应用于众多与图像相关的机器学习应用中，并且相较于诸如主成分分析（PCA）等先前方法，它展现出了卓越的性能。然而，KPCA的标准实现随着问题规模的增大扩展性很差，使得处理大规模问题的计算变得不可行。此外，标准KPCA计算方法的“批处理”性质不允许应用于需要在线处理的情况。这在一定程度上限制了KPCA可能应用的领域。本文介绍了一种用于KPCA的增量计算算法，以解决这两个问题。所提出解决方案的基础在于在内核诱导特征空间中计算增量线性主成分分析，并构建缩减集展开式以保持恒定的更新速度和内存使用量。我们还提供了实验结果，证明了该方法的有效性。
