Department of Physics and Technology, University of Tromsø, Tromsø, Norway.
IEEE Trans Pattern Anal Mach Intell. 2010 May;32(5):847-60. doi: 10.1109/TPAMI.2009.100.
We introduce kernel entropy component analysis (kernel ECA) as a new method for data transformation and dimensionality reduction. Kernel ECA reveals structure relating to the Renyi entropy of the input space data set, estimated via a kernel matrix using Parzen windowing. This is achieved by projections onto a subset of entropy preserving kernel principal component analysis (kernel PCA) axes. This subset does not need, in general, to correspond to the top eigenvalues of the kernel matrix, in contrast to the dimensionality reduction using kernel PCA. We show that kernel ECA may produce strikingly different transformed data sets compared to kernel PCA, with a distinct angle-based structure. A new spectral clustering algorithm utilizing this structure is developed with positive results. Furthermore, kernel ECA is shown to be an useful alternative for pattern denoising.
我们引入核熵分量分析（kernel ECA）作为一种新的数据转换和降维方法。Kernel ECA 揭示了与输入空间数据集的 Renyi 熵有关的结构，该熵通过核矩阵使用 Parzen 窗口进行估计。这是通过投影到熵保持核主成分分析（kernel PCA）轴的子集上来实现的。与使用 kernel PCA 进行降维不同，该子集通常不需要对应于核矩阵的前几个特征值。我们表明，与 kernel PCA 相比，kernel ECA 可能会产生截然不同的转换数据集，并且具有明显的基于角度的结构。开发了一种利用这种结构的新的谱聚类算法，并取得了积极的结果。此外，kernel ECA 被证明是一种有用的模式去噪的替代方法。
