Spectral feature analysis

We have seen a surge of interest in spectral-based methods and kernel-based methods for machine learning and data mining. Despite the significant research, these methods remain only loosely related. In this paper, we give theoretically an explicit relation between spectral clustering and weighted kernel principal component analysis (WKPCA). We show that spectral clustering is not only a method for data clustering, but also for feature extraction. We are then able to reinterpret the spectral clustering algorithm in terms of WKPCA and propose our spectral feature analysis (SFA) method. The spectral features extracted by SFA can capture the distinguishing information of data from different classes effectively. Finally some experimental results are presented to show the effectiveness of our method.