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In recent years, some spectral feature selection methods are proposed to choose those features with high power of preserving sample similarity. However, when there exist lots of irrelevant or noisy features in data, the similarity matrix constructed from all the un-weighted features may be not reliable, which then misleads existing spectral feature selection methods to select 'wrong' features. To solve this problem, we propose that feature importance should be evaluated according to their impacts on similarity matrix, which means features with high impacts on similarity matrix should be chosen as important ones. Since graph Laplaciancite{luxbury2007} is defined on the similarity matrix, then the impact of each feature on similarity matrix can be reflected on the change of graph Laplacian, especially on its eigen-system. Based on this point of view, we propose an Eigenvalue Sensitive Criteria (EVSC) for feature selection, which aims at seeking those features with high impact on graph Laplacian's eigenvalues. Empirical analysis demonstrates our proposed method outperforms some traditional spectral feature selection methods.

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