Abstract:
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Many popular dimensionality reduction methods are considered to be highly sensitive to outliers, and some robust procedures are proposed without a general and well-established criterion. Traditionally, the robustness study of a spectral dimension reduction method is through the influence function defined on the eigenvalues and eigenvectors of some real symmetric matrix. However, it is difficult to see the big picture from these vector-valued functions, and what we are essentially interested in is the whole low-dimensional subspace that spanned by the top eigenvectors. Moreover, considering the intrinsic dimensionality is to be estimated, the influence function should incorporate the intrinsic dimension estimation. In this talk, we will develop different types of influence function that defined on the distance between subspaces, possibly with different dimensionalites.
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