Effective Subspace Indexing via Interpolation on Stiefel and Grassmann manifolds
We propose a novel local Subspace Indexing Model with Interpolation (SIM-I) for low-dimensional embedding of image datasets. Our SIM-I is constructed via two steps: in the first step we build a piece-wise linear affinity-aware subspace model under a given partition of the dataset; in the second step we interpolate between several adjacent linear subspace models constructed previously using the "center of mass" calculation on Stiefel and Grassmann manifolds. The resulting subspace indexing model built by SIM-I is a globally non-linear low-dimensional embedding of the original data set. Furthermore, the interpolation step produces a "smoothed” version of the piece-wise linear embedding mapping constructed in the first step, and can be viewed as a regularization procedure. We provide experimental results validating the effectiveness of SIM-I, that improves PCA recovery for SIFT dataset and nearest-neighbor classification success rates for MNIST and CIFAR-10 datasets.
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