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.