Fully-Connected CRFs with Non-Parametric Pairwise Potentials Supplementary Material
نویسندگان
چکیده
Landmark Multidimensional Scaling (LMDS) The O(N) memory complexity of cMDS makes it an impractical choice when N is the number of pixels. Randomized approaches sample rows of the distance matrix to build approximate representatives of the entire matrix [4]. Depending on the coherence of the right singular vectors of D, it has been shown [2] that the Nyström approximation is the original matrix, under reasonable sampling conditions. We use a Nyström approach called Landmark-multidimensional-scaling (LMDS) [1] which first embeds only p + 1 of the points (known as landmark points), for a p-dimensional embedding, using classical MDS. In practice, due to potential degeneracies, the number of landmark points needs to be c > p + 1 to ensure that they span the p-D space. The remaining points are triangulated from the embedded points using
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