What makes a good similarity-preserving binary code? One option is to define a code as good if Hamming distance matches the original Euclidean distance. In this paper, we have shown that this definition may be problematic, since in applications where we care about retrieving \similar” neighbors, matching all distances exactly may be a waste of bits. Instead we have suggested an alter-native criterion, where the goal is to have Hamming affinity match the desired affinity matrix. We have shown that this leads to an intractable, binary matrix factorization problem but that the spectral relaxation can be used to build excellent codes with very simple learning algorithms.
Weiss, Yair, Rob Fergus, and Antonio Torralba. “Multidimensional spectral hashing.” European Conference on Computer Vision. Springer, Berlin, Heidelberg, 2012.