Fast Discrete Multi-Dimensional Scaling

Multi-dimensional scaling (MDS) is the process of transforming a set of vectors in a high dimensional space to a lower dimensional one while preserving the similarity structure of the vectors. While effective methods have been found for solving this problem in the general case, they depend on the vectors in the lower dimensional space having real-valued components. However, for some applications, the training of neural networks in particular, it is preferable to have vectors in a discrete, binary space. Unfortunately, performing optimized MDS into a low-dimensional discrete space appears to be much harder than into a continuous space. This paper presents a relatively fast and effective method for performing approximately optimized, discrete MDS.