Global Mapping Analysis: Stochastic Gradient Algorithm in SSTRESS and Classical MDS Stress

摘要

We propose a new on-line processing algorithm for solving multidimensional scaling, which is named "global mapping analysis" (GMA.) In GMA, stochastic gradient algorithm is applied to minimizing two well-known MDS criteria: SSTRESS [15] and classical MDS stress [16], [6]. By use of GMA on the two criteria, the required memory space is reduced from the square order of the number of signals to the linear one. We also show that GMA on classical MDS is equivalent to Oja's symmetrical PCA network rule [12], and it always converges to the global optimum. The numerical experiments on 1000000 controlled signals showed that weakly correlated signals are clustered clearly by GMA.