The Choice of Initial Configurations in Multidimensional Scaling: Local Minima, Fit, and Interpretability
Multidimensional scaling (MDS) algorithms can easily end up in local minima, depending on the starting configuration. This is particularly true for 2-dimensional ordinal MDS. A simulation study shows that there can be many local minima that all have an excellent model fit (i.e., small Stress) even if they do not recover a known latent configuration very well, and even if they differ substantially among each other. MDS programs give the user only one supposedly Stress-optimal solution. We here present a procedure for analyzing all MDS solutions resulting from using a variety of different starting configurations. The solutions are compared in terms of fit and configurational similarity. This allows the MDS user to identify different types of solutions with acceptable Stress, if they exist, and then pick the one that is best interpretable.
We study a new technique for optimal data compression subject to conditions of causality and different types of memory. The technique is based on the assumption that some information about compressed data can be obtained from a solution of the associated problem without constraints of causality and memory. This allows us to consider two separate problem related to compression and de- compression subject to those constraints. Their solutions are given and the analysis of the associated errors is provided. Keywords—stochastic signals, optimization problems in signal processing.