## Fast Embedding for JOFC Using the Raw Stress Criterion

**Human Language Technology Center of Excellence**

**Department of Applied Mathematics and Statistics**

**Center for Imaging Science**

**Johns Hopkins University**

and

**Department of Statistics**

**Indiana University**

V. Lyzinski, Y. Park, C.E. Priebe, M.W. Trosset, “Fast Embedding for JOFC Using the Raw Stress Criterion,” *Journal of Computational and Graphical Statistics*, in revision, 2017.

### Abstract

The Joint Optimization of Fidelity and Commensurability (JOFC) manifold matching methodology embeds an omnibus dissimilarity matrix consisting of multiple dissimilarities on the same set of objects. One approach to this embedding optimizes the preservation of fidelity to each individual dissimilarity matrix together with commensurability of each given observation across modalities via iterative majorization of a raw stress error criterion by successive Guttman transforms. In this paper, we exploit the special structure inherent to JOFC to exactly and efficiently compute the successive Guttman transforms, and as a result we are able to greatly speed up the JOFC procedure for both in-sample and out-of-sample embedding. We demonstrate the scalability of our implementation on both real and simulated data examples.

### Codes and Experiments

To run the experiemnts in the paper, please follow these steps:

```
source("packagesatstart_JCGS.R")
# Fig 1
source("fJOFC_Fig1Table2.R")
# Fig 2
source("fJOFC_Fig2.R")
# Figs 3 & 4
source("fJOFC_Figure3and4.R")
# Figs 5, 6, & 7
source("Wiki_experiment.R")
# Figs 8, 9, & 10
source("Zebrafish_Brain_Experiment.R")
```

Here are the results after running each code:

- Required
`R`

files:
- packagesatstart_JCGS.R: a routine to load required packages and utility functions
- fJOFC.R: a main function for fJOFC and a collection of required utility functions
- oosfJOFC.R: an utility function for out-of-sample embedding with weighted raw-stress

- Simulation:
- Real data experiments:

*prepared by [email protected] on Tue Mar 7 16:46:35 2017*