Goodness of Fit in MDS and t-SNE with Shepard Diagrams

The goodness of fit for data reduction techniques such as MDS and t-SNE can be easily assessed with Shepard diagrams. A Shepard diagram compares how far apart your data points are before and after you transform them (ie: goodness-of-fit) as a scatter plot. Shepard diagrams can be used for data reduction techniques like principal components analysis (PCA), multidimensional scaling (MDS), or t-SNE. In this post, I illustrate goodness of fit with Shapard diagrams using a simple example which maps the locations of cities in Europe using t-SNE and MDS. You will see that the t-SNE approach, which is not designed to preserve all distances in the data, produces an odd-looking map of Europe and a distorted Shepard diagram.