I successfully applied t-SNE to the number handwriting dataset. n=3823 data points (i.e. handwritten numbers) in an D=64 dimensional space (i.e. 8x8 pixels). Worked great.
Now I would like to cluster n≈60 data points in an D≈3000 dimensional space. Even after many iterations, t-SNE fairs far worse than say PCA.
Is there an upper bound on the number of dimensions (relative to the number of data points) above which applying t-SNE is not adviced?