Results: interpretation of the latent space dimensions

[donovanr]

Issue summary

can latent dims be associated with cell size etc?

Details

Another aspect of dimensionality reduction that is woefully underexplored is the possibility of interpretation of the latent space dimensions. Since they are sorted by the amount of variance explained, the first dimension (for all beta) should be something like cell size. This can be easily confirmed by generating images walking along that axis, where the value for z1 is varied from, say, -3 to +3 (in increments of 0.5) and the value for z2, z3 ... zn is kept at zero. I was intrigued to learn from Rory on Friday that the dimensions in the latent space should also be sort of orthogonal to each other. If this is correct, then the second dimension should be something like cell aspect ratio. Again, this can be easily constructed by generating images where z2 is varied and all the other values are kept at zero. If the beta-VAE is working as advertised, it should be able to be rationally substituted for traditional dimensionality reduction methods like PCA. Just inspecting the variation along the various latent space dimensions should go a long way toward demonstrating that utility.

TODO

• code
• manuscript text
• figure