Measuring the World With Images
As we known, t-sne focus on local relationship. In order to comparing two embedding result, we try to align those t-sne cluster into same place, which is intuitive to compare them.
The basic idea is adding a L2 distance term to align two t-sne embedding to together.
Here is the result:
Following is the original t-sne for two different embedding methods:
Following is the yoke t-sne for those two embedding result:
The implicit equation for an ellipse looks like f(x, y) = ax^2 + bxy + cy^2 + dx + ey + f = 0 . The idea here is that if we have at least five pieces of glitter that are "on" for some location of the camera and light (unknown), and we know the surface normals of those pieces of glitter, then we can use that information to determine the values of the coefficients in the implicit equation, thus defining a set of concentric ellipses associated with our set of "on" glitter. Then, we think the two foci of these concentric ellipses (which will be the same for each ellipse in the set) will define the camera and light locations.
In this image, we can see a sample simulation in which there are 10 pieces of glitter, all of which are "on", and the camera and light are location along a vertical line. Here, we expect to see a set of concentric, vertically oriented (major axis aligned with the y-axis) ellipses such that each ellipse is tangent to at least one piece of glitter.
Previously, we thought that this set of concentric ellipses may be defined by some a, b, c, d, and e that are fixed for the whole set of ellipses, and an f which is different for each of the ellipses. In other words, a, b, c, d, and e defined the shape, orientation and location of the ellipses and f defined the "size" of each ellipse.
I am starting to believe that this is not quite true, and that the "division of labor" of the coefficients is not so clearly defined. Perhaps it is the case that there is some function which defines how the coefficients are related to each other for a given set of concentric ellipses, but I am not sure what that function or relationship is.
This is a test post for the blog!
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