Mathematical multidimensional spiky spikes

A structure we conceptually called "Spiny spikes in higher dimensional space".

This is the reason for the 110,000 UMAP here.

https://gyazo.com/9ffbc15d64803a29d328244ea591a147

This means that in this of [Public Opinion Map 3970 UMAP

https://gyazo.com/30c9d0303e0de3e01269148c72184c1e

Mathematically.

$ N((0, ...) , \sigma) and a small number of $ N((4\sigma, 0, ...) , \sigma) and a small number of data (representation of one spike).

$ 4\sigma means "far enough away".

Since this is tedious, we will write this as 1 (just make $ \sigma that much smaller).

K spikes are (1, 0, 0, 0, ...) , (0, 1, 0, 0, ...) , (0, 0, 1, 0, ...) , ... like this

experiment

SD=0.1

https://gyazo.com/4c4036bfb0383007baa9e66e4a65ce22

SD=0.2

https://gyazo.com/7d9d089ca4db78a451d22fbfb3c762a6

SD=0.3

https://gyazo.com/cd61931f4c4677188428ec8994527616

When it's clearly separated, it's an enclave like UMAP with SD=0.1.

If it's too mixed, you can't tell the boundary, like SD=0.3.

It becomes spiky at its boundaries.

https://gyazo.com/75f8004dc6cbb748f1d0e81d22c24c77

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