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. -

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

• SD=0.2
• SD=0.3
• 

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.

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