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More Euclidean (n-space) notes..

December 25, 2006

Charles

So I’m back in the UK spending christmas with family, but had some time to think about the relationship between datasets and n-space’s.  An n space of 2 is pretty easy to work out as the dataset existing in that space can either be (1), (2) or (1,2) and has a direct relationship to the vector existing in the space the datasets reside. What gets trick is when the dimensions get bigger:

For instance a 3n space consists of 3 weights and datasets existing at aproximately 7 places at positions of 1 and infinite inbetween positions like so: [1], [2], [3], [1,2], [1,3], [2,3], [1,2,3] What gets tricky is that the if a dataset exists at [1,2,3] (a value of 1.0 at each dimension) with a vector in this space: [.5, .5, 0]. How does the dataset know about the 0?

We’ll it should’nt – infact this is what im doing with the dataset, if a dataset is at [1,1,0] then really its at [1,2] with a value along each of these dimensions. So this is what theoretically what im doing with the nspace – essentially its dynamic. If I have 3 weights but only 2 are greater than 0, then I only use them in my nspace like so,

[1,0,1] = [1,3]

then i’ll do a cross-check against these. Dont know if this is correct but, im gettting there slowly.

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