Analysis of projection |
- Utilizes Pythagoras' theorem
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- Assumes distance function
is a metric distance
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- Works fine for the first coordinate in the reduced dimensionality
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- Need a way to extend and generalize this
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- Assume an original dimensionality of
![](images/img6.png)
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- After first step project everything onto a
-hyperdimensional plane which is perpendicular to line
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- Modify distance
to work for dimensions
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- Modified distance
may not be a metric distance any more
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- Will be a metric if in Euclidean space
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