Data Mining - Global vs Local
About
Global refers to calculation that are made over the whole data set whereas local refers to calculations that are made local to a point or a partition.
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High dimension vs Local
In high dimension, it's really difficult to stay local.
Example: the percentage of volume that contains 10% of the data in an hypercube is:
- Two dimension: <math>1^2 - 0.9^2 = 1 - 0.81 = 0.19 = 19\%</math>
- Ten dimensions: <math>1^{10} - 0.9^{10} = 1 - 0.35 = 0.65 = 65\%</math>
To resolved this problem, (structured|parametrized) model have been introduced. The simplest one is the linear model.
Documentation / Reference
- interactive app in R Shiny on the Curse of Dimensionality.