Data Mining - Global vs Local

Thomas Bayes


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.

High dimension vs Local

In high dimension, it's really difficult to stay local.

Curse Of Dimensionality Radius Volume

Neighborhood Curse Of Dimensionality 1d 2d

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

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