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Review 6: Discretization

  • What is the connection between discretization and explanation?
  • In the following diagram, - Where are two examples of ranges where the independent values change the default class distribution? - Propose, and defend, two useful breaks in the following independent variables:

Unsupervised Discretization

Consider the following example:

0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,3,4,5,10,20,40,80,100
  • Define and distinguish EqualIntervalDiscretization (EID) from EqualFrequencyDiscretization (EFD)
  • Using the above data, show EID and EFD for 10 bins
  • Using EID and EFD and 10 bins, the above eample has several problems. List them.

Supervised Discretization

  • What extra information is used by supervised discretization over unsupervided discretization?
  • Explain: supervised discretization works by finding ``cliffs''.
  • Where are the ``cliffs'' in the following data (explain all your working): (1.0,A), (1.4,A), (1.7, A), (2.0,B), (3.0, B), (7.0, A),
  • Suppose a column of numbers has no cliffs. What does that mean about those numbers.
  • How can entropy or standard deviation amongst the class variable be used to find ``cliffs''? - What kind of class variable would be needed for entropy-based cliffs? - What kind of class variable would be needed for standard deviation-based cliffs?

Incremental Discretization

  • Gama and Pinto's PID algorithm uses two layers. - What is the connection between the upper and lower layer? - What is the size and purpose and use of the upper layer? - What is the size and purpose and use of the lower layer?
  • How can incremental discretization be used for anomaly detection?

Timm's rules for discretization

  • What is Cohen's rule and how is it calculated?
  • Given the lower and upper end of a bin, when is the bin too small?
  • What is a blunt/sharp range?
  • What is a relevant range?

BTW, here are some notes I should have shown last week.

Gaussian chops

Assume that a column of numbers comes from a Gaussian distribution.

Normalize all numbers by subtracting the mean and dividing by the standard deviation (which means the resulting numbers have a mean of zero and a standard deviation of one).

Then divide the numbers according to the desired number of bins using breaks take from the following table.

  bins                        breaks
  ---- -------------------------------------------------
  2:                           0                    
  3:                     -0.43   0.43               
  4:                     -0.67 0 0.67               
  5:               -0.84 -0.25   0.25 0.84          
  6:               -0.97 -0.43 0 0.43 0.97          
  7:         -1.07 -0.57 -0.18   0.18 0.57 1.07     
  8:         -1.15 -0.67 -0.32 0 0.32 0.67 1.15     
  9:   -1.22 -0.76 -0.43 -0.14   0.14 0.43 0.76 1.22
  10:  -1.28 -0.84 -0.52 -0.25 0 0.25 0.52 0.84 1.28