Handling%20nonnumerical%20variables%20(2)

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Handling nonnumerical variables (2)

• Sections 6.36.6

Kenrick Bingham http//iki.fi/kenny/
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Handling nonnumerical variables (2)

• Ordering alpha labels
• joint distribution tables
• when no numerical variables are available

• Dimension reduction
• multidimensional scaling (MDS)

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Ordering alpha labels

• Trivial ordering always possible (e.g.,
  alphabetical)
• Better idea Order labels of different variables
  so that correlations show

• How?

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Ordering alpha labels

• Two-way tables

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Ordering alpha labels

• Two-way tables
• Jigsaw puzzle

• Problems

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Ordering alpha labels

• Two-way tables
• Jigsaw puzzle

• Problems

• Implementation

• straightforward (?)
• always possible to numerate some of the variables
  (?)
• continue with mixed alpha-numeric methods
• More vars (dimensions) same procedure

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Dimension reduction

• Some variables may be known to be correlated and
  do not need to be modeled
• Project data into fewer dimensions, avoiding
  significant loss of information
• Example triangle

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Dimension reduction

• Error measured by "stress" change in perimeter
  of triangle

• if no distortion occurs, stress 0
• Generalization change in the sum of distances
  between all pairs of points

stress 0
stress gt 0
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Method suggested

• Dn original data set , dim Dn n, k n
• Project Dk into Dk 1 as follows
• rotate Dk randomly
• project Dk into k 1 dimensions and measure
  stress compared to Dn
• repeat until required "degree of confidence"
  acheived
• set Dk 1 to be the projection causing the
  least stress
• Set k k 1 and repeat until stress gets too
  big

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Dimension reduction Questions

• Why not use principle component analysis (PCA)?
• well understood, firm theoretical basis
• minimises the MSE
• MSE more widely used than "stress"
• no need for random iterations
• Why in the chapter "Handling nonnumerical
  variables"?