Measuring distance for categorical data

Cluster Analysis in R

Dmitriy (Dima) Gorenshteyn

Lead Data Scientist, Memorial Sloan Kettering Cancer Center

Binary data

	wine	beer	whiskey	vodka
1	TRUE	TRUE	FALSE	FALSE
2	FALSE	TRUE	TRUE	TRUE
...	...	...	...	...

Jaccard index

$$ J(A,B) = \frac{A \cap B}{A \cup B} $$

Calculating Jaccard distance

	wine	beer	whiskey	vodka
1	TRUE	TRUE	FALSE	FALSE
2	FALSE	TRUE	TRUE	TRUE

$$ J(1,2) = \frac{1 \cap 2}{1 \cup 2} = \frac{1}{4} = 0.25$$

$$ Distance(1,2) = 1 - J(1,2) = 0.75$$

Calculating Jaccard distance in R

print(survey_a)

   wine  beer whiskey vodka
  <lgl> <lgl>   <lgl> <lgl>
1  TRUE  TRUE   FALSE FALSE
2 FALSE  TRUE    TRUE  TRUE
3  TRUE FALSE    TRUE FALSE

dist(survey_a, method = "binary")

          1         2
2 0.7500000          
3 0.6666667 0.7500000

More than two categories

	color	sport
1	red	soccer
2	green	hockey
3	blue	hockey
4	blue	soccer

	colorblue	colorgreen	colorred	sporthockey	sportsoccer
1	0	0	1	0	1
2	0	1	0	1	0
3	1	0	0	1	0
4	1	0	0	0	1

Dummification in R

print(survey_b)

  color  sport
1   red soccer
2 green hockey
3  blue hockey
4  blue soccer

library(dummies)
dummy.data.frame(survey_b)

  colorblue colorgreen colorred sporthockey sportsoccer
1         0          0        1           0           1
2         0          1        0           1           0
3         1          0        0           1           0
4         1          0        0           0           1

Generalizing categorical distance in R

print(survey_b)

  color  sport
1   red soccer
2 green hockey
3  blue hockey
4  blue soccer

dummy_survey_b <- dummy.data.frame(survey_b)
dist(dummy_survey_b, method = 'binary')

          1         2         3
2 1.0000000                    
3 1.0000000 0.6666667          
4 0.6666667 1.0000000 0.6666667

Let's practice!

Cluster Analysis in R