Entropy-based Filters

Algorithms that find ranks of importance of discrete attributes, basing on their entropy with a continous class attribute. This function is a reimplementation of FSelector's information.gain, gain.ratio and symmetrical.uncertainty.

information_gain(
  formula,
  data,
  x,
  y,
  type = c("infogain", "gainratio", "symuncert"),
  equal = FALSE,
  discIntegers = TRUE,
  nbins = 5,
  threads = 1
)

Arguments

formula	An object of class formula with model description.
data	A data.frame accompanying formula.
x	A data.frame or sparse matrix with attributes.
y	A vector with response variable.
type	Method name.
equal	A logical. Whether to discretize dependent variable with the equal frequency binning discretization or not.
discIntegers	logical value. If true (default), then integers are treated as numeric vectors and they are discretized. If false integers are treated as factors and they are left as is.
nbins	Number of bins used for discretization. Only used if `equal = TRUE` and the response is numeric.
threads	defunct. Number of threads for parallel backend - now turned off because of safety reasons.

Value

data.frame with the following columns:

• attributes - variables names.

• importance - worth of the attributes.

Details

type = "infogain" is $$H(Class) + H(Attribute) - H(Class, Attribute)$$

type = "gainratio" is $$\frac{H(Class) + H(Attribute) - H(Class, Attribute)}{H(Attribute)}$$

type = "symuncert" is $$2\frac{H(Class) + H(Attribute) - H(Class, Attribute)}{H(Attribute) + H(Class)}$$

where H(X) is Shannon's Entropy for a variable X and H(X, Y) is a joint Shannon's Entropy for a variable X with a condition to Y.

Author

Zygmunt Zawadzki zygmunt@zstat.pl

Examples

irisX <- iris[-5]
y <- iris$Species

## data.frame interface
information_gain(x = irisX, y = y)
#>     attributes importance
#> 1 Sepal.Length  0.4521286
#> 2  Sepal.Width  0.2672750
#> 3 Petal.Length  0.9402853
#> 4  Petal.Width  0.9554360

# formula interface
information_gain(formula = Species ~ ., data = iris)
#>     attributes importance
#> 1 Sepal.Length  0.4521286
#> 2  Sepal.Width  0.2672750
#> 3 Petal.Length  0.9402853
#> 4  Petal.Width  0.9554360
information_gain(formula = Species ~ ., data = iris, type = "gainratio")
#>     attributes importance
#> 1 Sepal.Length  0.4196464
#> 2  Sepal.Width  0.2472972
#> 3 Petal.Length  0.8584937
#> 4  Petal.Width  0.8713692
information_gain(formula = Species ~ ., data = iris, type = "symuncert")
#>     attributes importance
#> 1 Sepal.Length  0.4155563
#> 2  Sepal.Width  0.2452743
#> 3 Petal.Length  0.8571872
#> 4  Petal.Width  0.8705214

# sparse matrix interface
library(Matrix)
i <- c(1, 3:8); j <- c(2, 9, 6:10); x <- 7 * (1:7)
x <- sparseMatrix(i, j, x = x)
y <- c(1, 1, 1, 1, 2, 2, 2, 2)

information_gain(x = x, y = y)
#>    attributes importance
#> 1           1          0
#> 2           2          0
#> 3           3          0
#> 4           4          0
#> 5           5          0
#> 6           6          0
#> 7           7          0
#> 8           8          0
#> 9           9          0
#> 10         10          0
information_gain(x = x, y = y, type = "gainratio")
#>    attributes importance
#> 1           1        NaN
#> 2           2        NaN
#> 3           3        NaN
#> 4           4        NaN
#> 5           5        NaN
#> 6           6        NaN
#> 7           7        NaN
#> 8           8        NaN
#> 9           9        NaN
#> 10         10        NaN
information_gain(x = x, y = y, type = "symuncert")
#>    attributes importance
#> 1           1          0
#> 2           2          0
#> 3           3          0
#> 4           4          0
#> 5           5          0
#> 6           6          0
#> 7           7          0
#> 8           8          0
#> 9           9          0
#> 10         10          0