Discriminant Analysis Based on Mahalanobis Distance — D2.disc • biotools

A function to perform discriminant analysis based on the squared generalized Mahalanobis distance (D2) of the observations to the center of the groups.

# S3 method for default
D2.disc(data, grouping, pooled.cov = NULL)
# S3 method for D2.disc
print(x, ...)
# S3 method for D2.disc
predict(object, newdata = NULL, ...)

Arguments

data	a numeric `data.frame` or `matrix` (n x p).
grouping	a vector of length n containing the class of each observation (row) in `data`.
pooled.cov	a `grouping`-pooled covariance matrix (p x p). If `NULL` (default), `D2.disc` will automatically compute a pooled covariance matrix.
x, object	an object of class `"D2.disc"`.
newdata	numeric `data.frame` or `matrix` of observations to be classified. If `NULL` (default), the input data used as argument in `D2.disc` will be used.
...	further arguments.

Value

A list of

call

the call which produced the result.

data

numeric matrix; the input data.

D2

a matrix containing the Mahalanobis distances between each row of data and the center of each class of grouping. In addition, the original and the predicted (lowest distance) class are displayed, as well as a chacater vector indicating where the misclassification has occured.

means

a matrix containing the vector of means of each class in grouping.

pooled

the pooled covariance matrix.

confusion.matrix

an object of class confusionmatrix.

References

Manly, B.F.J. (2004) Multivariate statistical methods: a primer. CRC Press. (p. 105-106).

Mahalanobis, P.C. (1936) On the generalized distance in statistics. Proceedings of The National Institute of Sciences of India, 12:49-55.

Author

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

See also

D2.dist, confusionmatrix, lda

Examples

data(iris)
(disc <- D2.disc(iris[, -5], iris[, 5]))
#> 
#> Call:
#> D2.disc.default(data = iris[, -5], grouping = iris[, 5])
#> 
#> Mahalanobis distances from each class and class prediction (first 6 rows):
#>      setosa versicolor virginica grouping   pred misclass
#> 1 0.2910898   98.88475  191.7886   setosa setosa         
#> 2 2.0313451   80.97126  169.1870   setosa setosa         
#> 3 0.5532814   87.28938  177.0701   setosa setosa         
#> 4 2.0866979   75.29369  160.7244   setosa setosa         
#> 5 0.5956300  100.92317  193.8540   setosa setosa         
#> 6 1.9447533   95.93997  183.1140   setosa setosa         
#> 
#> Class means:
#>            Sepal.Length Sepal.Width Petal.Length Petal.Width
#> setosa            5.006       3.428        1.462       0.246
#> versicolor        5.936       2.770        4.260       1.326
#> virginica         6.588       2.974        5.552       2.026
#> 
#> Confusion matrix:
#>            new setosa new versicolor new virginica
#> setosa             50              0             0
#> versicolor          0             48             2
#> virginica           0              1            49
first10 <- iris[1:10, -5]
predict(disc, first10)
#> $class
#>      1      2      3      4      5      6      7      8      9     10 
#> setosa setosa setosa setosa setosa setosa setosa setosa setosa setosa 
#> Levels: setosa versicolor virginica
#> 
#> $D2
#>       setosa versicolor virginica
#> 1  0.2910898   98.88475  191.7886
#> 2  2.0313451   80.97126  169.1870
#> 3  0.5532814   87.28938  177.0701
#> 4  2.0866979   75.29369  160.7244
#> 5  0.5956300  100.92317  193.8540
#> 6  1.9447533   95.93997  183.1140
#> 7  1.3336882   84.01179  170.0569
#> 8  0.1174084   89.51039  179.5753
#> 9  3.8501173   71.64100  155.9269
#> 10 1.4419412   84.12304  174.4342
#> 
predict(disc, iris[, -5])$class
#>   [1] setosa     setosa     setosa     setosa     setosa     setosa    
#>   [7] setosa     setosa     setosa     setosa     setosa     setosa    
#>  [13] setosa     setosa     setosa     setosa     setosa     setosa    
#>  [19] setosa     setosa     setosa     setosa     setosa     setosa    
#>  [25] setosa     setosa     setosa     setosa     setosa     setosa    
#>  [31] setosa     setosa     setosa     setosa     setosa     setosa    
#>  [37] setosa     setosa     setosa     setosa     setosa     setosa    
#>  [43] setosa     setosa     setosa     setosa     setosa     setosa    
#>  [49] setosa     setosa     versicolor versicolor versicolor versicolor
#>  [55] versicolor versicolor versicolor versicolor versicolor versicolor
#>  [61] versicolor versicolor versicolor versicolor versicolor versicolor
#>  [67] versicolor versicolor versicolor versicolor virginica  versicolor
#>  [73] versicolor versicolor versicolor versicolor versicolor versicolor
#>  [79] versicolor versicolor versicolor versicolor versicolor virginica 
#>  [85] versicolor versicolor versicolor versicolor versicolor versicolor
#>  [91] versicolor versicolor versicolor versicolor versicolor versicolor
#>  [97] versicolor versicolor versicolor versicolor virginica  virginica 
#> [103] virginica  virginica  virginica  virginica  virginica  virginica 
#> [109] virginica  virginica  virginica  virginica  virginica  virginica 
#> [115] virginica  virginica  virginica  virginica  virginica  virginica 
#> [121] virginica  virginica  virginica  virginica  virginica  virginica 
#> [127] virginica  virginica  virginica  virginica  virginica  virginica 
#> [133] virginica  versicolor virginica  virginica  virginica  virginica 
#> [139] virginica  virginica  virginica  virginica  virginica  virginica 
#> [145] virginica  virginica  virginica  virginica  virginica  virginica 
#> Levels: setosa versicolor virginica

# End (not run)