fda
From mda v0.4-8
by Trevor Hastie
Flexible Discriminant Analysis
Flexible discriminant analysis.
- Keywords
- classif
Usage
fda(formula, data, weights, theta, dimension, eps, method, keep.fitted, ...)Arguments
- formula
- of the form
y~xit describes the response and the predictors. The formula can be more complicated, such asy~log(x)+zetc (seeformulafor more details). The response should be a factor representing the response variable, or any vector that can be coerced to such (such as a logical variable). - data
- data frame containing the variables in the formula (optional).
- weights
- an optional vector of observation weights.
- theta
- an optional matrix of class scores, typically with less
than
J-1columns. - dimension
- The dimension of the solution, no greater than
J-1, whereJis the number classes. Default isJ-1. - eps
- a threshold for small singular values for excluding
discriminant variables; default is
.Machine$double.eps. - method
- regression method used in optimal scaling. Default is
linear regression via the function
polyreg, resulting in linear discriminant analysis. Other possibilities aremarsandbruto. For Penalized Discriminant analysisgen.ridgeis appropriate. - keep.fitted
- a logical variable, which determines whether the
(sometimes large) component
"fitted.values"of thefitcomponent of the returned fda object should be kept. The default isTRUEifn * dimension < 5000. - ...
- additional arguments to
method.
Value
-
an object of class
- percent.explained
- the percent between-group variance explained by each dimension (relative to the total explained.)
- values
- optimal scaling regression sum-of-squares for each
dimension (see reference). The usual discriminant analysis
eigenvalues are given by
values / (1-values), which are used to definepercent.explained. - means
- class means in the discriminant space. These are also
scaled versions of the final theta's or class scores, and can be
used in a subsequent call to
fda(this only makes sense if some columns of theta are omitted---see the references). - theta.mod
- (internal) a class scoring matrix which allows
predictto work properly. - dimension
- dimension of discriminant space.
- prior
- class proportions for the training data.
- fit
- fit object returned by
method. - call
- the call that created this object (allowing it to be
update-able) - confusion
- confusion matrix when classifying the training data. The
"fda". Use predict to extract
discriminant variables, posterior probabilities or predicted class
memberships. Other extractor functions are coef,
confusion and plot.The object has the following components:
method functions are required to take arguments x
and y where both can be matrices, and should produce a matrix
of fitted.values the same size as y. They can take
additional arguments weights and should all have a ...
for safety sake. Any arguments to method can be passed on via
the ... argument of fda. The default method
polyreg has a degree argument which allows
polynomial regression of the required total degree. See the
documentation for predict.fda for further requirements
of method. The package earth is suggested for this
package as well; earth is a more detailed implementation of
the mars model, and works as a method argument.
References
``Flexible Disriminant Analysis by Optimal Scoring'' by Hastie, Tibshirani and Buja, 1994, JASA, 1255-1270.
``Penalized Discriminant Analysis'' by Hastie, Buja and Tibshirani, 1995, Annals of Statistics, 73-102.
``Elements of Statisical Learning - Data Mining, Inference and Prediction'' (2nd edition, Chapter 12) by Hastie, Tibshirani and Friedman, 2009, Springer
See Also
predict.fda,
plot.fda,
mars,
bruto,
polyreg,
softmax,
confusion,
Examples
data(iris)
irisfit <- fda(Species ~ ., data = iris)
irisfit
## fda(formula = Species ~ ., data = iris)
##
## Dimension: 2
##
## Percent Between-Group Variance Explained:
## v1 v2
## 99.12 100.00
##
## Degrees of Freedom (per dimension): 5
##
## Training Misclassification Error: 0.02 ( N = 150 )
confusion(irisfit, iris)
## Setosa Versicolor Virginica
## Setosa 50 0 0
## Versicolor 0 48 1
## Virginica 0 2 49
## attr(, "error"):
## [1] 0.02
plot(irisfit)
coef(irisfit)
## [,1] [,2]
## [1,] -2.126479 -6.72910343
## [2,] -0.837798 0.02434685
## [3,] -1.550052 2.18649663
## [4,] 2.223560 -0.94138258
## [5,] 2.838994 2.86801283
marsfit <- fda(Species ~ ., data = iris, method = mars)
marsfit2 <- update(marsfit, degree = 2)
marsfit3 <- update(marsfit, theta = marsfit$means[, 1:2])
## this refits the model, using the fitted means (scaled theta's)
## from marsfit to start the iterations
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