Package 'DA'

Symmetrised Kullback - Leibler divergence (KL-Divergence)

Description

This function calculates Symmetrised Kullback - Leibler divergence (KL-Divergence) between each class. Designed for KLFDA.

Usage

KL_divergence(obj)

Arguments

obj	The KLFDA object. Users can mdify it to adapt your own purpose.

Value

Returns a symmetrised version of the KL divergence between each pair of class

Note

This function is useful for extimating the loss between reduced features and the original features. It has been adopted in TSNE to determine its projection performance.

Author(s)

[email protected]

References

Van Erven, T., & Harremos, P. (2014). Renyi divergence and Kullback-Leibler divergence. IEEE Transactions on Information Theory, 60(7), 3797-3820.

Pierre Enel (2019). Kernel Fisher Discriminant Analysis (https://www.github.com/p-enel/MatlabKFDA), GitHub.

---

Kernel Local Fisher Discriminant Analysis (KLFDA)

Description

Kernel Local Fisher Discriminant Analysis (KLFDA). This function implements the Kernel Local Fisher Discriminant Analysis with an unified Kernel function. Different from KLFDA function, which adopts the Multinomial Kernel as an example, this function empolys the kernel function that allows you to choose various types of kernels. See the kernel function from "kernelMatriax" (kernlab).

Usage

KLFDA(x, y, kernel = kernlab::polydot(degree = 1, scale = 1, offset = 1), 
r = 20, tol, prior, CV = FALSE, usekernel = TRUE, 
fL = 0.5, metric = c("weighted", "orthonormalized", "plain"), 
knn = 6, reg = 0.001, ...)

Arguments

x	The input training data
y	The training labels
kernel	The kernel function used to calculate kernel matrix. Choose the corresponding kernel you want, see details.
r	The number of reduced features you want to keep.
tol	The tolerance used to reject the uni-variance. This is important when the variance between classes is small, and setting the large tolerance will avoid the data distortion.
prior	The weight of each class, or the proportion of each class.
CV	Whether to do cross validation.
usekernel	whether to use kernel classifier, if TRUE, pass to Naive Bayes classifier.
fL	If usekernel is TRUE, pass to the kernel function.
metric	type of metric in the embedding space (default: 'weighted') 'weighted' - weighted eigenvectors 'orthonormalized' - orthonormalized 'plain' - raw eigenvectors
knn	The number of nearest neighbours
reg	The regularization parameter
...	additional arguments for the classifier

Details

This function empolys three different classifiers, the basic linear classifier, the Mabayes (Bayes rule and the Mahalanobis distance), and Niave Bayes classifier. The argeument "kernel" in the klfda function is the kernel function used to calculate the kernel matrix. If usekernel is TRUE, the corresponding kernel parameters will pass the the Naive Bayes kernel classifier. The kernel parameter can be set to any function, of class kernel, which computes the inner product in feature space between two vector arguments. kernlab provides the most popular kernel functions which can be initialized by using the following functions:

rbfdot Radial Basis kernel function

polydot Polynomial kernel function

vanilladot Linear kernel function

tanhdot Hyperbolic tangent kernel function

laplacedot Laplacian kernel function

besseldot Bessel kernel function

anovadot ANOVA RBF kernel function

splinedot the Spline kernel

(see example.)

kernelFast is mainly used in situations where columns of the kernel matrix are computed per invocation. In these cases, evaluating the norm of each row-entry over and over again would cause significant computational overhead.

Value

The results give the classified classes and the posterior possibility of each class using different classifier.

class	The class labels from linear classifier
posterior	The posterior possibility of each class from linear classifier
bayes_judgement	Discrimintion results using the Mabayes classifier
bayes_assigment	Discrimintion results using the Naive bayes classifier
Z	The reduced features

Author(s)

[email protected]

References

Sugiyama, M (2007).Dimensionality reduction of multimodal labeled data by local Fisher discriminant analysis. Journal of Machine Learning Research, vol.8, 1027-1061.

Sugiyama, M (2006). Local Fisher discriminant analysis for supervised dimensionality reduction. In W. W. Cohen and A. Moore (Eds.), Proceedings of 23rd International Conference on Machine Learning (ICML2006), 905-912.

Original Matlab Implementation: http://www.ms.k.u-tokyo.ac.jp/software.html#LFDA

Tang, Y., & Li, W. (2019). lfda: Local Fisher Discriminant Analysis inR. Journal of Open Source Software, 4(39), 1572.

Moore, A. W. (2004). Naive Bayes Classifiers. In School of Computer Science. Carnegie Mellon University.

Pierre Enel (2020). Kernel Fisher Discriminant Analysis (https://www.github.com/p-enel/MatlabKFDA), GitHub. Retrieved March 30, 2020.

Karatzoglou, A., Smola, A., Hornik, K., & Zeileis, A. (2004). kernlab-an S4 package for kernel methods in R. Journal of statistical software, 11(9), 1-20.

See Also

predict.KLFDA, KLFDAM

Examples

require(kernlab)
btest=KLFDA(as.matrix(iris[,1:4]),as.matrix(as.data.frame(iris[,5])),
kernel=kernlab::rbfdot(sigma = 0.1),
r=3,prior=NULL,tol=1e-90,
reg=0.01,metric =  'plain')
pred=predict.KLFDA(btest,testData=as.matrix(iris[1:10,1:4]),prior=NULL)

---

Kernel Local Fisher Discriminant Analysis (KLFDA)

Description

Kernel Local Fisher Discriminant Analysis (KLFDA). This function implements the Kernel Local Fisher Discriminant Analysis with an unified Kernel function. Different from KLFDA function, which adopts the Multinomial Kernel as an example, this function empolys the kernel function that allows you to choose various types of kernels. See the kernel function from "kernelMatriax" (kernlab).

Usage

klfda_1(x, y, kernel = kernlab::polydot(degree = 1, scale = 1, offset = 1), 
r = 20, tol, prior, CV = FALSE, usekernel = TRUE, 
fL = 0.5, metric = c("weighted", "orthonormalized", "plain"), 
knn = 6, reg = 0.001, ...)

Arguments

x	The input training data
y	The training labels
kernel	The kernel function used to calculate kernel matrix. Choose the corresponding kernel you want, see details.
r	The number of reduced features you want to keep.
tol	The tolerance used to reject the uni-variance. This is important when the variance between classes is small, and setting the large tolerance will avoid the data distortion.
prior	The weight of each class, or the proportion of each class.
CV	Whether to do cross validation.
usekernel	whether to use kernel classifier, if TRUE, pass to Naive Bayes classifier.
fL	If usekernel is TRUE, pass to the kernel function.
metric	type of metric in the embedding space (default: 'weighted') 'weighted' - weighted eigenvectors 'orthonormalized' - orthonormalized 'plain' - raw eigenvectors
knn	The number of nearest neighbours
reg	The regularization parameter
...	additional arguments for the classifier

Details

This function empolys three different classifiers, the basic linear classifier, the Mabayes (Bayes rule and the Mahalanobis distance), and Niave Bayes classifier. The argeument "kernel" in the klfda function is the kernel function used to calculate the kernel matrix. If usekernel is TRUE, the corresponding kernel parameters will pass the the Naive Bayes kernel classifier. The kernel parameter can be set to any function, of class kernel, which computes the inner product in feature space between two vector arguments. kernlab provides the most popular kernel functions which can be initialized by using the following functions:

rbfdot Radial Basis kernel function

polydot Polynomial kernel function

vanilladot Linear kernel function

tanhdot Hyperbolic tangent kernel function

laplacedot Laplacian kernel function

besseldot Bessel kernel function

anovadot ANOVA RBF kernel function

splinedot the Spline kernel

(see example.)

kernelFast is mainly used in situations where columns of the kernel matrix are computed per invocation. In these cases, evaluating the norm of each row-entry over and over again would cause significant computational overhead.

Value

The results give the classified classes and the posterior possibility of each class using different classifier.

class	The class labels from linear classifier
posterior	The posterior possibility of each class from linear classifier
bayes_judgement	Discrimintion results using the Mabayes classifier
bayes_assigment	Discrimintion results using the Naive bayes classifier
Z	The reduced features

Author(s)

[email protected]

References

Sugiyama, M (2007).Dimensionality reduction of multimodal labeled data by local Fisher discriminant analysis. Journal of Machine Learning Research, vol.8, 1027-1061.

Sugiyama, M (2006). Local Fisher discriminant analysis for supervised dimensionality reduction. In W. W. Cohen and A. Moore (Eds.), Proceedings of 23rd International Conference on Machine Learning (ICML2006), 905-912.

Original Matlab Implementation: http://www.ms.k.u-tokyo.ac.jp/software.html#LFDA

Tang, Y., & Li, W. (2019). lfda: Local Fisher Discriminant Analysis inR. Journal of Open Source Software, 4(39), 1572.

Moore, A. W. (2004). Naive Bayes Classifiers. In School of Computer Science. Carnegie Mellon University.

Pierre Enel (2020). Kernel Fisher Discriminant Analysis (https://www.github.com/p-enel/MatlabKFDA), GitHub. Retrieved March 30, 2020.

Karatzoglou, A., Smola, A., Hornik, K., & Zeileis, A. (2004). kernlab-an S4 package for kernel methods in R. Journal of statistical software, 11(9), 1-20.

See Also

predict.klfda_1, KLFDA

Examples

require(kernlab)
btest=klfda_1(as.matrix(iris[,1:4]),as.matrix(as.data.frame(iris[,5])),
kernel=kernlab::rbfdot(sigma = 0.1),
r=3,prior=NULL,tol=1e-90,
reg=0.01,metric =  'plain')
pred=predict.klfda_1(btest,testData=as.matrix(iris[1:10,1:4]),prior=NULL)

---

Kernel Local Fisher Discriminant Analysis (KLFDA) with Multinomial kernel

Description

Kernel Local Fisher Discriminant Analysis (KLFDA). This function implements the Kernel Local Fisher Discriminant Analysis with a Multinomial kernel.

Usage

KLFDA_mk(X, Y, r, order, regParam, 
usekernel = TRUE, fL = 0.5, 
priors, tol, reg, metric, 
plotFigures = FALSE, verbose, ...)

Arguments

X	The input training data
Y	The training labels
r	The number of reduced features
order	The order passing to Multinomial Kernel
regParam	The regularization parameter for kernel matrix
usekernel	Whether to used kernel classifier
fL	pass to kernel classifier if usekenel is TRUE
priors	The weight of each class
tol	The tolerance for rejecting uni-variance
reg	The regularization parameter
metric	Type of metric in the embedding space (default: 'weighted') 'weighted' - weighted eigenvectors 'orthonormalized' - orthonormalized 'plain' - raw eigenvectors
plotFigures	whether to plot the reduced features, 3D plot
verbose	silence the processing
...	additional arguments for the classifier

Details

This function uses Multinomial Kernel, users can replace the Multinomial Kernel based on your own purpose. The final discrimination employs three classifiers, the basic linear classifier, the Mabayes (Bayes rule and the Mahalanobis distance), and Niave Bayes classifier.

Value

class	The class labels from linear classifier
posterior	The posterior possibility of each class from linear classifier
bayes_judgement	Discrimintion results using the Mabayes classifier
bayes_assigment	Discrimintion results using the Naive bayes classifier
Z	The reduced features

Author(s)

[email protected]

References

Sugiyama, M (2007). Dimensionality reduction of multimodal labeled data by local Fisher discriminant analysis. Journal of Machine Learning Research, vol.8, 1027-1061.

Sugiyama, M (2006). Local Fisher discriminant analysis for supervised dimensionality reduction. In W. W. Cohen and A. Moore (Eds.), Proceedings of 23rd International Conference on Machine Learning (ICML2006), 905-912.

Original Matlab Implementation: http://www.ms.k.u-tokyo.ac.jp/software.html#LFDA

Tang, Y., & Li, W. (2019). lfda: Local Fisher Discriminant Analysis inR. Journal of Open Source Software, 4(39), 1572.

Moore, A. W. (2004). Naive Bayes Classifiers. In School of Computer Science. Carnegie Mellon University.

Pierre Enel (2020). Kernel Fisher Discriminant Analysis (https://www.github.com/p-enel/MatlabKFDA), GitHub. Retrieved March 30, 2020.

Karatzoglou, A., Smola, A., Hornik, K., & Zeileis, A. (2004). kernlab-an S4 package for kernel methods in R. Journal of statistical software, 11(9), 1-20.

See Also

predict.KLFDA_mk, klfda_1

Examples

btest=KLFDA_mk(X=as.matrix(iris[,1:4]),
Y=as.matrix(as.data.frame(iris[,5])),r=3,order=2,regParam=0.25, 
usekernel=TRUE,fL=0.5,
priors=NULL,tol=1e-90,reg=0.01,metric =  'plain',plotFigures=FALSE,
verbose=TRUE)
#pred=predict.KLFDA_mk(btest,as.matrix(iris[1:10,1:4]))

---

Kernel local Fisher discriminant analysis

Description

This function performs Kernel Local Fisher Discriminant Analysis. The function provided here allows users to carry out the KLFDA using a pairwise matrix. We used the gaussan matrix as example. Users can compute different kernel matrix or distance matrix as the input for this function.

Usage

KLFDAM(kdata, y, r,
metric = c("weighted", "orthonormalized", "plain"),
tol=1e-5,knn = 6, reg = 0.001)

Arguments

kdata	The input dataset (kernel matrix). The input data can be a genotype matrix, dataframe, species occurence matrix, or principal components. The dataset have to convert to a kernel matrix before feed into this function.
y	The group lables
r	Number of reduced features
metric	Type of metric in the embedding space (default: 'weighted') 'weighted' - weighted eigenvectors 'orthonormalized' - orthonormalized 'plain' - raw eigenvectors
knn	The number of nearest neighbours
tol	Tolerance to avoid singular values
reg	The regularization parameter

Details

Kernel Local Fisher Discriminant Analysis for any kernel matrix. It was proposed in Sugiyama, M (2006, 2007) as a non-linear improvement for discriminant analysis. This function is adopted from Tang et al. 2019.

Value

Z	The reduced features
Tr	The transformation matrix

References

Tang, Y., & Li, W. (2019). lfda: Local Fisher Discriminant Analysis inR. Journal of Open Source Software, 4(39), 1572.

Sugiyama, M (2007). Dimensionality reduction of multimodal labeled data by local Fisher discriminant analysis. Journal of Machine Learning Research, vol.8, 1027-1061.

Sugiyama, M (2006). Local Fisher discriminant analysis for supervised dimensionality reduction. In W. W. Cohen and A. Moore (Eds.), Proceedings of 23rd International Conference on Machine Learning (ICML2006), 905-912.

See Also

KLFDA

Examples

kmat <- kmatrixGauss(iris[, -5],sigma=1)
zklfda=KLFDAM(kmat, iris[, 5], r=3,metric = "plain",tol=1e-5 )
print(zklfda$Z)

---

Estimating Gaussian Kernel matrix

Description

This function estimates Gaussian kernel computation for klfda, which maps the original data space to non-linear and higher dimensions. See the deatils of kmatrixGauss from lfda.

Usage

kmatrixGauss(x, sigma = 1)

Arguments

x	Input data matrix or dataframe
sigma	The Gaussian kernel parameter

Details

Return a n*n matrix

Value

Return a n*n matrix

References

Tang, Y., & Li, W. (2019). lfda: Local Fisher Discriminant Analysis inR. Journal of Open Source Software, 4(39), 1572.

---

Linear Fisher discriminant analysis of kernel principal components (DAKPC)

Description

Linear Fisher discriminant analysis of kernel principal components (DAKPC). This function empolies the LDA and kpca. This function is called Kernel Fisher Discriminant Analysis (KFDA) in other package (kfda). "KFDA" is the misleading name and "KFDA" has crucial error in package kfda. This function rectifies the current existing error for kfda.

Usage

LDAKPC(x, y, n.pc, usekernel = FALSE, 
fL = 0, kernel.name = "rbfdot", 
kpar = list(0.001), kernel = "gaussian", 
threshold = 1e-05, ...)

Arguments

x	Input traing data
y	Input labels
n.pc	number of pcs that will be kept in analysis
usekernel	Whether to use kernel function, if TRUE, it will pass to the kernel.names
fL	if using kernel, pass to kernel function
kernel.name	if usekernel is TURE, this will take the kernel name and use the parameters set as you defined
kpar	the list of hyper-parameters (kernel parameters). This is a list which contains the parameters to be used with the kernel function. Valid parameters for existing kernels are : sigma inverse kernel width for the Radial Basis kernel function "rbfdot" and the Laplacian kernel "laplacedot". degree, scale, offset for the Polynomial kernel "polydot" scale, offset for the Hyperbolic tangent kernel function "tanhdot" sigma, order, degree for the Bessel kernel "besseldot". sigma, degree for the ANOVA kernel "anovadot". Hyper-parameters for user defined kernels can be passed through the kpar parameter as well.
kernel	kernel name if all the above are not used
threshold	the threshold for kpc: value of the eigenvalue under which principal components are ignored (only valid when features = 0). (default : 0.0001)
...	additional arguments for the classifier

Value

kpca	Results of kernel principal component analysis. Kernel Principal Components Analysis is a nonlinear form of principal component analysis
kpc	Kernel principal components. The scores of the components
LDAKPC	Linear discriminant anslysis of kernel principal components
LDs	The discriminant function. The scores of the components
label	The corresponding class of the data
n.pc	Number of Pcs kept in analysis

Author(s)

[email protected]

References

Karatzoglou, A., Smola, A., Hornik, K., & Zeileis, A. (2004). kernlab-an S4 package for kernel methods in R. Journal of statistical software, 11(9), 1-20.

Mika, S., Ratsch, G., Weston, J., Scholkopf, B., & Mullers, K. R. (1999, August). Fisher discriminant analysis with kernels. In Neural networks for signal processing IX: Proceedings of the 1999 IEEE signal processing society workshop (cat. no. 98th8468) (pp. 41-48). Ieee.

Examples

data(iris)
train=LDAKPC(iris[,1:4],y=iris[,5],n.pc=3,kernel.name = "rbfdot")
pred=predict.LDAKPC(train,testData = iris[1:10,1:4])

---

Local Fisher Discriminant Analysis (LFDA)

Description

This function implements local Fisher discriminant analysis. It gives the discriminant function with the posterior possibility of each class.

Usage

LFDA(x, y, r, prior = proportions,
CV = FALSE, usekernel = TRUE, fL = 0, 
tol, kernel = "gaussian", 
metric = c("orthonormalized", "plain", "weighted"), 
knn = 5, ...)

Arguments

x	Input training data
y	Training labels
r	Number of reduced features that will be kept
prior	Prior possibility of each class
CV	Whether to do cross validation
usekernel	Whether to use the kernel discrimination in native bayes classifier
fL	Feed to native bayes classifier. Factor for Laplace correction, default factor is 0, i.e. no correction.
tol	The tolerance used in Mabayes discrimination, see Mabayes
kernel	If usekernel is TRUE, specifying the kernel names, see NaiveBaye.
metric	The type of metric in the embedding space (no default), e.g., 'weighted', weighted eigenvectors; 'orthonormalized' , orthonormalized; 'plain', raw eigenvectors.
knn	Number of nearest neighbors
...	additional arguments for the classifier

Details

The results give the classified classes and the posterior possibility of each class using different classifier.

Value

class	The class labels
posterior	The posterior possibility of each class
bayes_judgement	Discrimintion results using the Mabayes classifier
bayes_assigment	Discrimintion results using the Naive bayes classifier
Z	The reduced features

Author(s)

[email protected]

References

Sugiyama, M (2007). Dimensionality reduction of multimodal labeled data by local Fisher discriminant analysis. Journal of Machine Learning Research, vol.8, 1027-1061.

Sugiyama, M (2006). Local Fisher discriminant analysis for supervised dimensionality reduction. In W. W. Cohen and A. Moore (Eds.), Proceedings of 23rd International Conference on Machine Learning (ICML2006), 905-912.

Tang, Y., & Li, W. (2019). lfda: Local Fisher Discriminant Analysis inR. Journal of Open Source Software, 4(39), 1572.

Moore, A. W. (2004). Naive Bayes Classifiers. In School of Computer Science. Carnegie Mellon University.

Pierre Enel (2020). Kernel Fisher Discriminant Analysis (https://www.github.com/p-enel/MatlabKFDA), GitHub. Retrieved March 30, 2020.

Examples

LFDAtest=LFDA(iris[,1:4],y=iris[,5],r=3, 
CV=FALSE,usekernel = TRUE, fL = 0,
kernel="gaussian",metric = "plain",knn = 6,tol = 1)
LFDApred=predict.LFDA(LFDAtest,iris[1:10,1:4],prior=NULL)

---

Local Fisher Discriminant Analysis of Kernel principle components (LFDAKPC)

Description

Local Fisher Discriminant Analysis of Kernel principle components

Usage

LFDAKPC(x, y, n.pc, 
usekernel = FALSE, fL = 0, 
kernel.name = "rbfdot", 
kpar = list(0.001), kernel = "gaussian", 
threshold = 1e-05, ...)

Arguments

x	Input traing data
y	Input labels
n.pc	number of pcs that will be kept in analysis
usekernel	Whether to use kernel function, if TRUE, it will pass to the kernel.names
fL	if using kernel, pass to kernel function
kernel.name	if usekernel is TURE, this will take the kernel name and use the parameters set as you defined
kpar	the list of hyper-parameters (kernel parameters). This is a list which contains the parameters to be used with the kernel function. Valid parameters for existing kernels are : sigma inverse kernel width for the Radial Basis kernel function "rbfdot" and the Laplacian kernel "laplacedot". degree, scale, offset for the Polynomial kernel "polydot" scale, offset for the Hyperbolic tangent kernel function "tanhdot" sigma, order, degree for the Bessel kernel "besseldot". sigma, degree for the ANOVA kernel "anovadot". Hyper-parameters for user defined kernels can be passed through the kpar parameter as well.
kernel	kernel name if all the above are not used
threshold	the threshold for kpc: value of the eigenvalue under which principal components are ignored (only valid when features = 0). (default : 0.0001)
...	additional arguments for the classifier

Value

kpca	Results of kernel principal component analysis. Kernel Principal Components Analysis is a nonlinear form of principal component analysis
kpc	Kernel principal components. The scores of the components
LFDAKPC	LOcal linear discriminant anslysis of kernel principal components
LDs	The discriminant function. The scores of the components
label	The corresponding class of the data
n.pc	Number of Pcs kept in analysis

Author(s)

[email protected]

References

Sugiyama, M (2007). Dimensionality reduction of multimodal labeled data by local Fisher discriminant analysis. Journal of Machine Learning Research, vol.8, 1027-1061.

Sugiyama, M (2006). Local Fisher discriminant analysis for supervised dimensionality reduction. In W. W. Cohen and A. Moore (Eds.), Proceedings of 23rd International Conference on Machine Learning (ICML2006), 905-912.

Tang, Y., & Li, W. (2019). lfda: Local Fisher Discriminant Analysis inR. Journal of Open Source Software, 4(39), 1572.

Karatzoglou, A., Smola, A., Hornik, K., & Zeileis, A. (2004). kernlab-an S4 package for kernel methods in R. Journal of statistical software, 11(9), 1-20.

Examples

train=LFDAKPC(iris[,1:4],y=iris[,5],tol=1,n.pc=3,kernel.name = "rbfdot")
pred=predict.LFDAKPC(train,prior=NULL,testData = iris[1:10,1:4])

---

Membership assignment by weighted Mahalanobis distance and bayes rule

Description

The function gives the discrimintion of the potential classes based on Bayes rule and the Mahalanobis distance. This function adopts the function from Bingpei Wu, 2012, WMDB 1.0 with some corrections of the judement rule.

Usage

Mabayes(TrnX, TrnG, p = rep(1, length(levels(TrnG))), TstX = NULL, var.equal = FALSE, tol)

Arguments

TrnX	Training data
TrnG	Training label
p	prior or proportion of each class
TstX	Test data
var.equal	whether the variance or the weight is equal between classes
tol	The threshold or tolerance value for the covariance and distance

Value

posterior and class

The posterior possibility and class labels

Author(s)

[email protected]

References

Bingpei Wu, 2012, WMDB 1.0: Discriminant Analysis Methods by Weight Mahalanobis Distance and bayes.

Ito, Y., Srinivasan, C., Izumi, H. (2006, September). Discriminant analysis by a neural network with Mahalanobis distance. In International Conference on Artificial Neural Networks (pp. 350-360). Springer, Berlin, Heidelberg.

Wolfel, M., Ekenel, H. K. (2005, September). Feature weighted Mahalanobis distance: improved robustness for Gaussian classifiers. In 2005 13th European signal processing conference (pp. 1-4). IEEE.

Examples

data(iris)
train=Mabayes(iris[,1:4],iris[,5],TstX= iris[1:10,1:4],tol = 1)

---

Predict method in DA for discriminant analysis

Description

Predict method for DA.

Usage

## S3 method for class 'KLFDA_mk'
predict(object,prior,testData, ...)
## S3 method for class 'KLFDA'
predict(object,prior,testData, ...)
## S3 method for class 'LDAKPC'
predict(object,prior,testData, ...)
## S3 method for class 'LFDA'
predict(object,prior,testData, ...)
## S3 method for class 'LFDAKPC'
predict(object,prior,testData, ...)

Arguments

object	One of the trained object from discriminant analysis
prior	The weights of the groups.
testData	The test data or new data
...	Arguments passed to the classifiers

Value

The predict function will output the predicted points and their predicted possibility

---