| Version: | 1.2.0 |
| Date: | 2021-07-11 |
| Title: | Discriminant Analysis for Evolutionary Inference |
| Description: | Discriminant Analysis (DA) for evolutionary inference (Qin, X. et al, 2020, <doi:10.22541/au.159256808.83862168>), especially for population genetic structure and community structure inference. This package incorporates the commonly used linear and non-linear, local and global supervised learning approaches (discriminant analysis), including Linear Discriminant Analysis of Kernel Principal Components (LDAKPC), Local (Fisher) Linear Discriminant Analysis (LFDA), Local (Fisher) Discriminant Analysis of Kernel Principal Components (LFDAKPC) and Kernel Local (Fisher) Discriminant Analysis (KLFDA). These discriminant analyses can be used to do ecological and evolutionary inference, including demography inference, species identification, and population/community structure inference. |
| biocViews: | BiomedicalInformatics, ChIPSeq, Clustering, Coverage, DNAMethylation, DifferentialExpression, DifferentialMethylation,Software, DifferentialSplicing, Epigenetics, FunctionalGenomics, GeneExpression, GeneSetEnrichment, Genetics, ImmunoOncology, MultipleComparison, Normalization, Pathways, QualityControl, RNASeq, Regression, SAGE, Sequencing, Software, SystemsBiology, TimeCourse, Transcription, Transcriptomics |
| Depends: | R (≥ 3.5) |
| License: | GPL-3 |
| SystemRequirements: | GNU make |
| URL: | https://xinghuq.github.io/DA/index.html |
| BugReports: | https://github.com/xinghuq/DA/issues |
| Imports: | adegenet,lfda,MASS,kernlab,klaR,plotly,rARPACK,grDevices,stats,utils |
| VignetteBuilder: | knitr |
| NeedsCompilation: | no |
| RoxygenNote: | 6.1.1 |
| Suggests: | knitr,testthat,rmarkdown |
| Packaged: | 2021-07-11 04:35:11 UTC; Qin_st_andrews |
| Author: | Xinghu Qin  [aut,
cre, cph] |
| Maintainer: | Xinghu Qin <qinxinghu@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2021-07-12 08:40:02 UTC |
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)
qinxinghu@gmail.com
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
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)
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)
qinxinghu@gmail.com
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]))
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)
qinxinghu@gmail.com
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)
qinxinghu@gmail.com
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)
qinxinghu@gmail.com
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)
qinxinghu@gmail.com
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)
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.
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