qkLLE: qKernel Locally Linear Embedding

In qkerntool: Q-Kernel-Based and Conditionally Negative Definite Kernel-Based Machine Learning Tools

Description

Computes the qkernel Locally Linear Embedding

Usage

## S4 method for signature 'matrix'
qkLLE(x, kernel = "rbfbase", qpar = list(sigma = 0.1, q = 0.9),
                         dims = 2, k, na.action = na.omit, ...)
## S4 method for signature 'cndkernmatrix'
qkLLE(x, dims = 2, k, na.action = na.omit, ...)
## S4 method for signature 'qkernmatrix'
qkLLE(x, dims = 2, k, na.action = na.omit,...)

Arguments

x	N x D matrix (N samples, D features) or a kernel matrix of cndkernmatrix or qkernmatrix.
kernel	the kernel function used in training and predicting. This parameter can be set to any function, of class kernel, which computes a kernel function value between two vector arguments. qkerntool provides the most popular kernel functions which can be used by setting the kernel parameter to the following strings: rbfbase Radial Basis qkernel function "Gaussian" nonlbase Non Linear qkernel function laplbase Laplbase qkernel function ratibase Rational Quadratic qkernel function multbase Multiquadric qkernel function invbase Inverse Multiquadric qkernel function wavbase Wave qkernel function powbase Power qkernel function logbase Log qkernel function caubase Cauchy qkernel function chibase Chi-Square qkernel function studbase Generalized T-Student qkernel function nonlcnd Non Linear cndkernel function polycnd Polynomial cndkernel function rbfcnd Radial Basis cndkernel function "Gaussian" laplcnd Laplacian cndkernel function anocnd ANOVA cndkernel function raticnd Rational Quadratic cndkernel function multcnd Multiquadric cndkernel function invcnd Inverse Multiquadric cndkernel function wavcnd Wave cndkernel function powcnd Power cndkernel function logcnd Log cndkernel function caucnd Cauchy cndkernel function chicnd Chi-Square cndkernel function studcnd Generalized T-Student cndkernel function The kernel parameter can also be set to a user defined function of class kernel by passing the function name as an argument.
qpar	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, q for the Radial Basis qkernel function "rbfbase" , the Laplacian qkernel function "laplbase" and the Cauchy qkernel function "caubase". alpha, q for the Non Linear qkernel function "nonlbase". c, q for the Rational Quadratic qkernel function "ratibase" , the Multiquadric qkernel function "multbase" and the Inverse Multiquadric qkernel function "invbase". theta, q for the Wave qkernel function "wavbase". d, q for the Power qkernel function "powbase" , the Log qkernel function "logbase" and the Generalized T-Student qkernel function "studbase". alpha for the Non Linear cndkernel function "nonlcnd". power, alpha, c for the Polynomial cndkernel function "polycnd". gamma for the Radial Basis cndkernel function "rbfcnd" and the Laplacian cndkernel function "laplcnd" and the Cauchy cndkernel function "caucnd". power, sigma for the ANOVA cndkernel function "anocnd". c for the Rational Quadratic cndkernel function "raticnd" , the Multiquadric cndkernel function "multcnd" and the Inverse Multiquadric cndkernel function "invcnd". theta for the Wave cndkernel function "wavcnd". power for the Power cndkernel function "powcnd" , the Log cndkernel function "logcnd" and the Generalized T-Student cndkernel function "studcnd". Hyper-parameters for user defined kernels can be passed through the qpar parameter as well.
dims	dimension of the target space
k	the number of nearest neighbours.
na.action	A function to specify the action to be taken if NAs are found. The default action is na.omit, which leads to rejection of cases with missing values on any required variable. An alternative is na.fail, which causes an error if NA cases are found. (NOTE: If given, this argument must be named.)
...	additional parameters

Details

The qkernel Locally Linear Embedding (qkLLE) preserves local properties of the data by representing each sample in the data by a linear combination of its k nearest neighbours with each neighbour weighted independently. qkLLE finally chooses the low-dimensional representation that best preserves the weights in the target space. It is an extension of Locally Linear Embedding (LLE) with qkernel method.

Value

It returns an S4 object containing the principal component vectors along with the corresponding eigenvalues.

prj	a matrix with the reduced input data
dims	dimension of the target space
eVal	The corresponding eigenvalues
eVec	The corresponding eigenvectors
cndkernf	the kernel function used

all the slots of the object can be accessed by accessor functions.

Author(s)

Yusen Zhang
[e-mail]

References

Roweis, Sam T. and Saul, Lawrence K., "Nonlinear Dimensionality Reduction by Locally Linear Embedding",2000;

Examples

## S4 method for signature 'matrix'
data(iris)
testset <- sample(1:150,20)
train <- as.matrix(iris[-testset,-5])
labeltrain<- as.integer(iris[-testset,5])
test <- as.matrix(iris[testset,-5])
plot(train ,col=labeltrain, xlab="1st Principal Component",ylab="2nd Principal Component")
# ratibase(c=1,q=0.8)
d_low <- qkLLE(train, kernel = "ratibase", qpar = list(c=1,q=0.8), dims=2, k=5)
#plot the data projection on the components
plot(prj(d_low),col=labeltrain, xlab="1st Principal Component",ylab="2nd Principal Component")

## S4 method for signature 'qkernmatrix'
# ratibase(c=0.1,q=0.8)
qkfunc <- ratibase(c=0.1,q=0.8)
ktrain1 <- qkernmatrix(qkfunc,train)
d_low <- qkLLE(ktrain1, dims = 2, k=5)
#plot the data projection on the components
plot(prj(d_low),col=labeltrain, xlab="1st Principal Component",ylab="2nd Principal Component")

qkerntool documentation built on May 2, 2019, 6:11 a.m.