| Type: | Package |
| Title: | Local Fisher Discriminant Analysis |
| Version: | 1.1.3 |
| Date: | 2019-07-31 |
| URL: | https://github.com/terrytangyuan/lfda |
| BugReports: | https://github.com/terrytangyuan/lfda/issues |
| Maintainer: | Yuan Tang <terrytangyuan@gmail.com> |
| License: | MIT + file LICENSE |
| Description: | Functions for performing and visualizing Local Fisher Discriminant Analysis(LFDA), Kernel Fisher Discriminant Analysis(KLFDA), and Semi-supervised Local Fisher Discriminant Analysis(SELF). |
| Depends: | R (≥ 3.1.0) |
| Imports: | plyr, grDevices, rARPACK |
| Suggests: | testthat, rgl |
| RoxygenNote: | 6.1.0 |
| NeedsCompilation: | no |
| Packaged: | 2019-07-31 16:46:28 UTC; yuan.tang |
| Author: | Yuan Tang  [aut,
cre],
Wenxuan Li [ctb],
Nan Xiao [ctb, cph],
Zachary Deane-Mayer [ctb] |
| Repository: | CRAN |
| Date/Publication: | 2019-07-31 17:10:02 UTC |
Negative One Half Matrix Power Operator
Description
This function defines operation for negative one half matrix power operator
Usage
x %^% n
Arguments
x |
the matrix we want to operate on |
n |
the exponent |
Value
the matrix after negative one half power
Assigning Colors to A Vector
Description
This function assigns a color to each distinct value in the given vector.
Usage
Cols(vec)
Arguments
vec |
The vector where each distinct value will be assigned a color. |
Value
The colors for each element in the given vector
Get Affinity Matrix
Description
This function returns an affinity matrix within knn-nearest neighbors from the distance matrix.
Usage
getAffinityMatrix(distance2, knn, nc)
Arguments
distance2 |
The distance matrix for each observation |
knn |
The number of nearest neighbors |
nc |
The number of observations for data in this class |
Value
an affinity matrix - the larger the element in the matrix, the closer two data points are
Get Requested Type of Transforming Metric
Description
This function returns the requested type of transforming metric.
Usage
getMetricOfType(metric, eigVec, eigVal, total)
Arguments
metric |
The type of metric to be requested |
eigVec |
The eigenvectors of the problem |
eigVal |
The eigenvalues of the problem |
total |
The number of total rows to be used for weighting denominator |
Value
The transformation metric in requested type
Kernel Local Fisher Discriminant Analysis for Supervised Dimensionality Reduction
Description
Performs kernel local fisher discriminant analysis on the given data,
which is the non-linear version of LFDA (see details lfda).
Usage
klfda(k, y, r, metric = c("weighted", "orthonormalized", "plain"),
knn = 6, reg = 0.001)
Arguments
k |
n x n kernel matrix. Result of the |
y |
n dimensional vector of class labels |
r |
dimensionality of reduced space (default: d) |
metric |
type of metric in the embedding space (default: 'weighted') 'weighted' — weighted eigenvectors 'orthonormalized' — orthonormalized 'plain' — raw eigenvectors |
knn |
parameter used in local scaling method (default: 6) |
reg |
regularization parameter (default: 0.001) |
Value
list of the LFDA results:
T |
d x r transformation matrix (Z = t(T) * X) |
Z |
r x n matrix of dimensionality reduced samples |
Author(s)
Yuan Tang
References
Sugiyama, M (2007). - contain implementation 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
See Also
See lfda for the linear version.
Examples
k <- kmatrixGauss(iris[, -5])
y <- iris[, 5]
r <- 3
klfda(k, y, r, metric = "plain")
Gaussian Kernel Computation (Particularly used in Kernel Local Fisher Discriminant Analysis)
Description
Gaussian kernel computation for klfda, which maps the original data space to non-linear and higher dimensions.
Usage
kmatrixGauss(x, sigma = 1)
Arguments
x |
n x d matrix of original samples. n is the number of samples. |
sigma |
dimensionality of reduced space. (default: 1) |
Value
K n x n kernel matrix. n is the number of samples.
Author(s)
Yuan Tang
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.
https://shapeofdata.wordpress.com/2013/07/23/gaussian-kernels/
See Also
See klfda for the computation of
kernel local fisher discriminant analysis
Examples
kmatrixGauss(iris[, -5])
Local Fisher Discriminant Analysis for Supervised Dimensionality Reduction
Description
Performs local fisher discriminant analysis (LFDA) on the given data.
Usage
lfda(x, y, r, metric = c("orthonormalized", "plain", "weighted"),
knn = 5)
Arguments
x |
n x d matrix of original samples. n is the number of samples. |
y |
length n vector of class labels |
r |
dimensionality of reduced space (default: d) |
metric |
type of metric in the embedding space (no default) 'weighted' — weighted eigenvectors 'orthonormalized' — orthonormalized 'plain' — raw eigenvectors |
knn |
parameter used in local scaling method (default: 5) |
Details
LFDA is a method for linear dimensionality reduction that maximizes between-class scatter and minimizes within-class scatter while at the same time maintain the local structure of the data so that multimodal data can be embedded appropriately. Its limitation is that it only looks for linear boundaries between clusters. In this case, a non-linear version called kernel LFDA will be used instead. Three metric types can be used if needed.
Value
list of the LFDA results:
T |
d x r transformation matrix (Z = x * T) |
Z |
n x r matrix of dimensionality reduced samples |
Author(s)
Yuan Tang
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.
See Also
See klfda for the kernelized variant of
LFDA (Kernel LFDA).
Examples
k <- iris[, -5]
y <- iris[, 5]
r <- 3
lfda(k, y, r, metric = "plain")
3D Visualization for LFDA/KLFDA Result
Description
This function plot 3 dimensions of the lfda/klfda result.
Usage
## S3 method for class 'lfda'
plot(x, labels, cleanText = FALSE, ...)
Arguments
x |
The lfda/klfda result. |
labels |
A list of class labels used for lfda/klfda training. |
cleanText |
A boolean value to specify whether to make the labels in the plot cleaner (default: FALSE) |
... |
Additional arguments |
See Also
See lfda and klfda for the metric learning method used for this visualization.
LFDA Transformation/Prediction on New Data
Description
This function transforms a data set, usually a testing set, using the trained LFDA metric
Usage
## S3 method for class 'lfda'
predict(object, newdata = NULL, type = "raw", ...)
Arguments
object |
The result from lfda function, which contains a transformed data and a transforming matrix that can be used for transforming testing set |
newdata |
The data to be transformed |
type |
The output type, in this case it defaults to "raw" since the output is a matrix |
... |
Additional arguments |
Value
the transformed matrix
Author(s)
Yuan Tang
Examples
k <- iris[, -5]
y <- iris[, 5]
r <- 3
model <- lfda(k, y, r = 4, metric = "plain")
predict(model, iris[, -5])
Print an lfda object
Description
Print an lfda object
Usage
## S3 method for class 'lfda'
print(x, ...)
Arguments
x |
The result from lfda function, which contains a transformed data and a transforming |
... |
ignored |
Matlab-Syntaxed Repmat
Description
This function mimics the behavior and syntax of repmat() in Matlab it generates a large matrix consisting of an N-by-M tiling copies of A
Usage
repmat(A, N, M)
Arguments
A |
original matrix to be used as copies |
N |
the number of rows of tiling copies of A |
M |
the number of columns of tiling copies of A |
Value
matrix consisting of an N-by-M tiling copies of A
Semi-Supervised Local Fisher Discriminant Analysis(SELF) for Semi-Supervised Dimensionality Reduction
Description
Performs semi-supervised local fisher discriminant analysis (SELF) on the given data. SELF is a linear semi-supervised dimensionality reduction method smoothly bridges supervised LFDA and unsupervised principal component analysis, by which a natural regularization effect can be obtained when only a small number of labeled samples are available.
Usage
self(X, Y, beta = 0.5, r, metric = c("orthonormalized", "plain",
"weighted"), kNN = 5, minObsPerLabel = 5)
Arguments
X |
n x d matrix of original samples. n is the number of samples. |
Y |
length n vector of class labels |
beta |
degree of semi-supervisedness (0 <= beta <= 1; default is 0.5 ) 0: totally supervised (discard all unlabeled samples) 1: totally unsupervised (discard all label information) |
r |
dimensionality of reduced space (default: d) |
metric |
type of metric in the embedding space (no default) 'weighted' — weighted eigenvectors 'orthonormalized' — orthonormalized 'plain' — raw eigenvectors |
kNN |
parameter used in local scaling method (default: 5) |
minObsPerLabel |
the minimum number observations required for each different label(default: 5) |
Value
list of the SELF results:
T |
d x r transformation matrix (Z = x * T) |
Z |
n x r matrix of dimensionality reduced samples |
Author(s)
Yuan Tang
References
Sugiyama, Masashi, et al (2010). Semi-supervised local Fisher discriminant analysis for dimensionality reduction. Machine learning 78.1-2: 35-61.
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
See lfda for LFDA and klfda for the kernelized variant of
LFDA (Kernel LFDA).
Examples
x <- iris[, -5]
y <- iris[, 5]
self(x, y, beta = 0.1, r = 3, metric = "plain")