Type: Package
Title: Ordered Homogeneity Pursuit Lasso for Group Variable Selection
Version: 1.4.1
Description: Ordered homogeneity pursuit lasso (OHPL) algorithm for group variable selection proposed in Lin et al. (2017) <doi:10.1016/j.chemolab.2017.07.004>. The OHPL method exploits the homogeneity structure in high-dimensional data and enjoys the grouping effect to select groups of important variables automatically. This feature makes it particularly useful for high-dimensional datasets with strongly correlated variables, such as spectroscopic data.
License: GPL-3 | file LICENSE
URL: https://ohpl.io, https://ohpl.io/doc/, https://github.com/nanxstats/OHPL
BugReports: https://github.com/nanxstats/OHPL/issues
Encoding: UTF-8
LazyData: true
Depends: R (≥ 3.0.2)
Imports: glmnet, mvtnorm, pls
RoxygenNote: 7.3.2
NeedsCompilation: no
Packaged: 2024-07-20 19:19:07 UTC; nanx
Author: You-Wu Lin [aut], Nan Xiao ORCID iD [aut, cre]
Maintainer: Nan Xiao <me@nanx.me>
Repository: CRAN
Date/Publication: 2024-07-20 19:50:02 UTC

OHPL: Ordered Homogeneity Pursuit Lasso for Group Variable Selection

Description

logo

Ordered homogeneity pursuit lasso (OHPL) algorithm for group variable selection proposed in Lin et al. (2017) doi:10.1016/j.chemolab.2017.07.004. The OHPL method exploits the homogeneity structure in high-dimensional data and enjoys the grouping effect to select groups of important variables automatically. This feature makes it particularly useful for high-dimensional datasets with strongly correlated variables, such as spectroscopic data.

Author(s)

Maintainer: Nan Xiao me@nanx.me (ORCID)

Authors:

See Also

Useful links:

Fisher optimal partition

Description

The Fisher optimal partition algorithm.

Usage

FOP(X, k, C)

Arguments

X

A set of samples.

k

Number of classes.

C

Statistic from the output of dlc().

Value

Index vector for each sample's classification.

References

W. D. Fisher (1958). On grouping for maximum homogeneity. Journal of the American Statistical Association, vol. 53, pp. 789–798.

Examples

X <- matrix(c(
  9.3, 1.8, 1.9, 1.7, 1.5, 1.3,
  1.4, 2.0, 1.9, 2.3, 2.1
))
C <- dlc(X, maxk = 8)$C
F <- FOP(X, 8, C)

Ordered Homogeneity Pursuit Lasso

Description

Fits the ordered homogeneity pursuit lasso (OHPL) model.

Usage

OHPL(
  x,
  y,
  maxcomp,
  gamma,
  cv.folds = 5L,
  G = 30L,
  type = c("max", "median"),
  scale = TRUE,
  pls.method = "simpls"
)

Arguments

x

Predictor matrix.

y

Response matrix with one column.

maxcomp

Maximum number of components for PLS.

gamma

A number between (0, 1) for generating the gamma sequence. An usual choice for gamma could be n * 0.05, where n is a number in 2, 3, ..., 19.

cv.folds

Number of cross-validation folds.

G

Maximum number of variable groups.

type

Find the maximum absolute correlation ("max") or find the median of absolute correlation ("median"). Default is "max".

scale

Should the predictor matrix be scaled? Default is TRUE.

pls.method

Method for fitting the PLS model. Default is "simpls". See the details section in pls::plsr() for all possible options.

Value

A list of fitted OHPL model object with performance metrics.

References

You-Wu Lin, Nan Xiao, Li-Li Wang, Chuan-Quan Li, and Qing-Song Xu (2017). Ordered homogeneity pursuit lasso for group variable selection with applications to spectroscopic data. Chemometrics and Intelligent Laboratory Systems 168, 62–71.

Examples

# Generate simulation data
dat <- OHPL.sim(
  n = 100, p = 100, rho = 0.8,
  coef = rep(1, 10), snr = 3, p.train = 0.5,
  seed = 1010
)

# Split training and test set
x <- dat$x.tr
y <- dat$y.tr
x.test <- dat$x.te
y.test <- dat$y.te

# Fit the OHPL model
fit <- OHPL(x, y, maxcomp = 3, gamma = 0.5, G = 10, type = "max")

# Selected variables
fit$Vsel

# Make predictions
y.pred <- predict(fit, x.test)

# Compute evaluation metric RMSEP, Q2 and MAE for the test set
perf <- OHPL.RMSEP(fit, x.test, y.test)
perf$RMSEP
perf$Q2
perf$MAE

Compute RMSEP, MAE, and Q2 for a test set

Description

Makes predictions on new data and computes the performance evaluation metrics RMSEP, MAE, and Q2.

Usage

OHPL.RMSEP(object, newx, newy)

Arguments

object

Object of class OHPL fitted by OHPL().

newx

Predictor matrix of the new data.

newy

Response matrix of the new data (matrix with one column).

Value

A list of the performance metrics.

Examples

# Generate simulation data
dat <- OHPL.sim(
  n = 100, p = 100, rho = 0.8,
  coef = rep(1, 10), snr = 3, p.train = 0.5,
  seed = 1010
)

# Split training and test set
x <- dat$x.tr
y <- dat$y.tr
x.test <- dat$x.te
y.test <- dat$y.te

# Fit the OHPL model
fit <- OHPL(x, y, maxcomp = 3, gamma = 0.5, G = 10, type = "max")

# Compute evaluation metric RMSEP, Q2 and MAE for the test set
perf <- OHPL.RMSEP(fit, x.test, y.test)
perf$RMSEP
perf$Q2
perf$MAE

Generate simulation data for benchmarking sparse regressions (Gaussian response)

Description

Generate simulation data (Gaussian case) following the settings in Xiao and Xu (2015).

Usage

OHPL.sim(
  n = 100,
  p = 100,
  rho = 0.8,
  coef = rep(1, 10),
  snr = 3,
  p.train = 0.5,
  seed = 1001
)

Arguments

n

Number of observations.

p

Number of variables.

rho

Correlation base for generating correlated variables.

coef

Vector of non-zero coefficients.

snr

Signal-to-noise ratio (SNR).

p.train

Percentage of training set.

seed

Random seed for reproducibility.

Value

A list containing x.tr, x.te, y.tr, and y.te.

Author(s)

Nan Xiao <\url{https://nanx.me}>

References

Nan Xiao and Qing-Song Xu. (2015). Multi-step adaptive elastic-net: reducing false positives in high-dimensional variable selection. Journal of Statistical Computation and Simulation 85(18), 3755–3765.

Examples

dat <- OHPL.sim(
  n = 100, p = 100, rho = 0.8,
  coef = rep(1, 10), snr = 3, p.train = 0.5,
  seed = 1010
)

dim(dat$x.tr)
dim(dat$x.te)

The beer dataset

Description

The beer dataset contains 60 samples published by Norgaard et al. Recorded with a 30mm quartz cell on the undiluted degassed beer and measured from 1100 to 2250 nm (576 data points) in steps of 2 nm.

Usage

data(beer)

References

Norgaard, L., Saudland, A., Wagner, J., Nielsen, J. P., Munck, L., & Engelsen, S. B. (2000). Interval partial least-squares regression (iPLS): a comparative chemometric study with an example from near-infrared spectroscopy. Applied Spectroscopy, 54(3), 413–419.

Examples

data("beer")
x.cal <- beer$xtrain
dim(x.cal)
x.test <- beer$xtest
dim(x.test)
y.cal <- beer$ytrain
dim(y.cal)
y.test <- beer$ytest
dim(y.test)

X <- rbind(x.cal, x.test)
y <- rbind(y.cal, y.test)
n <- nrow(y)

set.seed(1001)
samp.idx <- sample(1L:n, round(n * 0.7))
X.cal <- X[samp.idx, ]
y.cal <- y[samp.idx]
X.test <- X[-samp.idx, ]
y.test <- y[-samp.idx]

Cross-validation for Ordered Homogeneity Pursuit Lasso

Description

Use cross-validation to help select the optimal number of variable groups and the value of gamma.

Usage

cv.OHPL(
  X.cal,
  y.cal,
  maxcomp,
  gamma = seq(0.1, 0.9, 0.1),
  X.test,
  y.test,
  cv.folds = 5L,
  G = 30L,
  type = c("max", "median"),
  scale = TRUE,
  pls.method = "simpls"
)

Arguments

X.cal

Predictor matrix (training).

y.cal

Response matrix with one column (training).

maxcomp

Maximum number of components for PLS.

gamma

A vector of the gamma sequence between (0, 1).

X.test

X.test Predictor matrix (test).

y.test

y.test Response matrix with one column (test).

cv.folds

Number of cross-validation folds.

G

Maximum number of variable groups.

type

Find the maximum absolute correlation ("max") or find the median of absolute correlation ("median"). Default is "max".

scale

Should the predictor matrix be scaled? Default is TRUE.

pls.method

Method for fitting the PLS model. Default is "simpls". See the details section in pls::plsr() for all possible options.

Value

A list containing the optimal model, RMSEP, Q2, and other evaluation metrics. Also the optimal number of groups to use in group lasso.

Examples

data("wheat")

X <- wheat$x
y <- wheat$protein
n <- nrow(wheat$x)

set.seed(1001)
samp.idx <- sample(1L:n, round(n * 0.7))
X.cal <- X[samp.idx, ]
y.cal <- y[samp.idx]
X.test <- X[-samp.idx, ]
y.test <- y[-samp.idx]

# This could run for a while
## Not run: 
cv.fit <- cv.OHPL(
  x, y,
  maxcomp = 6, gamma = seq(0.1, 0.9, 0.1),
  x.test, y.test, cv.folds = 5, G = 30, type = "max"
)
# the optimal G and gamma
cv.fit$opt.G
cv.fit$opt.gamma

## End(Not run)

Compute D, L, and C in the Fisher optimal partitions algorithm

Description

Compute D, L, and C in the Fisher optimal partitions algorithm

Usage

dlc(X, maxk)

Arguments

X

A set of samples.

maxk

Maximum number of k.

Value

The D, L, and C statistics in the Fisher optimal partitions algorithm.

Make predictions based on the fitted OHPL model

Description

Make predictions on new data by an OHPL model object.

Usage

## S3 method for class 'OHPL'
predict(object, newx, ncomp = NULL, type = "response", ...)

Arguments

object

Object of class OHPL fitted by OHPL().

newx

Predictor matrix of the new data.

ncomp

Optimal number of components. If is NULL, the optimal number of components stored in the model object will be used.

type

Prediction type.

...

Additional parameters.

Value

Numeric matrix of the predicted values.

Examples

# generate simulation data
dat <- OHPL.sim(
  n = 100, p = 100, rho = 0.8,
  coef = rep(1, 10), snr = 3, p.train = 0.5,
  seed = 1010
)

# split training and test set
x <- dat$x.tr
y <- dat$y.tr
x.test <- dat$x.te
y.test <- dat$y.te

# fit the OHPL model
fit <- OHPL(x, y, maxcomp = 3, gamma = 0.5, G = 10, type = "max")
# make predictions
y.pred <- predict(fit, x.test)
y.pred

Extract the prototype from each variable group

Description

Extracts the prototype from each variable group.

Usage

proto(X, y, groups, type = c("max", "median"), mu = NULL)

Arguments

X

Predictor matrix.

y

Response matrix with one column.

groups

An group index vector containing the group number each variable belongs to. For example: c(1, 1, 1, 1, 1, 2, 2, 2, ...). Variable groups can be generated by the Fisher optimal partition algorithm implemented in FOP().

type

The rule for extracting the prototype. Possible options are "max" and "median".

mu

The mean value of y for standardization. Default is NULL, which uses the sample mean of y.

Value

The prototypes (variable index) extracted from each group (cluster).

The soil dataset

Description

The soil dataset contains 108 sample measurements from the wavelength range of 400–2500 nm (visible and near infrared spectrum) published by Rinnan et al.

Usage

data(soil)

References

Rinnan, R., & Rinnan, A. (2007). Application of near infrared reflectance (NIR) and fluorescence spectroscopy to analysis of microbiological and chemical properties of arctic soil. Soil biology and Biochemistry, 39(7), 1664–1673.

Examples

data("soil")

X <- soil$x
y <- soil$som
n <- nrow(soil$x)

set.seed(1001)
samp.idx <- sample(1L:n, round(n * 0.7))
X.cal <- X[samp.idx, ]
y.cal <- y[samp.idx]
X.test <- X[-samp.idx, ]
y.test <- y[-samp.idx]

The wheat dataset

Description

The wheat dataset contains 100 wheat samples with specified protein and moisture content, published by J. Kalivas. Samples were measured by diffuse reflectance as log (I/R) from 1100 to 2500 nm (701 data points) in 2 nm intervals.

Usage

data(wheat)

References

Kalivas, J. H. (1997). Two data sets of near infrared spectra. Chemometrics and Intelligent Laboratory Systems, 37(2), 255–259.

Examples

data("wheat")

X <- wheat$x
y <- wheat$protein
n <- nrow(wheat$x)

set.seed(1001)
samp.idx <- sample(1L:n, round(n * 0.7))
X.cal <- X[samp.idx, ]
y.cal <- y[samp.idx]
X.test <- X[-samp.idx, ]
y.test <- y[-samp.idx]