Vowel Recognition

Description

Speaker independent recognition of the eleven steady state vowels of British English using a specified training set of lpc derived log area ratios.

Format

A data frame with 990 observations on the following 12 variables.

y

Class label indicating vowel spoken

subset

a factor with levels test train

x.1

a numeric vector

x.2

a numeric vector

x.3

a numeric vector

x.4

a numeric vector

x.5

a numeric vector

x.6

a numeric vector

x.7

a numeric vector

x.8

a numeric vector

x.9

a numeric vector

x.10

a numeric vector

Details

The speech signals were low pass filtered at 4.7kHz and then digitised to 12 bits with a 10kHz sampling rate. Twelfth order linear predictive analysis was carried out on six 512 sample Hamming windowed segments from the steady part of the vowel. The reflection coefficients were used to calculate 10 log area parameters, giving a 10 dimensional input space. For a general introduction to speech processing and an explanation of this technique see Rabiner and Schafer [RabinerSchafer78].

Each speaker thus yielded six frames of speech from eleven vowels. This gave 528 frames from the eight speakers used to train the networks and 462 frames from the seven speakers used to test the networks.

The eleven vowels, along with words demonstrating their sound, are: i (heed) I (hid) E (head) A (had) a: (hard) Y (hud) O (hod) C: (hoard) U (hood) u: (who'd) 3: (heard)

Source

https://archive.ics.uci.edu/ml/machine-learning-databases/undocumented/connectionist-bench/vowel/

References

D. H. Deterding, 1989, University of Cambridge, "Speaker Normalisation for Automatic Speech Recognition", submitted for PhD.

Examples

data(Vowel)
summary(Vowel)

Fit glmnet using customized training

Description

Fit a regularized lasso model using customized training

Usage

customizedGlmnet(
  xTrain,
  yTrain,
  xTest,
  groupid = NULL,
  G = NULL,
  family = c("gaussian", "binomial", "multinomial"),
  dendrogram = NULL,
  dendrogramTestIndices = NULL
)

Arguments

Details

Identify customized training subsets of the training data through one of two methods: (1) If groupid is specified, grouping the test data, then for each test group find the 10 nearest neighbors of each observation in the group and use the union of these nearest neighbor sets as the customized training set or (2) If G is specified, jointly cluster the test and training data using hierarchical clustering with complete linkage. Within each cluster, the training data are used as the customized training subset for the test data. Once the customized training subsets have been identified, use glmnet to fit an l1-regularized regression model to each.

Value

an object with class customizedGlmnet

call

the call that produced this object

CTset

a list containing the customized training subsets for each test group

fit

a list containing the glmnet fit for each test group

groupid

a length-m vector containing the group memberships of the test data

x

a list containing train (which is the input xTrain) and test (which is the input xTest). Specified in function call

y

training response vector (specified in function call)

family

response type (specified in function call)

standard

the fit of glmnet to the entire training set using standard training

Examples

require(glmnet)

# Simulate synthetic data
n = m = 150
p = 50
q = 5
K = 3
sigmaC = 10
sigmaX = sigmaY = 1
set.seed(5914)

beta = matrix(0, nrow = p, ncol = K)
for (k in 1:K) beta[sample(1:p, q), k] = 1
c = matrix(rnorm(K*p, 0, sigmaC), K, p)
eta = rnorm(K)
pi = (exp(eta)+1)/sum(exp(eta)+1)
z = t(rmultinom(m + n, 1, pi))
x = crossprod(t(z), c) + matrix(rnorm((m + n)*p, 0, sigmaX), m + n, p)
y = rowSums(z*(crossprod(t(x), beta))) + rnorm(m + n, 0, sigmaY)

x.train = x[1:n, ]
y.train = y[1:n]
x.test = x[n + 1:m, ]
y.test = y[n + 1:m]

# Example 1: Use clustering to fit the customized training model to training
# and test data with no predefined test-set blocks

fit1 = customizedGlmnet(x.train, y.train, x.test, G = 3,
    family = "gaussian")

# Print the customized training model fit:
fit1

# Extract nonzero regression coefficients for each group:
nonzero(fit1, lambda = 10)

# Compute test error using the predict function:
mean((y.test - predict(fit1, lambda = 10))^2)

# Plot nonzero coefficients by group:
plot(fit1, lambda = 10)

# Example 2: If the test set has predefined blocks, use these blocks to define
# the customized training sets, instead of using clustering.
group.id = apply(z == 1, 1, which)[n + 1:m]

fit2 = customizedGlmnet(x.train, y.train, x.test, group.id)

# Print the customized training model fit:
fit2

# Extract nonzero regression coefficients for each group:
nonzero(fit2, lambda = 10)

# Compute test error using the predict function:
mean((y.test - predict(fit2, lambda = 10))^2)

# Plot nonzero coefficients by group:
plot(fit2, lambda = 10)

Cross validation for customizedGlmnet

Description

Does k-fold cross-validation for customizedGlmnet and returns a values for G and lambda

Usage

cv.customizedGlmnet(
  xTrain,
  yTrain,
  xTest = NULL,
  groupid = NULL,
  Gs = NULL,
  dendrogram = NULL,
  dendrogramCV = NULL,
  lambda = NULL,
  nfolds = 10,
  foldid = NULL,
  keep = FALSE,
  family = c("gaussian", "binomial", "multinomial"),
  verbose = FALSE
)

Arguments

Value

an object of class cv.customizedGlmnet

call

the call that produced this object

G.min

unless groupid is specified, the number of clusters minimizing CV error

lambda

the sequence of values of the regularization parameter lambda considered

lambda.min

the value of the regularization parameter lambda minimizing CV error

error

a matrix containing the CV error for each G and lambda

fit

a customizedGlmnet object fit using G.min and lambda.min. Only returned if xTest is not NULL.

prediction

a length-m vector of predictions for the test set, using the tuning parameters which minimize cross-validation error. Only returned if xTest is not NULL.

selected

a list of nonzero variables for each customized training set, using G.min and lambda.min. Only returned if xTest is not NULL.

cv.fit

a array containing fitted values on the training set from cross validation. Only returned if keep is TRUE.

Examples

require(glmnet)

# Simulate synthetic data
n = m = 150
p = 50
q = 5
K = 3
sigmaC = 10
sigmaX = sigmaY = 1
set.seed(5914)

beta = matrix(0, nrow = p, ncol = K)
for (k in 1:K) beta[sample(1:p, q), k] = 1
c = matrix(rnorm(K*p, 0, sigmaC), K, p)
eta = rnorm(K)
pi = (exp(eta)+1)/sum(exp(eta)+1)
z = t(rmultinom(m + n, 1, pi))
x = crossprod(t(z), c) + matrix(rnorm((m + n)*p, 0, sigmaX), m + n, p)
y = rowSums(z*(crossprod(t(x), beta))) + rnorm(m + n, 0, sigmaY)

x.train = x[1:n, ]
y.train = y[1:n]
x.test = x[n + 1:m, ]
y.test = y[n + 1:m]
foldid = sample(rep(1:10, length = nrow(x.train)))

# Example 1: Use clustering to fit the customized training model to training
# and test data with no predefined test-set blocks

fit1 = cv.customizedGlmnet(x.train, y.train, x.test, Gs = c(1, 2, 3, 5),
    family = "gaussian", foldid = foldid)

# Print the optimal number of groups and value of lambda:
fit1$G.min
fit1$lambda.min

# Print the customized training model fit:
fit1

# Compute test error using the predict function:
mean((y[n + 1:m] - predict(fit1))^2)

# Plot nonzero coefficients by group:
plot(fit1)

# Example 2: If the test set has predefined blocks, use these blocks to define
# the customized training sets, instead of using clustering.
foldid = apply(z == 1, 1, which)[1:n]
group.id = apply(z == 1, 1, which)[n + 1:m]

fit2 = cv.customizedGlmnet(x.train, y.train, x.test, group.id, foldid = foldid)

# Print the optimal value of lambda:
fit2$lambda.min

# Print the customized training model fit:
fit2

# Compute test error using the predict function:
mean((y[n + 1:m] - predict(fit2))^2)

# Plot nonzero coefficients by group:
plot(fit2)


# Example 3: If there is no test set, but the training set is organized into
# blocks, you can do cross validation with these blocks as the basis for the
# customized training sets.

fit3 = cv.customizedGlmnet(x.train, y.train, foldid = foldid)

# Print the optimal value of lambda:
fit3$lambda.min

# Print the customized training model fit:
fit3

# Compute test error using the predict function:
mean((y[n + 1:m] - predict(fit3))^2)

# Plot nonzero coefficients by group:
plot(fit3)

Return selected variables

Description

nonzero is a generic function for returning the set of variables selected by a model

Usage

nonzero(object, ...)

Arguments

Value

The form of the value returned by nonzero depends on the class of its argument. See the documentation of the particular methods for details of what is produced by that method.

Return selected variables from a customizedGlmnet object

Description

Returns a list of vectors of selected variables for each separate glmnet model fit by a customizedGlmnet object

Usage

## S3 method for class 'customizedGlmnet'
nonzero(object, lambda = NULL, ...)

Arguments

Value

a list of vectors, each vectors representing one of the glmnet models fit by the customizedGlmnet model. Each vector gives the indices of the variables selected by the model

Examples

require(glmnet)

# Simulate synthetic data
n = m = 150
p = 50
q = 5
K = 3
sigmaC = 10
sigmaX = sigmaY = 1
set.seed(5914)

beta = matrix(0, nrow = p, ncol = K)
for (k in 1:K) beta[sample(1:p, q), k] = 1
c = matrix(rnorm(K*p, 0, sigmaC), K, p)
eta = rnorm(K)
pi = (exp(eta)+1)/sum(exp(eta)+1)
z = t(rmultinom(m + n, 1, pi))
x = crossprod(t(z), c) + matrix(rnorm((m + n)*p, 0, sigmaX), m + n, p)
y = rowSums(z*(crossprod(t(x), beta))) + rnorm(m + n, 0, sigmaY)

x.train = x[1:n, ]
y.train = y[1:n]
x.test = x[n + 1:m, ]
y.test = y[n + 1:m]

# Example 1: Use clustering to fit the customized training model to training
# and test data with no predefined test-set blocks

fit1 = customizedGlmnet(x.train, y.train, x.test, G = 3,
    family = "gaussian")

# Extract nonzero regression coefficients for each group:
nonzero(fit1, lambda = 10)

# Example 2: If the test set has predefined blocks, use these blocks to define
# the customized training sets, instead of using clustering.
group.id = apply(z == 1, 1, which)[n + 1:m]

fit2 = customizedGlmnet(x.train, y.train, x.test, group.id)

# Extract nonzero regression coefficients for each group:
nonzero(fit2, lambda = 10)

Return selected variables from a singleton object

Description

Returns NULL. Intended for internal use only

Usage

## S3 method for class 'singleton'
nonzero(object, ...)

Arguments

Visualize variables selected in each customized training subset

Description

Produces a plot, with a row for each customized training submodel, showing the variables selected in the subset, with variables along the horizonal axis

Usage

## S3 method for class 'customizedGlmnet'
plot(x, lambda, ...)

Arguments

Value

the function returns silently

Examples

require(glmnet)

# Simulate synthetic data
n = m = 150
p = 50
q = 5
K = 3
sigmaC = 10
sigmaX = sigmaY = 1
set.seed(5914)

beta = matrix(0, nrow = p, ncol = K)
for (k in 1:K) beta[sample(1:p, q), k] = 1
c = matrix(rnorm(K*p, 0, sigmaC), K, p)
eta = rnorm(K)
pi = (exp(eta)+1)/sum(exp(eta)+1)
z = t(rmultinom(m + n, 1, pi))
x = crossprod(t(z), c) + matrix(rnorm((m + n)*p, 0, sigmaX), m + n, p)
y = rowSums(z*(crossprod(t(x), beta))) + rnorm(m + n, 0, sigmaY)

x.train = x[1:n, ]
y.train = y[1:n]
x.test = x[n + 1:m, ]
y.test = y[n + 1:m]

# Example 1: Use clustering to fit the customized training model to training
# and test data with no predefined test-set blocks

fit1 = customizedGlmnet(x.train, y.train, x.test, G = 3,
    family = "gaussian")

# Plot nonzero coefficients by group:
plot(fit1, lambda = 10)

# Example 2: If the test set has predefined blocks, use these blocks to define
# the customized training sets, instead of using clustering.
group.id = apply(z == 1, 1, which)[n + 1:m]

fit2 = customizedGlmnet(x.train, y.train, x.test, group.id)

# Plot nonzero coefficients by group:
plot(fit2, lambda = 10)

Visualize variables selected in each customized training subset, from a cross-validated model

Description

Produces a plot, with a row for each customized training submodel, showing the variables selected in the subset, with variables along the horizonal axis. The lambda used is the one which minimizes CV error.

Usage

## S3 method for class 'cv.customizedGlmnet'
plot(x, ...)

Arguments

Value

the function returns silently

Examples

require(glmnet)

# Simulate synthetic data
n = m = 150
p = 50
q = 5
K = 3
sigmaC = 10
sigmaX = sigmaY = 1
set.seed(5914)

beta = matrix(0, nrow = p, ncol = K)
for (k in 1:K) beta[sample(1:p, q), k] = 1
c = matrix(rnorm(K*p, 0, sigmaC), K, p)
eta = rnorm(K)
pi = (exp(eta)+1)/sum(exp(eta)+1)
z = t(rmultinom(m + n, 1, pi))
x = crossprod(t(z), c) + matrix(rnorm((m + n)*p, 0, sigmaX), m + n, p)
y = rowSums(z*(crossprod(t(x), beta))) + rnorm(m + n, 0, sigmaY)

x.train = x[1:n, ]
y.train = y[1:n]
x.test = x[n + 1:m, ]
y.test = y[n + 1:m]
foldid = sample(rep(1:10, length = nrow(x.train)))

# Example 1: Use clustering to fit the customized training model to training
# and test data with no predefined test-set blocks

fit1 = cv.customizedGlmnet(x.train, y.train, x.test, Gs = c(1, 2, 3, 5),
    family = "gaussian", foldid = foldid)

# Print the optimal number of groups and value of lambda:
fit1$G.min
fit1$lambda.min

# Print the customized training model fit:
fit1

# Compute test error using the predict function:
mean((y[n + 1:m] - predict(fit1))^2)

# Plot nonzero coefficients by group:
plot(fit1)

# Example 2: If the test set has predefined blocks, use these blocks to define
# the customized training sets, instead of using clustering.
foldid = apply(z == 1, 1, which)[1:n]
group.id = apply(z == 1, 1, which)[n + 1:m]

fit2 = cv.customizedGlmnet(x.train, y.train, x.test, group.id, foldid = foldid)

# Print the optimal value of lambda:
fit2$lambda.min

# Print the customized training model fit:
fit2

# Compute test error using the predict function:
mean((y[n + 1:m] - predict(fit2))^2)

# Plot nonzero coefficients by group:
plot(fit2)

# Example 3: If there is no test set, but the training set is organized into
# blocks, you can do cross validation with these blocks as the basis for the
# customized training sets.

fit3 = cv.customizedGlmnet(x.train, y.train, foldid = foldid)

# Print the optimal value of lambda:
fit3$lambda.min

# Print the customized training model fit:
fit3

# Compute test error using the predict function:
mean((y[n + 1:m] - predict(fit3))^2)

# Plot nonzero coefficients by group:
plot(fit3)

Make predictions from a customizedGlmnet object

Description

Returns predictions for the test set provided at the time of fitting the customizedGlmnet object.

Usage

## S3 method for class 'customizedGlmnet'
predict(object, lambda, type = c("response", "class"), ...)

Arguments

Value

a vector of predictions corresponding to the test data input to the model at the time of fitting

Examples

require(glmnet)

# Simulate synthetic data
n = m = 150
p = 50
q = 5
K = 3
sigmaC = 10
sigmaX = sigmaY = 1
set.seed(5914)

beta = matrix(0, nrow = p, ncol = K)
for (k in 1:K) beta[sample(1:p, q), k] = 1
c = matrix(rnorm(K*p, 0, sigmaC), K, p)
eta = rnorm(K)
pi = (exp(eta)+1)/sum(exp(eta)+1)
z = t(rmultinom(m + n, 1, pi))
x = crossprod(t(z), c) + matrix(rnorm((m + n)*p, 0, sigmaX), m + n, p)
y = rowSums(z*(crossprod(t(x), beta))) + rnorm(m + n, 0, sigmaY)

x.train = x[1:n, ]
y.train = y[1:n]
x.test = x[n + 1:m, ]
y.test = y[n + 1:m]

# Example 1: Use clustering to fit the customized training model to training
# and test data with no predefined test-set blocks

fit1 = customizedGlmnet(x.train, y.train, x.test, G = 3,
    family = "gaussian")

# Compute test error using the predict function:
mean((y.test - predict(fit1, lambda = 10))^2)

# Example 2: If the test set has predefined blocks, use these blocks to define
# the customized training sets, instead of using clustering.
group.id = apply(z == 1, 1, which)[n + 1:m]

fit2 = customizedGlmnet(x.train, y.train, x.test, group.id)

# Compute test error using the predict function:
mean((y.test - predict(fit2, lambda = 10))^2)

Make predictions from a cv.customizedGlmnet object

Description

Returns predictions for test set provided at time of fitting, using regulariztion parameter which minimizes CV error

Usage

## S3 method for class 'cv.customizedGlmnet'
predict(object, ...)

Arguments

Value

a vector of predictions corresponding to the test set provided when the model was fit. The results are for the regularization parameter chosen by cross-validation

Examples

require(glmnet)

# Simulate synthetic data
n = m = 150
p = 50
q = 5
K = 3
sigmaC = 10
sigmaX = sigmaY = 1
set.seed(5914)

beta = matrix(0, nrow = p, ncol = K)
for (k in 1:K) beta[sample(1:p, q), k] = 1
c = matrix(rnorm(K*p, 0, sigmaC), K, p)
eta = rnorm(K)
pi = (exp(eta)+1)/sum(exp(eta)+1)
z = t(rmultinom(m + n, 1, pi))
x = crossprod(t(z), c) + matrix(rnorm((m + n)*p, 0, sigmaX), m + n, p)
y = rowSums(z*(crossprod(t(x), beta))) + rnorm(m + n, 0, sigmaY)

x.train = x[1:n, ]
y.train = y[1:n]
x.test = x[n + 1:m, ]
y.test = y[n + 1:m]
foldid = sample(rep(1:10, length = nrow(x.train)))

# Example 1: Use clustering to fit the customized training model to training
# and test data with no predefined test-set blocks

fit1 = cv.customizedGlmnet(x.train, y.train, x.test, Gs = c(1, 2, 3, 5),
    family = "gaussian", foldid = foldid)

# Print the optimal number of groups and value of lambda:
fit1$G.min
fit1$lambda.min

# Print the customized training model fit:
fit1

# Compute test error using the predict function:
mean((y[n + 1:m] - predict(fit1))^2)

# Plot nonzero coefficients by group:
plot(fit1)

# Example 2: If the test set has predefined blocks, use these blocks to define
# the customized training sets, instead of using clustering.
foldid = apply(z == 1, 1, which)[1:n]
group.id = apply(z == 1, 1, which)[n + 1:m]

fit2 = cv.customizedGlmnet(x.train, y.train, x.test, group.id, foldid = foldid)

# Print the optimal value of lambda:
fit2$lambda.min

# Print the customized training model fit:
fit2

# Compute test error using the predict function:
mean((y[n + 1:m] - predict(fit2))^2)

# Plot nonzero coefficients by group:
plot(fit2)

# Example 3: If there is no test set, but the training set is organized into
# blocks, you can do cross validation with these blocks as the basis for the
# customized training sets.

fit3 = cv.customizedGlmnet(x.train, y.train, foldid = foldid)

# Print the optimal value of lambda:
fit3$lambda.min

# Print the customized training model fit:
fit3

# Compute test error using the predict function:
mean((y[n + 1:m] - predict(fit3))^2)

# Plot nonzero coefficients by group:
plot(fit3)

Make predictions from a “singleton” object

Description

Returns the value stored in the singleton. Intended for internal use only.

Usage

## S3 method for class 'singleton'
predict(object, type = c("response", "class", "nonzero"), ...)

Arguments

Value

The value of the singleton

Print the summary of a fitted customizedGlmnet object

Description

Print the numbers of training observations and test observations in each submodel of the customizedGlmnet fit

Usage

## S3 method for class 'customizedGlmnet'
print(x, ...)

Arguments

Examples

require(glmnet)

# Simulate synthetic data
n = m = 150
p = 50
q = 5
K = 3
sigmaC = 10
sigmaX = sigmaY = 1
set.seed(5914)

beta = matrix(0, nrow = p, ncol = K)
for (k in 1:K) beta[sample(1:p, q), k] = 1
c = matrix(rnorm(K*p, 0, sigmaC), K, p)
eta = rnorm(K)
pi = (exp(eta)+1)/sum(exp(eta)+1)
z = t(rmultinom(m + n, 1, pi))
x = crossprod(t(z), c) + matrix(rnorm((m + n)*p, 0, sigmaX), m + n, p)
y = rowSums(z*(crossprod(t(x), beta))) + rnorm(m + n, 0, sigmaY)

x.train = x[1:n, ]
y.train = y[1:n]
x.test = x[n + 1:m, ]
y.test = y[n + 1:m]

# Example 1: Use clustering to fit the customized training model to training
# and test data with no predefined test-set blocks

fit1 = customizedGlmnet(x.train, y.train, x.test, G = 3,
    family = "gaussian")

# Print the customized training model fit:
fit1

# Example 2: If the test set has predefined blocks, use these blocks to define
# the customized training sets, instead of using clustering.
group.id = apply(z == 1, 1, which)[n + 1:m]

fit2 = customizedGlmnet(x.train, y.train, x.test, group.id)

# Print the customized training model fit:
fit2

Print a “cv.customizedGlmnet” object

Description

Print the number of customized training subsets chosen by cross-validation and the number of variables selected in each training subset.

Usage

## S3 method for class 'cv.customizedGlmnet'
print(x, ...)

Arguments

Examples

require(glmnet)

# Simulate synthetic data
n = m = 150
p = 50
q = 5
K = 3
sigmaC = 10
sigmaX = sigmaY = 1
set.seed(5914)

beta = matrix(0, nrow = p, ncol = K)
for (k in 1:K) beta[sample(1:p, q), k] = 1
c = matrix(rnorm(K*p, 0, sigmaC), K, p)
eta = rnorm(K)
pi = (exp(eta)+1)/sum(exp(eta)+1)
z = t(rmultinom(m + n, 1, pi))
x = crossprod(t(z), c) + matrix(rnorm((m + n)*p, 0, sigmaX), m + n, p)
y = rowSums(z*(crossprod(t(x), beta))) + rnorm(m + n, 0, sigmaY)

x.train = x[1:n, ]
y.train = y[1:n]
x.test = x[n + 1:m, ]
y.test = y[n + 1:m]
foldid = sample(rep(1:10, length = nrow(x.train)))

# Example 1: Use clustering to fit the customized training model to training
# and test data with no predefined test-set blocks

fit1 = cv.customizedGlmnet(x.train, y.train, x.test, Gs = c(1, 2, 3, 5),
    family = "gaussian", foldid = foldid)

# Print the optimal number of groups and value of lambda:
fit1$G.min
fit1$lambda.min

# Print the customized training model fit:
fit1

# Compute test error using the predict function:
mean((y[n + 1:m] - predict(fit1))^2)

# Plot nonzero coefficients by group:
plot(fit1)

# Example 2: If the test set has predefined blocks, use these blocks to define
# the customized training sets, instead of using clustering.
foldid = apply(z == 1, 1, which)[1:n]
group.id = apply(z == 1, 1, which)[n + 1:m]

fit2 = cv.customizedGlmnet(x.train, y.train, x.test, group.id, foldid = foldid)

# Print the optimal value of lambda:
fit2$lambda.min

# Print the customized training model fit:
fit2

# Compute test error using the predict function:
mean((y[n + 1:m] - predict(fit2))^2)

# Plot nonzero coefficients by group:
plot(fit2)

# Example 3: If there is no test set, but the training set is organized into
# blocks, you can do cross validation with these blocks as the basis for the
# customized training sets.

fit3 = cv.customizedGlmnet(x.train, y.train, foldid = foldid)

# Print the optimal value of lambda:
fit3$lambda.min

# Print the customized training model fit:
fit3

# Compute test error using the predict function:
mean((y[n + 1:m] - predict(fit3))^2)

# Plot nonzero coefficients by group:
plot(fit3)