Weighted Nearest Neighbor Imputation of Missing Values using Selected Variables

Description

This package introduces new non-parametric tools for the imputation of missing values in high-dimensional data. It includes weighted nearest neighbor imputation methods that use distances for selected covariates. The careful selection of distances that carry information about the missing values yields an imputation tool. It does not require pre-specified k, unlike other kNN methods. It can be used to impute missing values in high-dimensional data when n<p.

Details

The main function of the package is wNNSel for implementing the nonparameteric procedure of nearest neighbors imputaiton. See wNNSel for more details.

Note

*Author's Last name changed to Faisal from Ramzan in 2016.

Author(s)

Shahla Faisal <shahla_ramzan@yahoo.com>

References

Tutz, G. and Ramzan,S*. (2015). Improved methods for the imputation of missing data by nearest neighbor methods. Computational Statistics and Data Analysis, Vol. 90, pp. 84-99.

Faisal, S.* and Tutz, G. (2017). Missing value imputation for gene expression data by tailored nearest neighbors. Statistical Application in Genetics and Molecular Biology. Vol. 16(2), pp. 95-106.

Introduce MCAR Missing Values in a matrix

Description

This function artificially introduces missing values in a data matrix under missing completely at random (MCAR) mechanism.

Usage

artifNA(x, miss.prop = 0.1)

Arguments

Value

a matrix with missing values

Examples

 set.seed(3)
 x = matrix(rnorm(100),10,10)
 ## create 10% missing values in x
 artifNA(x, 0.10)

Introduce MCAR Missing Values in a matrix for cross validation

Description

This function introduces additional missing values in a missing data matrix artificially. The missing values are introduced under missing completely at random (MCAR) mechanism.

Usage

artifNA.cv(x, testNA.prop = 0.1)

Arguments

Value

a list contatining a matrix with artifical missing values, removed indices and the provided x matrix

See Also

cv.wNNSel

Examples

 set.seed(3)
 x = matrix(rnorm(100),10,10)
 ## create 10% missing values in x
 x.miss<- artifNA(x, 0.10)
 ## create another 10% missing values in x
 x.miss.cv<- artifNA.cv(x, 0.10)
 summary(x.miss)
 summary(x.miss.cv)

Mean Absolute Imputation Error

Description

This function computes the mean absolute imputation error for a given complete/true data matrix, imputed data matrix and the data matrix with missing values.

Usage

computeMAIE(x.miss, x.impute, x.true)

Arguments

Value

value of MSIE

Examples

  set.seed(3)
  x.true = matrix(rnorm(100),10,10)
  ## create 10% missing values in x
  x.miss = artifNA(x.true, 0.10)
  ## impute using wNNSel method
  x.impute = wNNSel.impute(x.miss)
  computeMAIE(x.miss, x.impute, x.true)

Mean Squared Imputation Error

Description

This function computes the mean squared imputation error for a given complete/true data matrix, imputed data matrix and the data matrix with missing values.

Usage

computeMSIE(x.miss, x.impute, x.true)

Arguments

Value

value of MSIE

Examples

 set.seed(3)
 x.true = matrix(rnorm(100),10,10)
 ## create 10% missing values in x
 x.miss = artifNA(x.true, 0.10)
 ## impute using wNNSel method
 x.impute = wNNSel.impute(x.miss)
 computeMSIE(x.miss, x.impute, x.true)

Normalized Root Mean Squared Imputatoin Error

Description

This function computes the nrmalized root mean squared imputation error for a given complete/true data matrix, imputed data matrix and the data matrix with missing values.

Usage

computeNRMSE(x.miss, x.impute, x.true)

Arguments

Value

value of MSIE

Examples

  set.seed(3)
  x.true = matrix(rnorm(100),10,10)
  ## create 10% missing values in x
  x.miss = artifNA(x.true, 0.10)
  ## impute using wNNSel method
  x.impute = wNNSel.impute(x.miss)
  computeNRMSE(x.miss, x.impute, x.true)

Cross Validation for wNNSel Imputation

Description

This function aims to search for optimal values of the tuning parameters for the wNNSel imputation.

Usage

cv.wNNSel(x, kernel = "gaussian", x.dist = "euclidean", method = "2",
  m.values = seq(2, 8, by = 2), c.values = seq(0.1, 0.5, by = 0.1),
  lambda.values = seq(0, 0.6, by = 0.01)[-1], times.max = 5,
  testNA.prop = 0.05)

Arguments

Details

Some values are artificially deleted and wNNSel is run multiple times, varying \lambda and m. For each pair of \lambda and m, compute MSIE on the subset of the data matrix x for which the the values were deleted artificially. (See References for more detail).

Value

a list containing

Author(s)

Shahla Faisal <shahla_ramzan@yahoo.com>

References

Tutz, G. and Ramzan,S. (2015). Improved methods for the imputation of missing data by nearest neighbor methods. Computational Statistics and Data Analysis, Vol. 90, pp. 84-99.

Faisal, S. and Tutz, G. (2017). Missing value imputation for gene expression data by tailored nearest neighbors. Statistical Application in Genetics and Molecular Biology. Vol. 16(2), pp. 95-106.

See Also

artifNA.cv, wNNSel

Examples

 set.seed(3)
 x.true = matrix(rnorm(100),10,10)
 ## create 10% missing values in x
 x.miss = artifNA(x.true, 0.10)
 ## use cross validation to find optimal values
 result = cv.wNNSel(x.miss)
 ## optimal values are
 result$lambda.opt
 result$m.opt
 ## Now use these values to get final imputation
 x.impute = wNNSel.impute(x.miss, lambda=result$lambda.opt, m=result$m.opt)
 ## and final MSIE
 computeMSIE(x.miss, x.impute, x.true)

Imputatin using wNNSel method.

Description

'wNNSel' is used to impute the missing values particularly in high dimensional data. It uses a cross validation procedure for selecting the best values of the tuning parameters. It also works when the samples are smaller than the covariates.

Usage

wNNSel(x, x.initial = NULL, x.true = NULL, k, useAll = TRUE,
  x.dist = "euclidean", kernel = "gaussian", method = "2", impute.fn,
  convex = TRUE, m.values = seq(2, 8, by = 2), c.values = seq(0.1, 0.5, by
  = 0.1), lambda.values = seq(0, 0.6, by = 0.01)[-1], times.max = 5,
  testNA.prop = 0.05, withinFolds = FALSE, folds, verbose = TRUE)

Arguments

Details

For each sample, identify missinng features. For each missing feature find the nearest neighbors which have that feature. Impute the missing value using the imputation function on the selected vector of values found from the neighbors. By default the wNNSel method automatically searches for optimal values for a given data matrix.

The default method uses x.dist="euclidean" including selected covariates. The specific distancs are computed using important covariates only. If mehtod="1", the linear function in absolute value of r is used, defined by

\frac{|r|}{1-c} - \frac{c}{1-c},

for |r|>c, and, 0 , otherwise. By default, the power function |r|^m is used when mehtod="2". For more detailed discussion, see references.

Value

a list containing imputed data matrix, and cross validation results

References

Tutz, G. and Ramzan,S. (2015). Improved methods for the imputation of missing data by nearest neighbor methods. Computational Statistics and Data Analysis, Vol. 90, pp. 84-99.

Faisal, S. and Tutz, G. (2017). Missing value imputation for gene expression data by tailored nearest neighbors. Statistical Application in Genetics and Molecular Biology. Vol. 16(2), pp. 95-106.

See Also

cv.wNNSel, wNNSel.impute

Examples

 set.seed(3)
 x.true = matrix(rnorm(100),10,10)
 ## create 10% missing values in x
 x.miss = artifNA(x.true, 0.10)
 ## imputed matrix
 result <- wNNSel(x.miss)
 result$x.impute
 ## cross validation result can be accessed using
 result$cross.val

Weighted Nearest Neighbor Imputation of Missing Values using Selected Variables

Description

This function imputes the missing values using user-spefied values of the tuning parameters. It also works when the samples are smaller than the covariates.

Usage

wNNSel.impute(x, k, useAll = TRUE, x.initial = NULL, x.dist = "euclidean",
  kernel = "gaussian", lambda = 0.3, impute.fn, convex = TRUE,
  method = "2", m = 2, c = 0.3, withinFolds = FALSE, folds,
  verbose = TRUE, verbose2 = FALSE)

Arguments

Details

For each sample, identify missinng features. For each missing feature find the nearest neighbors which have that feature. Impute the missing value using the imputation function on the selected vector of values found from the neighbors.

Value

imputed data matrix

See Also

cv.wNNSel, wNNSel

Examples

  set.seed(3)
  x = matrix(rnorm(100),10,10)
  x.miss = x > 1
  x[x.miss] = NA
  wNNSel.impute(x)
  wNNSel.impute(x, lambda=0.5, m=2)