Package 'eimpute'

Data standardization

Description

Standardize a matrix rows and/or columns to have zero mean or unit variance

Usage

biscale(x, thresh.sd = 1e-05, maxit.sd = 100, control = list(...), ...)

Arguments

x	an $m$ by $n$ matrix possibly with NAs.
thresh.sd	convergence threshold, measured as the relative change in the Frobenius norm between two successive estimates.
maxit.sd	maximum number of iterations.
control	a list of parameters that control details of standard procedure. See biscale.control.
...	arguments to be used to form the default control argument if it is not supplied directly.

Value

A list is returned

x.st	The matrix after standardization.
alpha	The row mean after iterative process.
beta	The column mean after iterative process.
tau	The row standard deviation after iterative process.
gamma	The column standard deviation after iterative process.

References

Hastie, Trevor, Rahul Mazumder, Jason D. Lee, and Reza Zadeh. Matrix completion and low-rank SVD via fast alternating least squares. The Journal of Machine Learning Research 16, no. 1 (2015): 3367-3402.

Examples

################# Quick Start #################
m <- 100
n <- 100
r <- 10
x_na <- incomplete.generator(m, n, r)

###### Standardize both mean and variance
xs <- biscale(x_na)

###### Only standardize mean ######
xs_mean <- biscale(x_na, row.mean = TRUE, col.mean = TRUE)

###### Only standardize variance ######
xs_std <- biscale(x_na, row.std = TRUE, col.std = TRUE)

---

Control for standard procedure

Description

Various parameters that control aspects of the standard procedure.

Usage

biscale.control(
  row.mean = FALSE,
  row.std = FALSE,
  col.mean = FALSE,
  col.std = FALSE
)

Arguments

row.mean	if row.mean = TRUE (the default), row centering will be performed resulting in a matrix with row means zero. If row.mean is a vector, it will be used in the iterative process. If row.mean = FALSE nothing is done.
row.std	if row.std = TRUE , row scaling will be performed resulting in a matrix with row variance one. If row.std is a vector, it will be used in the iterative process. If row.std = FALSE (the default) nothing is done.
col.mean	similar to row.mean.
col.std	similar to row.std.

Value

A list with components named as the arguments.

---

Efficiently impute missing values for a large scale matrix

Description

Fit a low-rank matrix approximation to a matrix with missing values. The algorithm iterates like EM: filling the missing values with the current guess, and then approximating the complete matrix via truncated SVD.

Usage

eimpute(
  x,
  r,
  svd.method = c("tsvd", "rsvd"),
  noise.var = 0,
  thresh = 1e-05,
  maxit = 100,
  init = FALSE,
  init.mat = 0,
  override = FALSE,
  control = list(...),
  ...
)

Arguments

x	an $m$ by $n$ matrix with NAs.
r	the rank of low-rank matrix for approximating x
svd.method	a character string indicating the truncated SVD method. If svd.method = "rsvd", a randomized SVD is used, else if svd.method = "tsvd", standard truncated SVD is used. Any unambiguous substring can be given. Default svd.method = "tsvd".
noise.var	the variance of noise.
thresh	convergence threshold, measured as the relative change in the Frobenius norm between two successive estimates.
maxit	maximal number of iterations.
init	if init = FALSE(the default), the missing entries will initialize with mean.
init.mat	the initialization matrix.
override	logical value indicating whether the observed elements in x should be overwritten by its low-rank approximation.
control	a list of parameters that control details of standard procedure, See biscale.control.
...	arguments to be used to form the default control argument if it is not supplied directly.

Value

A list containing the following components

x.imp	the matrix after completion.
rmse	the relative mean square error of matrix completion, i.e., training error.
iter.count	the number of iterations.

References

Rahul Mazumder, Trevor Hastie and Rob Tibshirani (2010) Spectral Regularization Algorithms for Learning Large Incomplete Matrices, Journal of Machine Learning Research 11, 2287-2322

Nathan Halko, Per-Gunnar Martinsson, Joel A. Tropp (2011) Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions, Siam Review Vol. 53, num. 2, pp. 217-288

Examples

################# Quick Start #################
m <- 100
n <- 100
r <- 10
x_na <- incomplete.generator(m, n, r)
head(x_na[, 1:6])
x_impute <- eimpute(x_na, r)
head(x_impute[["x.imp"]][, 1:6])
x_impute[["rmse"]]

---

Incomplete data generator

Description

Generate a matrix with missing values, where the indices of missing values are uniformly randomly distributed in the matrix.

Usage

incomplete.generator(m, n, r, snr = 3, prop = 0.5, seed = 1)

Arguments

m	the rows of the matrix.
n	the columns of the matrix.
r	the rank of the matrix.
snr	the signal-to-noise ratio in generating the matrix. Default snr = 3.
prop	the proportion of missing observations. Default prop = 0.5.
seed	the random seed. Default seed = 1.

Details

We generate the matrix by $UV + \epsilon$, where $U$, $V$ are $m$ by $r$, $r$ by $n$ matrix satisfy standard normal distribution. $\epsilon$ has a normal distribution with mean 0 and variance $\frac{r}{snr}$.

Value

A matrix with missing values.

Examples

m <- 100
n <- 100
r <- 10
x_na <- incomplete.generator(m, n, r)
head(x_na[, 1:6])

---

Search rank magnitude of the best approximating matrix

Description

Estimate a preferable matrix rank magnitude for fitting a low-rank matrix approximation to a matrix with missing values. The algorithm use GIC/CV to search the rank in a given range, and then fill the missing values with the estimated rank.

Usage

r.search(
  x,
  r.min = 1,
  r.max = "auto",
  svd.method = c("tsvd", "rsvd"),
  rule.type = c("gic", "cv"),
  noise.var = 0,
  init = FALSE,
  init.mat = 0,
  maxit.rank = 1,
  nfolds = 5,
  thresh = 1e-05,
  maxit = 100,
  override = FALSE,
  control = list(...),
  ...
)

Arguments

x	an $m$ by $n$ matrix with NAs.
r.min	the start rank for searching. Default r.min = 1.
r.max	the max rank for searching.
svd.method	a character string indicating the truncated SVD method. If svd.method = "rsvd", a randomized SVD is used, else if svd.method = "tsvd", standard truncated SVD is used. Any unambiguous substring can be given. Default svd.method = "tsvd".
rule.type	a character string indicating the information criterion rule. If rule.type = "gic", generalized information criterion rule is used, else if rule.type = "cv", cross validation is used. Any unambiguous substring can be given. Default rule.type = "gic".
noise.var	the variance of noise.
init	if init = FALSE(the default), the missing entries will initialize with mean.
init.mat	the initialization matrix.
maxit.rank	maximal number of iterations in searching rank. Default maxit.rank = 1.
nfolds	number of folds in cross validation. Default nfolds = 5.
thresh	convergence threshold, measured as the relative change in the Frobenius norm between two successive estimates.
maxit	maximal number of iterations.
override	logical value indicating whether the observed elements in x should be overwritten by its low-rank approximation.
control	a list of parameters that control details of standard procedure, See biscale.control.
...	arguments to be used to form the default control argument if it is not supplied directly.

Value

A list containing the following components

x.imp	the matrix after completion with the estimated rank.
r.est	the rank estimation.
rmse	the relative mean square error of matrix completion, i.e., training error.
iter.count	the number of iterations.

Examples

################# Quick Start #################
m <- 100
n <- 100
r <- 10
x_na <- incomplete.generator(m, n, r)
head(x_na[, 1:6])
x_impute <- r.search(x_na, 1, 15, "rsvd", "gic")
x_impute[["r.est"]]

---