Package 'TrendTM'

Example of data

Description

A simulated matrix with a low rank k and with temporal structure based on independent Gaussian.

Usage

data(Data_Series)

Format

A matrix with 30 rows (30 times series) and 100 columns (size of each temporal series).

Examples

library(TrendTM)
data(Data_Series)
head(Data_Series)
TrendTM(Data_Series,k_max=3)

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It performs the factorization for a fixed rank k and a temporal structure with a fixed tau

Description

It performs the factorization for a fixed rank k and a temporal structure with a fixed tau

Usage

FM_kt(
  Data_Series,
  k = 2,
  tau = floor(n/2),
  struct_temp = "none",
  type_soft = "als"
)

Arguments

Data_Series	the data matrix with d rows and n columns containing the d temporal series with size n.
k	the fixed rank of X. Default is 2.
tau	the fixed value for tau . Default is floor(n/2).
struct_temp	a name indicating the temporal structure. Could be none, periodic or smooth. Default is none.
type_soft	the option type of the function softImpute. Default is als.

Value

A list containing

• M_est the estimation of M.

• U_est the component U of the decomposition of M_est.

• V_est the component V of the decomposition of M_est.

• contrast the Frobenius norm of X-M_est.

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It performs the slope heuristic for the selection of a penalty constant

Description

It performs the slope heuristic for the selection of a penalty constant

Usage

OurSlope(contrast, grille, penalty)

Arguments

contrast	the Frobenius norm of X-M_est for all the value of the grid grille
grille	the ordered grid of potential values for the penalty constant
penalty	the penalty calculated for each value of the grid grille

Value

Model_Selected the selected parameter

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Matrix Factorization for Multivariate Time Series Analysis

Description

It is the main function. It performs the factorization for a selected rank and a temporal structure with a selected tau if the selection is requested otherwise it is fixed

Usage

TrendTM(
  Data_Series,
  k_select = FALSE,
  k_max = 20,
  struct_temp = "none",
  tau_select = FALSE,
  tau_max = floor(n/2),
  type_soft = "als"
)

Arguments

Data_Series	the data matrix with d rows and n columns containing the d temporal series with size n.
k_select	a boolean indicating if the rank of the matrix Data_Series will be selected. Default is FALSE.
k_max	the fixed rank of Data_Series if k_select=FALSE. The maximal value of the rank if k_select=TRUE (must be lower than the minimum between d and n). Default is 20.
struct_temp	a name indicating the temporal structure. Could be none, periodic or smooth. Default is none.
tau_select	a boolean indicating if the parameter tau will be selected. This can be possible only when struct_temp=smooth. Default is FALSE.
tau_max	the fixed value for tau if tau_select=FALSE. The maximal value of tau if tau_select=TRUE (must be lower than n). Default is floor(n/2).
type_soft	the option type of the function softImpute. Default is als.

Details

The penalty constant(s) is(are) calibrated using the slope heuristic from package capushe. We adapt this heuristic as follows: the final dimension is the one correspind to the majority of the selected dimension for the considered different penalties.

Value

A list containing

• k_est the selected rank if k_select==TRUE or k_max if k_select==FALSE.

• tau_est the selected tau if tau_select==TRUE or tau_max if tau_select==FALSE.

• U_est the component U of the decomposition of the final estimator M_est.

• V_est the component V of the decomposition of the final estimator M_est.

• M_est the estimation of M.

• contrast the Frobenius norm of Data_Series-M_est. This is a value when k_select==FALSE and tau_select==FALSE, a vector when k_select==TRUE or tau_select==TRUE, and a matrix when k_select==TRUE and tau_select==TRUE with k_max rows and tau_max columns.

Examples

data(Data_Series)
result <- TrendTM(Data_Series, k_max = 3)

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