bs_cor_rank {TensorPreAve}

Bootstrap Rank Estimation.

Description

Function to estimate the rank of the core tensor by Bootstrapped Correlation Thresholding.

Usage

bs_cor_rank(X, initial_direction, r_range = NULL, C_range = NULL, B = 50)

Arguments

X

A 'Tensor' object defined in package rTensor with K+1 modes. Mode-1 should correspond to the time mode.

initial_direction

Direction corresponds to the strongest factors, written in a list of K vectors. This can be obtained from the iterative projection procedure by using function iter_proj.

r_range

Approximate range of r_k (number of factors) to search from, written in a list of K vectors (e.g. z = list(c(1,10),c(1,10)) for K = 2). Default range is 1 to 10 for all modes.

C_range

The range of constant C for calculating threshold. Default is seq(0,100,0.1), and set to be automatically tuned as data-driven.

B

Number of bootstrap samples. Default is 50. Can be set as 10 to save time when dimension is large.

Details

Input a tensor time series and estimated directions corresponding to the strongest factors, return the estimated rank of core tensor.

Value

A vector of length K, indicating estimated number of factors in each mode.

Examples

# Example of real data set
set.seed(10)
Q_PRE = pre_est(value_weight_tensor)
Q_PROJ = iter_proj(value_weight_tensor, initial_direction = Q_PRE)
bs_rank = bs_cor_rank(value_weight_tensor, Q_PROJ)
bs_rank


# Example using generated data
K = 2
T = 100
d = c(40,40)
r = c(2,2)
re = c(2,2)
eta = list(c(0,0),c(0,0))
u = list(c(-2,2),c(-2,2))
set.seed(10)
Data_test = tensor_data_gen(K,T,d,r,re,eta,u)
X = Data_test$X
Q_PRE = pre_est(X)
Q_PROJ = iter_proj(X, initial_direction = Q_PRE)
bs_rank = bs_cor_rank(X, Q_PROJ)
bs_rank