SmoothHOOI is an R package that implements methods described in “Smooth Tensor Decomposition with Application to Ambulatory Blood Pressure Monitoring Data” [arxiv]. The application to real and synthetic ABPM data can be found here.
You can install the development version of SmoothHOOI from GitHub with:
# install.packages("devtools")
devtools::install_github("IrinaStatsLab/SmoothHOOI")This is a simple example which shows you how to use this package.
library(SmoothHOOI)
set.seed(1234321)
# Generate a random tensor with missing data, in the array format
dims <- c(24, 3, 207)
tnsr <- array(rnorm(prod(dims), mean = 0, sd = 1), dim = dims)
missing_prob <- 0.2
missing_indices <- sample(length(tnsr), size = floor(length(tnsr) * missing_prob))
tnsr[missing_indices] <- NA# Make the second order difference matrix with circular nature
D2 <- SecDiffMat(24)# Find optimal hyperparameter with 5-fold cross-validation
kcv_res <- kcv(tnsr, rank_grid=as.matrix(expand.grid(r1<-seq(3,6,by=1), r2<-c(2,3))), lambda_seq=seq(1,10,by=1), k=5, L0=NULL, D=D2, tol=0.01, max_iter=500, init=0)
kcv_res$MSE_mat # matrix for CV error (rows representing ranks, cols representing lambda)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 1.172131 1.166626 1.161576 1.158826 1.156901 1.155217 1.153676 1.152170
#> [2,] 1.227177 1.205206 1.190116 1.181757 1.175460 1.170243 1.165838 1.162020
#> [3,] 1.278286 1.251227 1.232606 1.218674 1.207836 1.199102 1.191896 1.185804
#> [4,] 1.292700 1.251249 1.226943 1.210377 1.202834 1.193628 1.186046 1.179746
#> [5,] 1.262352 1.252891 1.250023 1.245784 1.242255 1.239026 1.236034 1.233090
#> [6,] 1.345476 1.317767 1.301480 1.288158 1.277483 1.268686 1.261294 1.254862
#> [7,] 1.469506 1.414205 1.376974 1.349758 1.328841 1.312307 1.298713 1.287339
#> [8,] 1.465609 1.392685 1.351531 1.323935 1.303719 1.288109 1.275645 1.265289
#> [,9] [,10]
#> [1,] 1.150657 1.149116
#> [2,] 1.158628 1.155584
#> [3,] 1.180579 1.176029
#> [4,] 1.174367 1.169655
#> [5,] 1.230345 1.227648
#> [6,] 1.249189 1.244159
#> [7,] 1.277729 1.269320
#> [8,] 1.256500 1.248908
kcv_res$opt_para # optimal hyperparameters
#> [,1] [,2] [,3]
#> [1,] 3 2 10# Run SmoothHOOI algorithm with the optimal hyperparameters
res <- mglram(tnsr, ranks = c(3, 2), init=0, D = D2,
lambda = 10, max_iter = 500, tol = 1e-5, L0 = NULL)
res$conv # check convergence
#> [1] TRUE# Rotation for Identifiability
tilde <- MakeIdent(L=res$L, G=res$G, R=res$R)
tilde$L_tilde
#> [,1] [,2] [,3]
#> [1,] -0.076664031 0.299039188 -0.201257836
#> [2,] -0.034462738 0.313950831 -0.128575363
#> [3,] 0.002837489 0.322577973 -0.041876176
#> [4,] 0.030006785 0.327236749 0.047662495
#> [5,] 0.042933955 0.321622435 0.132258788
#> [6,] 0.037855655 0.304793481 0.207728255
#> [7,] 0.015013668 0.275458956 0.263496525
#> [8,] -0.022353592 0.234403947 0.295443612
#> [9,] -0.072918581 0.181376161 0.304221700
#> [10,] -0.132438500 0.118441802 0.292474823
#> [11,] -0.192233673 0.053152657 0.266509439
#> [12,] -0.242449631 -0.005008934 0.234147329
#> [13,] -0.281398641 -0.053545019 0.198188052
#> [14,] -0.304307991 -0.090818852 0.161378679
#> [15,] -0.317266471 -0.113160101 0.117183434
#> [16,] -0.322129268 -0.117733398 0.063350895
#> [17,] -0.320556710 -0.103954596 0.001451675
#> [18,] -0.311773461 -0.070556550 -0.066237379
#> [19,] -0.294637784 -0.019694494 -0.136527093
#> [20,] -0.268641612 0.043705177 -0.199602787
#> [21,] -0.235093174 0.110442486 -0.246335905
#> [22,] -0.197714498 0.172777116 -0.271842409
#> [23,] -0.159799543 0.228670861 -0.272874407
#> [24,] -0.119932297 0.271526977 -0.250310897
tilde$R_tilde
#> [,1] [,2]
#> [1,] -0.4215993 0.8839439
#> [2,] 0.1862318 -0.1338599
#> [3,] 0.8874524 0.4480230
tilde$G_tilde[ , ,1]
#> [,1] [,2]
#> [1,] 0.5721879 -1.459163
#> [2,] 0.6924006 1.595611
#> [3,] 0.4895365 0.329901