tempted {tempted}

Decomposition of temporal tensor

Description

This is the main function of tempted.

Usage

tempted(
  datlist,
  r = 3,
  smooth = 1e-06,
  interval = NULL,
  resolution = 101,
  maxiter = 20,
  epsilon = 1e-04
)

Arguments

datlist

A length n list of matrices. Each matrix represents a subject, with columns representing samples from this subject, the first row representing the sampling time points, and the following rows representing the feature values.

r

Number of components to decompose into, i.e. rank of the CP type decomposition. Default is set to 3.

smooth

Smoothing parameter for RKHS norm. Larger means smoother temporal loading functions. Default is set to be 1e-8. Value can be adjusted depending on the dataset by checking the smoothness of the estimated temporal loading function in plot.

interval

The range of time points to ran the decomposition for. Default is set to be the range of all observed time points. User can set it to be a shorter interval than the observed range.

resolution

Number of time points to evaluate the value of the temporal loading function. Default is set to 101. It does not affect the subject or feature loadings.

maxiter

Maximum number of iteration. Default is 20.

epsilon

Convergence criteria for difference between iterations. Default is 1e-4.

Value

The estimations of the loadings.

A_hat

Subject loading, a subject by r matrix.

B_hat

Feature loading, a feature by r matrix.

Phi_hat

Temporal loading function, a resolution by r matrix.

time_Phi

The time points where the temporal loading function is evaluated.

Lambda

Eigen value, a length r vector.

r_square

Variance explained by each component. This is the R-squared of the linear regression of the vectorized temporal tensor against the vectorized low-rank reconstruction using individual components.

accum_r_square

Variance explained by the first few components accumulated. This is the R-squared of the linear regression of the vectorized temporal tensor against the vectorized low-rank reconstruction using the first few components.

Examples

# Take a subset of the samples so the example runs faster

# Here we are taking samples from the odd months
sub_sample <- rownames(meta_table)[(meta_table$day_of_life%/%12)%%2==1]
count_table_sub <- count_table[sub_sample,]
processed_table_sub <- processed_table[sub_sample,]
meta_table_sub <- meta_table[sub_sample,]

# for count data from longitudinal microbiome studies

datlist <- format_tempted(count_table_sub,
                          meta_table_sub$day_of_life,
                          meta_table_sub$studyid,
                          pseudo=0.5,
                          transform="clr")

mean_svd <- svd_centralize(datlist, r=1)

res_tempted <- tempted(mean_svd$datlist, r=2, smooth=1e-5)

# for preprocessed data that do not need to be transformed

datlist <- format_tempted(processed_table_sub,
                          meta_table_sub$day_of_life,
                          meta_table_sub$studyid,
                          pseudo=NULL,
                          transform="none")

mean_svd <- svd_centralize(datlist, r=1)

res_tempted <- tempted(mean_svd$datlist, r=2, smooth=1e-5)

# plot the temporal loading

plot_time_loading(res_tempted, r=2)