Help for package tempted

Type:

Package

Title:

Temporal Tensor Decomposition, a Dimensionality Reduction Tool for Longitudinal Multivariate Data

Version:

0.1.1

Date:

2024-5-8

Depends:

R (≥ 4.2.0), np (≥ 0.60-17), ggplot2 (≥ 3.4.0), methods (≥ 4.2.1)

Author:

Pixu Shi

Maintainer:

Pixu Shi <pixu.shi@duke.edu>

Description:

TEMPoral TEnsor Decomposition (TEMPTED), is a dimension reduction method for multivariate longitudinal data with varying temporal sampling. It formats the data into a temporal tensor and decomposes it into a summation of low-dimensional components, each consisting of a subject loading vector, a feature loading vector, and a continuous temporal loading function. These loadings provide a low-dimensional representation of subjects or samples and can be used to identify features associated with clusters of subjects or samples. TEMPTED provides the flexibility of allowing subjects to have different temporal sampling, so time points do not need to be binned, and missing time points do not need to be imputed.

URL:

https://github.com/pixushi/tempted

License:

GPL-3

Encoding:

UTF-8

LazyData:

true

RoxygenNote:

7.3.1

NeedsCompilation:

Packaged:

2024-05-09 02:14:27 UTC; pixushi

Repository:

CRAN

Date/Publication:

2024-05-09 02:40:02 UTC

Aggregate features using feature loadings

Description

This function aggregate the features into "meta features" by calculating a weighted summation of the features using feature loading of each component as weights. It can also aggregate features by using the combination of multiple components by ranking the features by a linear combination of feature loadings from multiple components.

Usage

aggregate_feature(
  res_tempted,
  mean_svd = NULL,
  datlist,
  pct = 1,
  contrast = NULL
)

Arguments

res_tempted

Output of tempted.

mean_svd

Output of svd_centralize.

datlist

Output of format_tempted, the original temporal tensor that will be aggregated.

pct

The percent of features to aggregate, features ranked by absolute value of the feature loading of each component. Default is 1, which means 100% of features are aggregated. Setting pct=0.01 means top 1% of features is aggregated, where features are ranked in absolute value of feature loading of each component.

contrast

A matrix choosing how components are combined, each column is a contrast of length r and used to calculate the linear combination of the feature loadings of r components.

Value

A list of results.

metafeature_aggregate: The meta feature obtained by aggregating the observed temporal tensor. It is a data.frame with four columns: "value" for the meta feature values, "subID" for the subject ID, "timepoint" for the time points, and "PC" indicating which component was used to construct the meta feature.
metafeature_aggregate_est: The meta feature obtained by aggregating the denoised temporal tensor. It has the same structure as metafeature_aggregate.
contrast: The contrast used to linearly combine the components from input.
toppct: A matrix of TRUE/FALSE indicating which features are aggregated in each component and contrast.

References

Shi P, Martino C, Han R, Janssen S, Buck G, Serrano M, Owzar K, Knight R, Shenhav L, Zhang AR. (2023) Time-Informed Dimensionality Reduction for Longitudinal Microbiome Studies. bioRxiv. doi: 10.1101/550749. https://www.biorxiv.org/content/10.1101/550749.

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,]

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)

contrast <- matrix(c(1/2,1), 2, 1)

res_aggregate <- aggregate_feature(res_tempted,
                                   mean_svd,
                                   datlist,
                                   pct=1,
                                   contrast=contrast)

# plot the aggregated features


group <- unique(meta_table[, c("studyid", "delivery")])

plot_metafeature(res_aggregate$metafeature_aggregate, group, bws=30)

Caculate the Bernoulli kernel

Description

This function is used to calculate the kernel matrix for the RKHS regression that iteratively updates the temporal loading function.

Usage

bernoulli_kernel(x, y)

Arguments

x, y

Two values between which the Bernoulli kernel is calculated.

Value

The calculated kernel between x and y.

References

Han, R., Shi, P. and Zhang, A.R. (2023) Guaranteed functional tensor singular value decomposition. Journal of the American Statistical Association, pp.1-13. doi: 10.1080/01621459.2022.2153689.

OTU read count table from the ECAM data

Description

OTU read count table from the ECAM data

Usage

count_table

Format

A data.frame with rows representing samples and matching with data.frame meta_table and columns representing microbial features (i.e. OTUs). Each entry is a read count.

References

Bokulich, Nicholas A., et al. "Antibiotics, birth mode, and diet shape microbiome maturation during early life." Science translational medicine 8.343 (2016): 343ra82-343ra82.

Estimate subject loading of testing data

Description

This function estimates the subject loading of the testing data based on feature and temporal loading from training data, so that both the testing data and training data have the same dimensionality reduction.

Usage

est_test_subject(datlist, res_tempted, mean_svd = NULL)

Arguments

datlist

Testing data formatted into datlist in the same fashion as the training data. The same transformation needs to be used for both training and testing data.

res_tempted

Result from tempted ran on the training data.

mean_svd

Result from svd_centralize ran on the training data.

Value

estimated subject loading of testing data

References

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,]

# split the example data into training and testing

id_test <- meta_table_sub$studyid=="2"

count_train <- count_table_sub[!id_test,]
meta_train <- meta_table_sub[!id_test,]

count_test <- count_table_sub[id_test,]
meta_test <- meta_table_sub[id_test,]

# run tempted on training data

datlist_train <- format_tempted(count_train,
                                meta_train$day_of_life,
                                meta_train$studyid,
                                threshold=0.95,
                                pseudo=0.5,
                                transform="clr")

mean_svd_train <- svd_centralize(datlist_train, r=1)

res_tempted_train <- tempted(mean_svd_train$datlist,
r=2, smooth=1e-5)

# get the overlapping features

count_test <- count_test[,rownames(datlist_train[[1]])[-1]]

datlist_test <- format_tempted(count_test,
                               meta_test$day_of_life,
                               meta_test$studyid,
                               threshold=1,
                               pseudo=0.5,
                               transform="clr")

# estimate the subject loading of the testing subject

sub_test <- est_test_subject(datlist_test, res_tempted_train, mean_svd_train)

# train logistic regression classifier on training subjects

metauni <- unique(meta_table_sub[,c("studyid", "delivery")])
rownames(metauni) <- metauni$studyid
Atrain <- as.data.frame(res_tempted_train$A_hat)
Atrain$delivery <- metauni[rownames(Atrain),"delivery"]=="Cesarean"
glm_train <- glm(delivery ~ PC1+PC2,
                 data=Atrain, family=binomial(link="logit"))
summary(glm_train)

# predict the label of testing subject, whose true label is "Cesarean"

predict(glm_train, newdata=as.data.frame(sub_test), type="response")

Format data table into the input of tempted

Description

This function applies a variety of transformations to the read counts and format the sample by feature table and meta data into a data list that can be used as the input of tempted and svd_centralize. For data that are not read counts, or data that are not microbiome data, the user can apply their desired transformation to the data before formatting into list.

Usage

format_tempted(
  featuretable,
  timepoint,
  subjectID,
  threshold = 0.95,
  pseudo = NULL,
  transform = "clr"
)

Arguments

featuretable

A sample by feature matrix.

timepoint

The time stamp of each sample, matched with the rows of featuretable.

subjectID

The subject ID of each sample, matched with the rows of featuretable.

threshold

A threshold for feature filtering for microbiome data. Features with zero value percentage > threshold will be excluded. Default is 0.95.

pseudo

A small number to add to all the counts before normalizing into proportions and log transformation. Default is 1/2 of the smallest non-zero value that is specific for each sample. This pseudo count is added for transform=c("logcomp", "clr", "logit").

transform

The transformation applied to the data. "logcomp" for log of compositions. "comp" for compositions. "ast" for arcsine squared transformation. "clr" for central log ratio transformation. "lfb" for log 2 fold change over baseline (first time point) transformation. "logit" for logit transformation. "none" for no transformation. Default transform="clr" is recommended for microbiome data. For data that are already transformed, use transform="none".

Value

A length n list of matrices as the input of tempted and svd_centralize. 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.

Meta data table from the ECAM data

Description

Meta data table from the ECAM data

Usage

meta_table

Format

A data.frame with rows representing samples and matching with data.frame count_table and processed_table and three columns:

studyid: character denoting the subject ID of the infants.
delivery: character denoting the delivery mode of the infants.
day_of_life: character denoting the age of infants measured in days when microbiome sample was taken.

References

Bokulich, Nicholas A., et al. "Antibiotics, birth mode, and diet shape microbiome maturation during early life." Science translational medicine 8.343 (2016): 343ra82-343ra82.

Plot nonparametric smoothed mean and error bands of features versus time

Description

This is a handy function to plot the smoothed mean and error bands for multiple features.

Usage

plot_feature_summary(
  feature_mat,
  time_vec,
  group_vec,
  coverage = 0.95,
  bws = NULL,
  nrow = 1
)

Arguments

feature_mat

A sample by feature matrix. Each feature will be plotted separately as a facet. The features can be original features, meta features, log ratios, or any variables of interest.

time_vec

A vector of time points matched to the rows of feature_mat.

group_vec

A vector of factor variable indicating the group membership of samples matched to the rows of feature_mat.

coverage

The coverage rate for the error band. Default is 0.95.

bws

The smoothness parameter for the smoothing lines and error bands. A larger value means a smoother line. Default is NULL and calculated by function np::npreg().

nrow

The number of rows to plot the features used in function ggplot2::facet_wrap().

Value

A ggplot2 object.

Examples

# plot the summary of selected features

feat.names <- c("OTU4447072", "OTU4467447")

proportion_table <- count_table/rowSums(count_table)

plot_feature_summary(proportion_table[,feat.names],
                     meta_table$day_of_life,
                     meta_table$delivery,
                     bws=30)

Plot nonparametric smoothed mesan and error bands of meta features versus time

Description

This function plot the smoothed mean and error band of meta features grouped by a factor variable provided by the user.

Usage

plot_metafeature(metafeature, group, coverage = 0.95, bws = NULL, nrow = 1)

Arguments

metafeature

metafeature_ratio from the output of ratio_feature and tempted_all, metafeature_aggregate from the output of ratio_feature and tempted_all, or metafeature_aggregate_est from the output of ratio_feature.

group

A subject by 2 data.frame with the first column for subject ID and second column for group membership.

coverage

The coverage rate for the error band. Default is 0.95.

bws

The smoothness parameter for the smoothing lines and error bands. A larger value means a smoother line. Default is NULL and calculated by function np::npreg().

nrow

The number of rows to plot the features used in function ggplot2::facet_wrap().

Value

A ggplot2 object.

Plot the temporal loading functions

Description

This function uses ggplot2::geom_line() in ggplot2 to plot the temporal loading functions from tempted.

Usage

plot_time_loading(res, r = NULL, ...)

Arguments

res

Output of function tempted.

r

The number of components to plot. By default all the components estimated by tempted will be plotted.

...

Arguments to put in ggplot2::geom_line(aes(...)).

Value

An ggplot2 object.

Central-log-ratio (clr) transformed OTU table from the ECAM data

Description

Central-log-ratio (clr) transformed OTU table from the ECAM data

Usage

processed_table

Format

A data.frame with rows representing samples and matching with data.frame meta_table and columns representing microbial features (i.e. OTUs). Entries do not need to be transformed, and will be directly used by tempted. This data.frame is used to illustrate how tempted can be used for general form of multivariate longitudinal data already preprocessed by user.

References

Bokulich, Nicholas A., et al. "Antibiotics, birth mode, and diet shape microbiome maturation during early life." Science translational medicine 8.343 (2016): 343ra82-343ra82.

Take log ratio of the abundance of top features over bottom features

Description

Top and bottom ranking features are picked based on feature loadings (and their contrasts). The log ratio abundance of the top ranking features over the bottom ranking features is produced as the main result. This function and its result is designed for longitudinal microbiome data, and may not be meaningful for other type of temporal data.

Usage

ratio_feature(
  res_tempted,
  datlist,
  pct = 0.05,
  absolute = FALSE,
  contrast = NULL
)

Arguments

res_tempted

Output of tempted.

datlist

Output of format_tempted(, transform="none"), the temporal tensor that include the raw read counts.

pct

The percent of features to sum up. Default is 0.05, i.e. 5%.

absolute

absolute = TRUE means features are ranked by the absolute value of feature loadings, and the top pct percent of features are picked. absolute = FALSE means features are ranked by the original value of feature loadings, and the top and bottom pct percent of features are picked. Then ratio is taken as the abundance of the features with positive loading over the abundance of the features with negative loading.

contrast

A matrix choosing how components are combined, each column is a contrast of length r and used to calculate the linear combination of the feature loadings of r components.

Value

A list of results:

metafeature_ratio: The log ratio abundance of the top over bottom ranking features. It is a data.frame with five columns: "value" for the log ratio values, "subID" for the subject ID, and "timepoint" for the time points, and "PC" indicating which component was used to construct the meta feature.
contrast: The contrast used to linearly combine the components from input.
toppct: A matrix of TRUE/FALSE indicating which features are ranked top in each component (and contrast) and used as the numerator of the log ratio.
bottompct: A matrix of TRUE/FALSE indicating which features are ranked bottom in each component (and contrast) and used as the denominator of the log ratio.

References

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,]

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)

datalist_raw <- format_tempted(count_table_sub, meta_table_sub$day_of_life, meta_table_sub$studyid,
transform="none")

contrast <- cbind(c(1,1), c(1,-1))

res_ratio <- ratio_feature(res_tempted, datalist_raw, pct=0.1,
absolute=FALSE, contrast=contrast)

group <- unique(meta_table[, c("studyid", "delivery")])

# plot the log ratios

plot_metafeature(res_ratio$metafeature_ratio, group, bws=30)

Reconstruct tensor from low dimensional components

Description

This function reconstructs the temporal tensor from the low dimensional components extracted by tempted and svd_centralize.

Usage

reconstruct(res_tempted, res_svd = NULL, datlist = NULL, r_reconstruct = NULL)

Arguments

res_tempted

Output of function tempted.

res_svd

Output of function svd_centralize if mean subtraction svd_centralize was performed before tempted. If mean subtraction was not performed, specify res_svd=NULL and provide datlist.

datlist

Output of function format_tempted if mean subtraction was not performed and res_svd=NULL, or left as NULL if mean subtraction was performed and res_svd is provided.

r_reconstruct

The number of components from TEMPTED to be used for the tensor reconstruction.

Value

datlist_est The reconstructed tensor stored in a datlist format same as the output of format_tempted.

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$day_of_life%/%12)%%2==1]
count_table_sub <- count_table[sub_sample,]
processed_table_sub <- processed_table[sub_sample,]
meta_table_sub <- meta_table[sub_sample,]
# reconstruct with mean subtraction
datlist <- format_tempted(processed_table_sub,
                          meta_table_sub$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)

datlist_est <- reconstruct(res_tempted, mean_svd, datlist=NULL, r_reconstruct=2)
vec_est <- unlist(sapply(datlist_est, function(x){x[-1,]}))
vec_obs <- unlist(sapply(datlist, function(x){x[-1,]}))
R2 <- 1-sum((vec_est-vec_obs)^2)/sum(vec_obs^2)
R2

# reconstruct without mean subtraction
datlist <- format_tempted(processed_table_sub,
                          meta_table_sub$day_of_life,
                          meta_table_sub$studyid,
                          pseudo=NULL,
                          transform="none")

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

datlist_est <- reconstruct(res_tempted, res_svd=NULL, datlist=datlist, r_reconstruct=2)
vec_est <- unlist(sapply(datlist_est, function(x){x[-1,]}))
vec_obs <- unlist(sapply(datlist, function(x){x[-1,]}))
R2 <- 1-sum((vec_est-vec_obs)^2)/sum(vec_obs^2)
R2

Remove the mean structure of the temporal tensor

Description

This function first average the feature value of all time points for each subject to form a subject by feature matrix. Next, it performs a singular value decomposition of this matrix and construct the matrix's rank-r approximation. Then, it subtracts this rank-r subject by feature matrix from the temporal tensor.

Usage

svd_centralize(datlist, r = 1)

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

The number of ranks in the mean structure. Default is 1.

Value

A list of results.

datlist: The new temporal tensor after mean structure is removed.
A_tilde: The subject singular vector of the mean structure, a subject by r matrix.
B_tilde: The feature singular vector of the mean structure, a feature by r matrix.
lambda_tilde: The singular value of the mean structure, a length r vector.

References

Calculate the de-noised temporal tensor

Description

This function constructs a de-noised version of the temporal tensor using the low-rank components obtained by svd_centralize tempted and uses the loadings to

Usage

tdenoise(res_tempted, mean_svd = NULL)

Arguments

res_tempted

Output of tempted

mean_svd

Output of svd_centralize

Value

The de-noised functional tensor

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

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)

Run all major functions of tempted

Description

This function wraps functions format_tempted, svd_centralize, tempted, ratio_feature, \ and aggregate_feature.

Usage

tempted_all(
  featuretable,
  timepoint,
  subjectID,
  threshold = 0.95,
  pseudo = NULL,
  transform = "clr",
  r = 3,
  smooth = 1e-06,
  interval = NULL,
  resolution = 51,
  maxiter = 20,
  epsilon = 1e-04,
  r_svd = 1,
  do_ratio = TRUE,
  pct_ratio = 0.05,
  absolute = FALSE,
  pct_aggregate = 1,
  contrast = NULL
)

Arguments

featuretable

A sample by feature matrix. It is an input for format_tempted.

timepoint

The time stamp of each sample, matched with the rows of featuretable. It is an input for format_tempted.

subjectID

The subject ID of each sample, matched with the rows of featuretable. It is an input for format_tempted.

threshold

A threshold for feature filtering for microbiome data. Features with zero value percentage >= threshold will be excluded. Default is 0.95. It is an input for format_tempted.

pseudo

transform

The transformation applied to the data. "logcomp" for log of compositions. "comp" for compositions. "ast" for arcsine squared transformation. "clr" for central log ratio transformation. "logit" for logit transformation. "none" for no transformation. Default transform="clr" is recommended for microbiome data. For data that are already transformed, use transform="none". It is an input for format_tempted.

r

Number of components to decompose into, i.e. rank of the CP type decomposition. Default is set to 3. It is an input for tempted.

smooth

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. It is an input for tempted.

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. It is an input for tempted.

maxiter

Maximum number of iteration. Default is 20. It is an input for tempted.

epsilon

Convergence criteria for difference between iterations. Default is 1e-4. It is an input for tempted.

r_svd

The number of ranks in the mean structure. Default is 1. It is an input for svd_centralize.

do_ratio

Whether to calculate the log ratio of features.

pct_ratio

The percent of features to sum up. Default is 0.05, i.e. 5%. It is an input for ratio_feature.

absolute

absolute = TRUE means features are ranked by the absolute value of feature loadings, and the top pct_ratio percent of features are picked. absolute = FALSE means features are ranked by the original value of feature loadings, and the top and bottom pct_ratio percent of features are picked. Then ratio is taken as the abundance of the features with positive loading over the abundance of the features with negative loading. It is an input for ratio_feature.

pct_aggregate

The percent of features to aggregate, features ranked by absolute value of the feature loading of each component. Default is 1, which means 100% of features are aggregated. Setting pct_aggregate=0.01 means top 1% of features is aggregated, where features are ranked in absolute value of feature loading of each component. It is an input for aggregate_feature.

contrast

A matrix choosing how components are combined, each column is a contrast of length r and used to calculate the linear combination of the feature loadings of r components. It is an input for ratio_feature and It is an input for aggregate_feature.

Value

A list including all the input and output of functions format_tempted, svd_centralize, tempted, ratio_feature, and aggregate_feature.

input: All the input options of function tempted_all.
datalist_raw: Output of format_tempted with option transform="none".
datlist: Output of format_tempted.
mean_svd: Output of svd_centralize.
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.
metafeature_ratio: The log ratio abundance of the top over bottom ranking features. It is a data.frame with five columns: "value" for the log ratio values, "subID" for the subject ID, and "timepoint" for the time points, and "PC" indicating which component was used to construct the meta feature.
toppct_ratio: A matrix of TRUE/FALSE indicating which features are ranked top in each component (and contrast) and used as the numerator of the log ratio.
bottompct_ratio: A matrix of TRUE/FALSE indicating which features are ranked bottom in each component (and contrast) and used as the denominator of the log ratio.
metafeature_aggregate: The meta feature obtained by aggregating the observed temporal tensor. It is a data.frame with four columns: "value" for the meta feature values, "subID" for the subject ID, "timepoint" for the time points, and "PC" indicating which component was used to construct the meta feature.
toppct_aggregate: A matrix of TRUE/FALSE indicating which features are aggregated in each component and contrast.
contrast: The contrast used to linearly combine the components from input.

References

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 preprocessed data that do not need to be transformed


res.processed <- tempted_all(processed_table_sub,
                             meta_table_sub$day_of_life,
                            meta_table_sub$studyid,
                             threshold=1,
                             transform="none",
                             r=2,
                             smooth=1e-5,
                             do_ratio=FALSE)

# for count data that will have pseudo added and clr transformed

res.count <- tempted_all(count_table_sub,
                         meta_table_sub$day_of_life,
                         meta_table_sub$studyid,
                         threshold=0.95,
                         transform="clr",
                         pseudo=0.5,
                         r=2,
                         smooth=1e-5,
                         pct_ratio=0.1,
                         pct_aggregate=1)

# for proportional data that will have pseudo added and clr transformed

res.proportion <- tempted_all(count_table_sub/rowSums(count_table_sub),
                              meta_table_sub$day_of_life,
                              meta_table_sub$studyid,
                              threshold=0.95,
                              transform="clr",
                              pseudo=NULL,
                              r=2,
                              smooth=1e-5,
                              pct_ratio=0.1,
                              pct_aggregate=1)

# plot the temporal loading and subject trajectories grouped by delivery mode

plot_time_loading(res.proportion, r=2)

group <- unique(meta_table[,c("studyid", "delivery")])

# plot the aggregated features

plot_metafeature(res.proportion$metafeature_aggregate, group, bws=30)

Aggregate features using feature loadings

Description

Usage

Arguments

Value

References

Examples

Caculate the Bernoulli kernel

Description

Usage

Arguments

Value

References

OTU read count table from the ECAM data

Description

Usage

Format

References

Estimate subject loading of testing data

Description

Usage

Arguments

Value

References

Examples

Format data table into the input of tempted

Description

Usage

Arguments

Value

See Also

Meta data table from the ECAM data

Description

Usage

Format

References

Plot nonparametric smoothed mean and error bands of features versus time

Description

Usage

Arguments

Value

Examples

Plot nonparametric smoothed mesan and error bands of meta features versus time

Description

Usage

Arguments

Value

See Also

Plot the temporal loading functions

Description

Usage

Arguments

Value

See Also

Central-log-ratio (clr) transformed OTU table from the ECAM data

Description

Usage

Format

References

Take log ratio of the abundance of top features over bottom features

Description

Usage

Arguments

Value

References

Examples

Reconstruct tensor from low dimensional components

Description

Usage

Arguments

Value

Examples

Remove the mean structure of the temporal tensor

Description

Usage

Arguments

Value

References

See Also

Calculate the de-noised temporal tensor