Tutorial for asmbPLS package
Runzhi Zhang, Ph.D.
Department of
Biostatistics
University of Florida
2023-04-13
1 Requirements
Please install the R package prior to use asmbPLS.
library(asmbPLS) ## load the R package
set.seed(123) ## set seed to generate the same resultsIf you want to see the list of functions in asmbPLS, please use
?asmbPLS.
If you want to see the detailed description for each function, please
use ?function, for example ?asmbPLS.cv.
2 asmbPLS
2.1 Example data for asmbPLS algorithm
data(asmbPLS.example) ## load the example data set for asmbPLS8 components are included in the asmbPLS.example:
1) X.matrix, a matrix with 100 samples (rows) and 400
features (columns, 1-200 are microbial taxa, 201-400 are
metabolites);
2) X.matrix.new, a matrix to be predicted with 100 samples
(rows) and 400 features (columns, 1-200 are microbial taxa, 201-400 are
metabolites);
3) Y.matrix, a matrix with 100 samples (rows) and 1 column
(log-transformed survival time);
4) X.dim, dimension of the two blocks in
X.matrix;
5) PLS.comp, selected number of PLS components;
6) quantile.comb, selected quantile combinations;
7) quantile.comb.table.cv, pre-defined quantile
combinations for cross validation;
8) Y.indicator, a vector containing the event indicator for
each sample.
Pre-processing has been applied to the two different types of data in
X.matrix.
Different types of omics data require specific pre-processing steps
tailored to their unique characteristics.
## show the first 5 microbial taxa and the first 5 metabolites for the first 5 samples.
asmbPLS.example$X.matrix[1:5, c(1:5, 201:205)]
#> Taxa_1 Taxa_2 Taxa_3 Taxa_4 Taxa_5 metabolite_1
#> [1,] -1.63175165 2.4625929 2.6119703 -0.7154609 -4.1166583 6.900372
#> [2,] -3.27012529 1.9821481 -0.3256863 0.1956106 0.6617003 8.074607
#> [3,] 1.81855927 -0.5863047 1.7614009 -2.0526417 -3.8444012 7.669377
#> [4,] -4.29551101 -0.8943136 0.3488799 1.0889840 2.5439654 7.876529
#> [5,] 0.03458501 0.9299691 -0.4423391 2.7631137 -4.0258580 6.538369
#> metabolite_2 metabolite_3 metabolite_4 metabolite_5
#> [1,] 3.905864 3.411215 5.802873 5.910157
#> [2,] 2.919310 5.032784 6.013281 5.080354
#> [3,] 3.815648 6.653860 4.064987 5.377000
#> [4,] 1.731010 4.232027 6.144947 5.382338
#> [5,] 3.829668 4.680280 4.678092 5.505065
## show the outcome for the first 5 samples.
asmbPLS.example$Y.matrix[1:5,]
#> [1] 6.410580 5.899169 5.684940 7.034513 5.8422382.2 Cross Validation
The 5-fold CV with 5 repetitions is implemented to help find the best quantile combination for each PLS component as well as the optimal number of PLS components.
X.matrix = asmbPLS.example$X.matrix
X.matrix.new = asmbPLS.example$X.matrix.new
Y.matrix = asmbPLS.example$Y.matrix
PLS.comp = asmbPLS.example$PLS.comp
X.dim = asmbPLS.example$X.dim
quantile.comb.table.cv = asmbPLS.example$quantile.comb.table.cv
Y.indicator = asmbPLS.example$Y.indicator
## cv to find the best quantile combinations for model fitting
cv.results <- asmbPLS.cv(X.matrix = X.matrix,
Y.matrix = Y.matrix,
PLS.comp = PLS.comp,
X.dim = X.dim,
quantile.comb.table = quantile.comb.table.cv,
Y.indicator = Y.indicator,
k = 5,
ncv = 5)
## obtain the best quantile combination for each PLS component
quantile.comb <- cv.results$quantile_table_CV[,1:length(X.dim)]
## obtain the optimal number of PLS components
n.PLS <- cv.results$optimal_nPLS 2.3 Model Fit
The selected quantile combination for each PLS component and the
optimal number of PLS components can be used as input for the
asmbPLS.fit function to fit the final model.
asmbPLS.results <- asmbPLS.fit(X.matrix = X.matrix,
Y.matrix = Y.matrix,
PLS.comp = n.PLS,
X.dim = X.dim,
quantile.comb = quantile.comb)2.4 Prediction
Once the model is fitted, you can use the model to do the prediction
using the new data set (X.matrix.new).
Y.pred <- asmbPLS.predict(asmbPLS.results, X.matrix.new, n.PLS)
head(Y.pred$Y_pred)
#> [,1]
#> [1,] 6.064187
#> [2,] 6.764513
#> [3,] 6.238559
#> [4,] 5.912458
#> [5,] 7.243043
#> [6,] 6.143728Also, you can do the prediction using the original data set
X.matrix to check the model fit.
## prediction for original data to check the data fit
Y.fit <- asmbPLS.predict(asmbPLS.results, X.matrix, n.PLS)
check.fit <- cbind(Y.matrix, Y.fit$Y_pred)
head(check.fit)
#> [,1] [,2]
#> [1,] 6.410580 6.374432
#> [2,] 5.899169 6.108969
#> [3,] 5.684940 5.408893
#> [4,] 7.034513 6.961441
#> [5,] 5.842238 5.759226
#> [6,] 7.429254 6.8337433 asmbPLS-DA
3.1 Example data for asmbPLS-DA algorithm
data(asmbPLSDA.example) ## load the example data set for asmbPLS-DA8 components are included in the
asmbPLSDA.example:
1) X.matrix, a matrix with 100 samples (rows) and 400
features, features 1-200 are from block 1 and features 201-400 are from
block 2;
2) X.matrix.new, a matrix to be predicted with 100 samples
(rows) and 400 features, features 1-200 are from block 1 and features
201-400 are from block 2;
3) Y.matrix.binary, a matrix with 100 samples (rows) and 1
column;
4) Y.matrix.morethan2levels, a matrix with 100 samples
(rows) and 3 columns (3 levels);
5) X.dim, dimension of the two blocks in
X.matrix;
6) PLS.comp, selected number of PLS components;
7) quantile.comb, selected quantile combinations;
8) quantile.comb.table.cv, pre-defined quantile
combinations for cross validation.
## show the first 5 features from block 1 and the first 5 features from block 2 for the first 5 samples.
asmbPLSDA.example$X.matrix[1:5, c(1:5, 201:205)]
#> G1_feature_1 G1_feature_2 G1_feature_3 G1_feature_4 G1_feature_5
#> [1,] 0.2444821 0.3715013 -0.21780418 0.58436337 -1.19637830
#> [2,] -0.2323967 -0.2874724 -0.31100383 -0.11253287 -0.03668811
#> [3,] -1.0820464 0.4585036 0.03601036 -0.76487964 0.72843992
#> [4,] 1.0914838 2.0047015 -0.15045351 0.16187751 -1.24755651
#> [5,] 1.0288807 -1.0768499 -0.12903603 0.08122353 1.75583752
#> G2_feature_1 G2_feature_2 G2_feature_3 G2_feature_4 G2_feature_5
#> [1,] -0.7820185 -0.05832018 -2.3319625 -1.6828910 0.9156531
#> [2,] -0.4364726 -2.19203919 -0.1741337 -1.3169466 0.3992667
#> [3,] -0.1695784 0.24391203 0.8735221 0.5688791 -0.1548541
#> [4,] 0.8182932 1.38808419 -0.9268429 -1.8371658 1.1532969
#> [5,] -0.8297609 0.01371050 0.6736516 -0.7678065 -0.7571429
## show the binary outcome for the first 5 samples.
asmbPLSDA.example$Y.matrix.binary[1:5,]
#> [1] 0 0 1 1 1
## show the multiclass outcome for the first 5 samples.
asmbPLSDA.example$Y.matrix.morethan2levels[1:5,]
#> [,1] [,2] [,3]
#> [1,] 0 1 0
#> [2,] 0 0 1
#> [3,] 0 1 0
#> [4,] 0 1 0
#> [5,] 0 1 0In the example data set, we include both binary outcome and multiclass outcome.
3.2 Cross Validation
Similarly, the 5-fold CV with 5 repetitions is implemented to help
find the best quantile combination for each PLS component as well as the
optimal number of PLS components.
You can use different decision rules (method in the
function, the default is fixed_cutoff for the binary
outcome and Max_Y for the multiclass outcome) and different
measure (The default is balanced accuracy
B_accuracy) for the CV.
Also, note that you need to set different outcome.type for
different types of outcomes.
Extract the components from the example data list:
X.matrix = asmbPLSDA.example$X.matrix
X.matrix.new = asmbPLSDA.example$X.matrix.new
Y.matrix.binary = asmbPLSDA.example$Y.matrix.binary
Y.matrix.multiclass = asmbPLSDA.example$Y.matrix.morethan2levels
X.dim = asmbPLSDA.example$X.dim
PLS.comp = asmbPLSDA.example$PLS.comp
quantile.comb.table.cv = asmbPLSDA.example$quantile.comb.table.cvCV for the binary outcome:
## cv to find the best quantile combinations for model fitting (binary outcome)
cv.results.binary <- asmbPLSDA.cv(X.matrix = X.matrix,
Y.matrix = Y.matrix.binary,
PLS.comp = PLS.comp,
X.dim = X.dim,
quantile.comb.table = quantile.comb.table.cv,
outcome.type = "binary",
k = 5,
ncv = 5)
quantile.comb.binary <- cv.results.binary$quantile_table_CV[,1:length(X.dim)]
n.PLS.binary <- cv.results.binary$optimal_nPLSCV for the multiclass outcome:
## cv to find the best quantile combinations for model fitting
## (categorical outcome with more than 2 levels)
cv.results.multiclass <- asmbPLSDA.cv(X.matrix = X.matrix,
Y.matrix = Y.matrix.multiclass,
PLS.comp = PLS.comp,
X.dim = X.dim,
quantile.comb.table = quantile.comb.table.cv,
outcome.type = "multiclass",
k = 5,
ncv = 5)
quantile.comb.multiclass <- cv.results.multiclass$quantile_table_CV[,1:length(X.dim)]
n.PLS.multiclass <- cv.results.multiclass$optimal_nPLS3.3 Model Fit
asmbPLSDA.fit function is used to fit the final model
for both the binary and multiclass outcome.
Model fit for the binary outcome:
## asmbPLSDA fit using the selected quantile combination (binary outcome)
asmbPLSDA.fit.binary <- asmbPLSDA.fit(X.matrix = X.matrix,
Y.matrix = Y.matrix.binary,
PLS.comp = n.PLS.binary,
X.dim = X.dim,
quantile.comb = quantile.comb.binary,
outcome.type = "binary")Model fit for the multiclass outcome:
## asmbPLSDA fit (categorical outcome with more than 2 levels)
asmbPLSDA.fit.multiclass <- asmbPLSDA.fit(X.matrix = X.matrix,
Y.matrix = Y.matrix.multiclass,
PLS.comp = n.PLS.multiclass,
X.dim = X.dim,
quantile.comb = quantile.comb.multiclass,
outcome.type = "multiclass")3.4 Classification
asmbPLSDA.predict function is used to classify the
sample group for the new sample.
## classification for the new data based on the asmbPLS-DA model with the binary outcome.
Y.pred.binary <- asmbPLSDA.predict(asmbPLSDA.fit.binary,
X.matrix.new,
PLS.comp = n.PLS.binary)
## classification for the new data based on the asmbPLS-DA model with the multiclass outcome.
Y.pred.multiclass <- asmbPLSDA.predict(asmbPLSDA.fit.multiclass,
X.matrix.new,
PLS.comp = n.PLS.multiclass)3.5 Vote Function
When we have multiple models using different decision rules, we can
use the vote functions to combine the classification results.
For example, for the binary outcome, we have already built the
asmbPLS-DA model with fixed cutoff as our decision rule. We want to
build two more models with different decision rules
Euclidean_distance_X and
Mahalanobis_distance_X and then combine the results using
the vote function.
cv.results.cutoff <- cv.results.binary
quantile.comb.cutoff <- cv.results.cutoff$quantile_table_CV
## Cross validation using Euclidean distance of X super score
cv.results.EDX <- asmbPLSDA.cv(X.matrix = X.matrix,
Y.matrix = Y.matrix.binary,
PLS.comp = PLS.comp,
X.dim = X.dim,
quantile.comb.table = quantile.comb.table.cv,
outcome.type = "binary",
method = "Euclidean_distance_X",
k = 5,
ncv = 5)
quantile.comb.EDX <- cv.results.EDX$quantile_table_CV
## Cross validation using Mahalanobis distance of X super score
cv.results.MDX <- asmbPLSDA.cv(X.matrix = X.matrix,
Y.matrix = Y.matrix.binary,
PLS.comp = PLS.comp,
X.dim = X.dim,
quantile.comb.table = quantile.comb.table.cv,
outcome.type = "binary",
method = "Mahalanobis_distance_X",
k = 5,
ncv = 5)
quantile.comb.MDX <- cv.results.MDX$quantile_table_CVPut selected quantile combination with corresponding measure from different models in one list:
#### vote list ####
cv.results.list = list(fixed_cutoff = quantile.comb.cutoff,
Euclidean_distance_X = quantile.comb.EDX,
Mahalanobis_distance_X = quantile.comb.MDX)Use asmbPLSDA.vote.fit function to fit the vote model,
the order of nPLS should correspond to the order of
different decision rules in cv.results.list.
Also, you can try with different vote function, the default is
method = "weighted".
vote.fit <- asmbPLSDA.vote.fit(X.matrix = X.matrix,
Y.matrix = Y.matrix.binary,
X.dim = X.dim,
nPLS = c(cv.results.cutoff$optimal_nPLS,
cv.results.EDX$optimal_nPLS,
cv.results.MDX$optimal_nPLS),
cv.results.list = cv.results.list,
outcome.type = "binary",
method = "weighted")Final classification using the vote function:
## classification
vote.predict <- asmbPLSDA.vote.predict(vote.fit, X.matrix.new)
head(vote.predict)
#> [,1]
#> [1,] 0
#> [2,] 1
#> [3,] 0
#> [4,] 0
#> [5,] 1
#> [6,] 04 Visualization
4.1 Correlation between different blocks
You can use function plotCor to visualize correlations
between PLS components from different blocks using the model fitted by
the function asmbPLSDA.fit. For here, we use the first
block score from each block to make the plot.
block.name should be a vector containing the named
character for each block. It must be ordered and match each block.
group.name should be a vector containing the named
character for each sample group. For binary outcome, first group name
matchs Y.matrix = 0, second group name matchs Y.matrix = 1. For
multiclass outcome, ith group name matches ith column of Y.matrix =
1.
## custom block.name and group.name
plotCor(asmbPLSDA.fit.binary,
ncomp = 1,
block.name = c("mRNA", "protein"),
group.name = c("control", "case"))
4.2 PLS plot
You can use function plotPLS to visualize cluster of
samples using super score of different PLS components. It can only be
used for the output of asmbPLSDA.fit function.
## custom block.name and group.name
plotPLS(asmbPLSDA.fit.binary,
comp.X = 1,
comp.Y = 2,
group.name = c("control", "case"))
4.3 Relevance plot
You can use function plotRelevance to visualize the most
relevant features (relevant to the outcome) in each block. Both the
fitted asmbPLS and asmbPLS-DA models can be used as input.
plotRelevance(asmbPLSDA.fit.binary,
n.top = 5,
block.name = c("mRNA", "protein"))