Statistical Analysis
Zhiqiang Pang, Jasmine Chong, Jeff Xia
2023-07-24
1. Introduction
MetaboAnalystR, in parallel with the webserver, provides a
comprehensive suite of statistical analyses to perform on a
user-uploaded data set. While researchers may have several goals for
their metabolomics data, the ultimate goal is to identify any
significant metabolite/s indicitive of a disease state, drugs, diet,
environment, geographical location, etc.
The standard workflow for statistical analysis is as follows:
Processed metabolomic data -> Univariate analysis ->
Multivariate analysis -> Biological interpretation
Univariate tests differ from multivariate tests in that they assess
the importance of each variable seperately. Meanwhile, multivariate
tests assess two or more variables at once, while also taking into
consideration the relationship between the variables. Finally,
biological interpretation provides a biological context for the
significant metabolites identified using univariate/multivariate
methods. Below, we will discuss the various statistical methods in
greater detail. For the tutorial, we will be using a dataset consisting
of concentrations of 77 urine samples from cancer patients (cachexic
vs. control) measured by 1H NMR - Eisner
et al. 2010.
2. Univariate Methods
To begin the SA module, we will start with identifying important
features from the data set using various univariate tests, including
classical methods such as the Student’s t-test and ANOVA, as well as
other methods such as the volcano plot and correlation analysis.
# Load MetaboAnalystR
library(MetaboAnalystR)
# Clean global environment
rm(list = ls())
library(MetaboAnalystR)
mSet<-InitDataObjects("conc", "stat", FALSE);
## Starting Rserve:
## /opt/R/4.2.2/lib/R/bin/R CMD /opt/R/4.2.2/lib/R/library/Rserve/libs//Rserve --no-save
##
## [1] "MetaboAnalyst R objects initialized ..."
mSet<-Read.TextData(mSet, "https://www.xialab.ca/api/download/metaboanalyst/human_cachexia.csv", "rowu", "disc");
mSet<-SanityCheckData(mSet);
## [1] "Successfully passed sanity check!"
## [2] "Samples are not paired."
## [3] "2 groups were detected in samples."
## [4] "Only English letters, numbers, underscore, hyphen and forward slash (/) are allowed."
## [5] "<font color=\"orange\">Other special characters or punctuations (if any) will be stripped off.</font>"
## [6] "All data values are numeric."
## [7] "A total of 0 (0%) missing values were detected."
## [8] "<u>By default, missing values will be replaced by 1/5 of min positive values of their corresponding variables</u>"
## [9] "Click the <b>Proceed</b> button if you accept the default practice;"
## [10] "Or click the <b>Missing Values</b> button to use other methods."
mSet<-ReplaceMin(mSet);
mSet<-PreparePrenormData(mSet);
mSet<-Normalization(mSet, "NULL", "LogNorm", "MeanCenter", "S10T0", ratio=FALSE, ratioNum=20);
## [1] 77 63
mSet<-PlotNormSummary(mSet, "norm_0_", format ="png", dpi=72, width=NA);
mSet<-PlotSampleNormSummary(mSet, "snorm_0_", format = "png", dpi=72, width=NA);
2.1 Fold-change analysis
The goal of fold-change (FC) analysis is to compare the absolute
value of change between two group means. Since column-wise normalization
(i.e. log transformation, mean-centering) will significantly alter
absolute values, FC is calculated as the ratio between two group means
using the data before column-wise normalization was applied.
For paired analysis, the program first counts the number of pairs
with consistent change above the given FC threshold. If this number
exceeds a given count threshold, the variable will be reported as
significant.
# Perform fold-change analysis on uploaded data, unpaired
mSet<-FC.Anal(mSet, 2.0, 0, FALSE)
# Plot fold-change analysis
mSet<-PlotFC(mSet, "fc_0_", "png", 72, width=NA)
# To view fold-change
mSet$analSet$fc$fc.log
## 1,6-Anhydro-beta-D-glucose 1-Methylnicotinamide
## 0.888690 -0.052019
## 2-Aminobutyrate 2-Hydroxyisobutyrate
## 1.312700 0.633520
## 2-Oxoglutarate 3-Aminoisobutyrate
## 1.098400 1.329100
## 3-Hydroxybutyrate 3-Hydroxyisovalerate
## 1.563700 1.164900
## 3-Indoxylsulfate 4-Hydroxyphenylacetate
## 0.857170 0.263810
## Acetate Acetone
## 1.266100 0.664560
## Adipate Alanine
## 1.952900 1.141300
## Asparagine Betaine
## 0.852650 1.004000
## Carnitine Citrate
## 0.994090 0.883620
## Creatine Creatinine
## 1.763900 0.932160
## Dimethylamine Ethanolamine
## 1.120000 0.729170
## Formate Fucose
## 1.150600 0.918770
## Fumarate Glucose
## 1.262700 2.553000
## Glutamine Glycine
## 1.166100 0.869890
## Glycolate Guanidoacetate
## 0.657790 0.506100
## Hippurate Histidine
## 1.075800 1.013100
## Hypoxanthine Isoleucine
## 0.375470 0.420550
## Lactate Leucine
## 1.726900 1.205400
## Lysine Methylamine
## 0.442780 0.901220
## Methylguanidine N,N-Dimethylglycine
## 0.517770 1.342900
## O-Acetylcarnitine Pantothenate
## 1.270300 -0.397700
## Pyroglutamate Pyruvate
## 1.180400 1.096200
## Quinolinate Serine
## 1.090600 1.007700
## Succinate Sucrose
## 1.416200 1.432600
## Tartrate Taurine
## 0.720000 1.032700
## Threonine Trigonelline
## 0.990220 1.460400
## Trimethylamine N-oxide Tryptophan
## 1.077700 0.967880
## Tyrosine Uracil
## 0.953700 0.207270
## Valine Xylose
## 1.178900 1.194000
## cis-Aconitate myo-Inositol
## 1.589400 1.537500
## trans-Aconitate pi-Methylhistidine
## 0.811730 0.771640
## tau-Methylhistidine
## 0.708800
2.2 T-Test
MetaboAnalystR supports various options for performing T-test
analysis. Users can select the analysis type (paired), the
group variance (equal.var), whether the test is parametric or
non-parametric (nonpar), and the adjusted p-value (FDR) cut-off
(threshp).
Note, for a large data set (> 1000 variables), both the paired
information and the group variance will be ignored, and the default
parameters will be used for t-tests to save computational time. If you
choose non-parametric tests (Wilcoxon rank-sum test), the group variance
will be ignored.
# Perform T-test (parametric)
mSet<-Ttests.Anal(mSet, nonpar=F, threshp=0.05, paired=FALSE, equal.var=TRUE, "fdr", FALSE)
## Loading required package: memoise
## [1] "Performing regular t-tests ...."
## [1] "A total of 53 significant features were found."
# Plot of the T-test results
mSet<-PlotTT(mSet, imgName = "tt_0_", format = "png", dpi = 72, width=NA)
The t test results for MS1 feature table can be used for function
analysis.
2.3 Volcano Plot
The volcano plot is a combination of fold change and t-test values.
Note, for unpaired samples, the x-axis is log2(FC). For paired analysis,
the x-axis is number of significant counts. The y-axis is
-log10(p.value) for both cases, and can be based on raw or FDR adjusted
p values from the t-tests. In Volcano.Anal, users can specify
if the data are paired, the FC threshold, the comparison type, the
signigicant count threshold if data are paired, whether the test is
parametric or non-parametric, the p-value threshold, and the group
variance.
# Perform the volcano analysis
mSet<-Volcano.Anal(mSet, FALSE, 2.0, 0, F, 0.1, TRUE, "raw")
## [1] "A total of 57 significant features were found."
# Create the volcano plot
mSet<-PlotVolcano(mSet, "volcano_0_", 1, 0, format ="png", dpi=72, width=NA)
## Loading required package: ggplot2
## Warning: Removed 30 rows containing missing values (`geom_text_repel()`).
2.4 One-way Analysis of Variance (ANOVA) - ONLY FOR MULTI-GROUP
ANALYSIS!
ANOVA can only be computed on data with more than one group.
Please note that the below example uses data from a different
example dataset, which contains more than 2 groups.
# Perform ANOVA
mSet <- ANOVA.Anal(mSet, F, 0.05, "fisher")
# Plot ANOVA
mSet <- PlotANOVA(mSet, "aov_0_", "png", 72, width=NA)
2.5 Correlation Analysis
To perform correlation analysis to evaluate the correlation between
all features or samples, use PlotCorrHeatMap. Here, users must
specify the mSet object, the dimensions to be correlated, the name of
the heatmap that will be created, the output, dpi, and width of the
image, the distance measure (Pearson, Spearman, or Kendall), to view the
heatmap as an overview or detailed view, to fix the colour distribution,
the colors, and whether or not to perform clustering. Please refer to
the user manual for more details.
Note, the heatmap will only show correlations for a maximum of 1000
features. For larger datasets, only top 1000 features will be selected
based on their interquantile range (IQR). When color distribution is
fixed, you can potentially compare the correlation patterns among
different data sets. In this case, you can choose “do not perform
clustering” for all data set, or only to perform clustering on a single
reference data set, then manually re-arranged other data sets according
to the clustering pattern of the reference data set.
### OPTION 1 - Heatmap specifying pearson distance and an overview
mSet<-PlotCorrHeatMap(mSet, "corr_0_", "png", 72, width=NA, "col", "pearson", "bwm", "overview", F, F, 0.0)
The following command shows the detailed view (zoomed-in) of the
above heatmap.
### OPTION 2 - Heatmap specifying pearson correlation and a detailed view
mSet<-PlotCorrHeatMap(mSet, "corr_1_", format = "png", dpi=72, width=NA, "col", "spearman", "bwm", "detail", F, F, 999)
2.6 Pattern Searching
Correlation analysis can be performed either against a given feature
or against a given pattern. The pattern is specified as a series of
numbers separated by “-”. Each number corresponds to the expected
expression pattern in the corresponding group. For example, a 1-2-3-4
pattern is used to search for features that increase linearly with time
in a time-series data with four time points (or four groups). The order
of the groups is given as the first item in the predefined patterns.
Indicate the mSet object, the distance measure (Pearson, Spearman, or
Kendall), and the pattern to use.
# Perform correlation analysis on a pattern (a feature of interest in this case)
mSet<-FeatureCorrelation(mSet, "pearson", "1,6-Anhydro-beta-D-glucose")
# Plot the correlation analysis on a pattern
mSet<-PlotCorr(mSet, "ptn_3_", format="png", dpi=72, width=NA)
2.7 Principal Component Analysis (PCA)
To perform PCA, first use PCA.Anal. MetaboAnalystR has the
options to create a scree plot (PlotPCAScree), score plot
(PlotPCA2DScore or PlotPCA3DScore), loadings plot
(PlotPCALoading), and biplot (PlotPCABiplot). For the
score plots, users will create both a static as well as interactive 3D
score plot. To view the interactive plot, type “mSet$imgSet$pca.3d” into
your R console. Please refer to the user manual for details about each
function.
# Perform PCA analysis
mSet<-PCA.Anal(mSet)
# Create PCA overview
mSet<-PlotPCAPairSummary(mSet, "pca_pair_0_", format = "png", dpi = 72, width=NA, 5)
# Create PCA scree plot
mSet<-PlotPCAScree(mSet, "pca_scree_0_", "png", dpi = 72, width=NA, 5)
# Create a 2D PCA score plot
mSet<-PlotPCA2DScore(mSet, "pca_score2d_0_", format = "png", dpi=72, width=NA, 1, 2, 0.95, 1, 0)
# Create a 3D PCA score plot
mSet<-PlotPCA3DScoreImg(mSet, "pca_score3d_0_", "png", 72, width=NA, 1,2,3, 40)
# Create a PCA loadings Plots
mSet<-PlotPCALoading(mSet, "pca_loading_0_", "png", 72, width=NA, 1,2);
# Create a PCA Biplot
mSet<-PlotPCABiplot(mSet, "pca_biplot_0_", format = "png", dpi = 72, width=NA, 1, 2)
# View the 3D interactive PLS-DA score plot
mSet$imgSet$pca.3d
2.8 Partial Least Squares - Discriminant Analysis (PLS-DA)
To perform PLS-DA, first use PLSR.Anal. MetaboAnalystR has
the options to create a plot component pairs
(PlotPLSPairSummary), score plot (PlotPLS2DScore),
loadings plot (PlotPLSLoading), perform cross-validation and
permutation (PLSDA.CV and PLSDA.Permut), and plot the
results of the cross-validation and permutation (PlotPLS.Imp
and PlotPLS.Permutation). For the score plots, users will
create both a static as well as interactive 3D score plot. To view the
interactive plot, type “mSet$imgSet$plsda.3d” into your R console.
Please refer to the user manual for details about each function.
mSet<-PLSR.Anal(mSet, reg=TRUE)
mSet<-PlotPLSPairSummary(mSet, "pls_pair_0_", "png", 72, width=NA, 5)
mSet<-PlotPLS2DScore(mSet, "pls_score2d_0_", "png", 72, width=NA, 1,2,0.95,1,0)
mSet<-PlotPLS3DScoreImg(mSet, "pls_score3d_0_", "png", 72, width=NA, 1,2,3, 40)
mSet<-PlotPLSLoading(mSet, "pls_loading_0_", "png", 72, width=NA, 1, 2);
mSet<-PLSDA.CV(mSet, "5", 5,5, "Q2")
## Loading required package: lattice
##
## Attaching package: 'caret'
## The following object is masked from 'package:MetaboAnalystR':
##
## splsda
## Loading required package: pls
##
## Attaching package: 'pls'
## The following object is masked from 'package:caret':
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## R2
## The following object is masked from 'package:stats':
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## loadings
mSet<-PlotPLS.Classification(mSet, "pls_cv_0_", "png", 72, width=NA)
mSet<-PlotPLS.Imp(mSet, "pls_imp_0_", "png", 72, width=NA, "vip", "Comp. 1", 15, FALSE)
mSet<-PLSDA.Permut(mSet, 100, "accu")
## [1] "performing 100 permutations ..."
## [1] "Empirical p value: p = 0.02 (2/100)"
mSet<-PlotPLS.Permutation(mSet, "pls_perm_1_", "png", 72, width=NA)
# View the 3D interactive PLS-DA score plot
mSet$imgSet$plsda.3d
2.9 Sparse Partial Least Squares - Discriminant Analysis
(sPLS-DA)
The sparse PLS-DA (sPLS-DA) algorithm can effectively reduce the
number of variables (metabolites) in high-dimensional metabolomics data
to produce robust and easy-to-interpret models. Users can control the
“sparseness” of the model by controlling the number of components
included in the model and the number of variables within each component.
More details can be found from Le Cao et. al 2011 (PMC3133555).
To begin, use SPLSR.Anal. MetaboAnalystR has the options to
create an overview of the sPLS-DA analysis
(PlotSPLSPairSummary), a score plot (PlotSPLS2DScore
or PlotSPLS3DScore), loadings plot (PlotSPLSLoading),
and classification plot (PlotSPLSDA.Classification). For the
score plots, users will create both a static as well as interactive 3D
score plot. To view the interactive plot, type “mSet$imgSet$splsda.3d”
into your R console. Please refer to the user manual for details about
each function. Note that the loadings plot shows the variables selected
by the sPLS-DA model for a given component. The variables are ranked by
the absolute values of their loadings.
To evaluate the performance of the created sPLS-DA models for
classification, use PlotSPLSDA.Classification. The performance
of the sPLS-DA models are evaluated using cross validations (CV) with
increasing numbers of components created using the specified number of
the variables. Users can choose to use either 5-fold CVs or leave one
out cross-validation (LOOCV). Please note that the results from 5-fold
CV may change slightly due to random subsampling procedures.
# Perform sPLS-DA analysis
mSet<-SPLSR.Anal(mSet, 5, 10, "same", "Mfold", 5, T)
# Plot sPLS-DA overview
mSet<-PlotSPLSPairSummary(mSet, "spls_pair_0_", format = "png", dpi=72, width=NA, 5)
# Create 2D sPLS-DA Score Plot
mSet<-PlotSPLS2DScore(mSet, "spls_score2d_0_", format = "png", dpi=72, width=NA, 1, 2, 0.95, 1, 0)
# Create 3D sPLS-DA Score Plot
mSet<-PlotSPLS3DScoreImg(mSet, "spls_score3d_0_", format = "png", 72, width=NA, 1, 2, 3, 40)
# Create sPLS-DA loadings plot
mSet<-PlotSPLSLoading(mSet, "spls_loading_0_", format = "png", dpi=72, width=NA, 1,"overview")
# Perform cross-validation and plot sPLS-DA classification
mSet<-PlotSPLSDA.Classification(mSet, "spls_cv_0_", format = "png", dpi=72, width=NA)
# View the 3D interactive PLS-DA score plot
mSet$imgSet$splsda.3d
2.10 Orthogonal Partial Least Squares - Discriminant Analysis
(orthoPLS-DA)
MetaboAnalystR can create several outputs for oPLS-DA analysis. To
begin, use the OPLSR.Anal function. The outputs for oPLS-DA
include a score plot, a plot to identify significant features, a model
overview plot, and a plot of model permutations. For the significant
features plot, the plot visualizes the variable influence in the
orthogonal PLS-DA model. It combines the covariance and correlation
loading profiles. This corresponds to combining the contribution or
magnitude (covariance) with the effect and reliability (correlation) for
the model variables with respect to model component scores (details). To
begin, please use the OPLSR.Anal function. Please refer to the
user manual for further details on the functions.
# Perform oPLS-DA analysis
mSet<-OPLSR.Anal(mSet, reg=TRUE)
# Create a 2D oPLS-DA score plot
mSet<-PlotOPLS2DScore(mSet, "opls_score2d_0_", format = "png", dpi=72, width=NA, 1,2,0.95,1,0)
# Create a significant features plot
mSet<-PlotOPLS.Splot(mSet, "opls_splot_0_", "all", "png", 72, width=NA);
# Create a plot of features ranked by importance
mSet<-PlotOPLS.Imp(mSet, "opls_imp_0_", "png", 72, width=NA, "vip", "tscore", 15,FALSE)
# Create a plot of the model overview
mSet<-PlotOPLS.MDL(mSet, "opls_mdl_0_", format = "png", dpi=72, width=NA)
# Perform and plot oPLS-DA permutation
mSet<-OPLSDA.Permut(mSet, 100)
## [1] "time taken for 10 permutations: 0.0561895370483398"
mSet<-PlotOPLS.Permutation(mSet, "opls_perm_2_", format = "png", dpi=72, width=NA)
## [1] "Empirical p-values Q2: p < 0.01 (0/100) and R2Y: p = 0.01 (1/100)"
More plots can be found in your working directory.
2.11 Significance Analysis of Microarrary (and Metabolites)
(SAM)
SAM is a well-established statistical method for identification of
differentially expressed genes in mi- croarray data analysis. It is
designed to address the false discovery rate (FDR) when running multiple
tests on high-dimensional microarray data. SAM assigns a significance
score to each variable based on its change relative to the standard
deviation of repeated measurements. For a variable with scores greater
than an adjustable threshold, its relative difference is compared to the
distribution estimated by random permutations of the class labels. For
each threshold, a certain proportion of the variables in the permutation
set will be found to be significant by chance. The proportion is used to
calculate the FDR. SAM is performed using the siggenes package.
Users need to specify the Delta value to control FDR in order to
proceed. To begin the SAM analysis, use the SAM.Anal function.
Please refer to the user manual for further details on the
functions.
# Perform SAM analysis
mSet<-SAM.Anal(mSet, "d.stat", FALSE, TRUE, 0.0, "sam_imp_0_")
## Loading required package: Biobase
## Loading required package: BiocGenerics
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## Attaching package: 'BiocGenerics'
## The following objects are masked from 'package:stats':
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## IQR, mad, sd, var, xtabs
## The following objects are masked from 'package:base':
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## Welcome to Bioconductor
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## Vignettes contain introductory material; view with
## 'browseVignettes()'. To cite Bioconductor, see
## 'citation("Biobase")', and for packages 'citation("pkgname")'.
## Loading required package: multtest
## Loading required package: splines
## Warning: Expected class labels are 0 and 1. cachexic is set to 0, and control
## is set to 1.
## Warning: The spline based estimation of pi0 results in a non-positive value of pi0.
## Therefore, pi0 is estimated by using lambda = 0.5.
# Create a SAM plot of FDR values
mSet<-PlotSAM.FDR(mSet, "sam_view_0_", format = "png", dpi=72, width=NA)
# Create a SAM plot of results
mSet<-PlotSAM.Cmpd(mSet, "sam_imp_0_", format = "png", dpi=72, width=NA)
2.13 Hierarchical Clustering: Dendogram
In (agglomerative) hierarchical cluster analysis, each sample begins
as a separate cluster and the algo- rithm proceeds to combine them until
all samples belong to one cluster. Two parameters need to be considered
when performing hierarchical clustering. The first one is distance
measure, including the Euclidean distance, Pearson’s correlation, or
Spearman’s rank correlation. The other parameter is the clustering
algorithm, which includes the average linkage (clustering uses the
centroids of the observations), complete linkage (clustering uses the
farthest pair of observations between the two groups), single linkage
(clustering uses the closest pair of observations) and Ward’s linkage
(clustering to minimize the sum of squares of any two clusters). Heatmap
is often presented as a visual aid in addition to the dendrogram.
Hierachical clustering is performed with the hclust function in
package stat. Use the PlotHCTree to create the dendogram, where
users can specify the distance measure and the clustering algorithm.
Please refer to the user manual for further details on the function.
# Perform hierarchical clustering and plot dendogram
mSet<-PlotHCTree(mSet, "tree_0_", format = "png", dpi=72, width=NA, "euclidean", "ward.D")
2.14 Hierarchical Clustering: Heatmaps
The heatmap provides intuitive visualization of the metabolomics data
table. Each colored cell on the map corresponds to a concentration value
in the user’s data table, with samples in rows and features/compounds in
columns. Users can use a heatmap to identify samples/features that are
unusually high/low. Further, the heatmap is often presented as a visual
aid in addition to the dendrogram.
In (agglomerative) hierarchical cluster analysis, each sample begins
as a separate cluster and the algorithm proceeds to combine them until
all samples belong to one cluster. Two parameters need to be considered
when performing hierarchical clustering. The first one is the similarity
measure, options in MetaboAnalystR include Euclidean distance, Pearson’s
correlation, and Spearman’s rank correlation. The other parameter is the
choice of clustering algorithms, including average linkage (clustering
uses the centroids of the observations), complete linkage (clustering
uses the farthest pair of observations between the two groups), single
linkage (clustering uses the closest pair of observations) and Ward’s
linkage (clustering to minimize the sum of squares of any two clusters).
Hierachical clustering is performed with the hclust function in
package stat. Use the PlotHeatMap function, where users can
specify the distance measure, the clustering algorithm, the color
contrast, a detailed or overview view of the data, and options for the
data input for the heatmap. Please refer to the user manual for further
details.
# Perform hierarchical clustering and plot heat map
mSet<-PlotHeatMap(mSet, "heatmap_0_", "png", 72, width=NA, "norm", "row", "euclidean", "ward.D","bwm", 8, "overview", T, T, NULL, T, F, T, T, T)
2.15 Partitional Clustering: K-Means
K-means clustering is a nonhierarchical clustering technique. It
begins by creating k random clusters (k is supplied by user). The
program then calculates the mean of each cluster. If an observation is
closer to the centroid of another cluster then the observation is made a
member of that cluster. This process is repeated until none of the
observations are reassigned to a different cluster. K-means analysis is
performed using the kmeans function in the package
stat. To begin, use the Kmeans.Anal function, and then
the PlotKmeans function to create a plot of the analysis.
# Perform K-means analysis
mSet<-Kmeans.Anal(mSet, 3)
# Plot K-means analysis
mSet<-PlotKmeans(mSet, "km_0_", format = "png", dpi=72, width=NA)
## Loading required package: data.table
2.16 Partitional Clustering: Self Organizing Maps (SOM)
SOM is an unsupervised neural network algorithm used to automatically
identify major trends present in high-dimensional data. SOM is based on
a grid of interconnected nodes, each of which represents a model. These
models begin as random values, but during the process of iterative
training they are updated to represent different subsets of the training
set. Users need to specify the x and y dimension of the grid to perform
SOM analysis. The SOM is performed using the som R package.
Please refer to the user manual for further details on the
functions.
MetaboAnalystR performs several outputs for self organizing maps. To
begin, use the SOM.Anal function to perform SOM analysis. Then
use the PlotSOM to create a plot of the SOM analysis.
# Perform SOM analysis
mSet<-SOM.Anal(mSet, 1, 3,"linear","gaussian")
# Plot SOM analysis
mSet<-PlotSOM(mSet, "som_0_", format = "png", dpi=72, width=NA)
2.17 Random Forest
Random Forest is a supervised learning algorithm suitable for high
dimensional data analysis. It uses an ensemble of classification trees,
each of which is grown by random feature selection from a bootstrap
sample at each branch. Class prediction is based on the majority vote of
the ensemble. RF also provides other useful information such as OOB
(out-of-bag) error, variable importance measure, and outlier mea- sures.
During tree construction, about one-third of the instances are left out
of the bootstrap sample. This OOB data is then used as test sample to
obtain an unbiased estimate of the classification error (OOB error).
Variable importance is evaluated by measuring the increase of the OOB
error when it is permuted. The outlier measures are based on the
proximities during tree construction. RF analysis is performed using the
randomForest R package.
MetaboAnalystR performs several outputs for the random forest
analysis. To begin, use the RF.Anal function. The
PlotRF.Classify function creates a plot of the out-of-the-bag
error rate for the random forest classification. The PlotRF.VIP
function creates a plot of the contributions of variables with high
importance to the classification of the random forest model. In this
plot, the features are ranked by their contributions to classification
accuracy (Mean Dicrease Accuracy). The PlotRF.Outlier creates a
plot of the outlying samples in the random forest model.
# Perform random forest analysis
mSet<-RF.Anal(mSet, 500, 7, 1)
## Warning in rm(.Random.seed): object '.Random.seed' not found
# Plot random forest classification
mSet<-PlotRF.Classify(mSet, "rf_cls_0_", format = "png", dpi=72, width=NA)
# Plot random forest variables of importance
mSet<-PlotRF.VIP(mSet, "rf_imp_0_", format = "png", dpi=72, width=NA)
# Plot random forest outliers
mSet<-PlotRF.Outlier(mSet, "rf_outlier_0_", format = "png", dpi=72, width=NA)
2.18 Support Vector Machine (SVM)
SVM aims to find a nonlinear decision function in the input space by
mapping the data into a higher dimensional feature space and separating
it there by means of a maximum margin hyperplane. The SVM- based
recursive feature selection and classification is performed using the
R-SVM script11. The process is performed recursively using decreasing
series of feature subsets (ladder) so that different classification
models can be calculated. Feature importance is evaluated based on its
frequencies being selected in the best classifier identified by
recursive classification and cross-validation. Please note, R-SVM is
very computationally intensive. Only the top 50 features (ranked by
their p values from t-tests) will be evaluated.
# Perform SVM
mSet<-RSVM.Anal(mSet, 10)
mSet<-PlotRSVM.Classification(mSet, "svm_cls_0_", format = "png", dpi=72, width=NA)
mSet<-PlotRSVM.Cmpd(mSet, "svm_imp_0_", format = "png", dpi=72, width=NA)
