CoGAPS - Coordinated Gene Association in Pattern Sets
24 October 2023
Contents
1 Vignette Version
This vignette was built using CoGAPS version:
packageVersion("CoGAPS")## [1] '3.22.0'2 Introduction
Coordinated Gene Association in Pattern Sets (CoGAPS) is a technique for latent space learning in gene expression data. CoGAPS is a member of the Nonnegative Matrix Factorization (NMF) class of algorithms. NMFs factorize a data matrix into two related matrices containing gene weights, the Amplitude (A) matrix, and sample weights, the Pattern (P) Matrix. Each column of A or row of P defines a feature and together this set of features defines the latent space among genes and samples, respectively. In NMF, the values of the elements in the A and P matrices are constrained to be greater than or equal to zero. This constraint simultaneously reflects the non-negative nature of gene expression data and enforces the additive nature of the resulting feature dimensions, generating solutions that are biologically intuitive to interpret (Seung and Lee (1999)).
3 Software Setup
CoGAPS can be installed directly from the FertigLab Github Repository using R devtools or from Bioconductor
devtools::install_github("FertigLab/CoGAPS")
# To install via BioConductor:
install.packages("BiocManager")
BiocManager::install("FertigLab/CoGAPS")When CoGAPS has installed correctly, you will see this message:
** installing vignettes
** testing if installed package can be loaded from temporary location
** checking absolute paths in shared objects and dynamic libraries
** testing if installed package can be loaded from final location
** testing if installed package keeps a record of temporary installation path
* DONE (CoGAPS)
4 Running CoGAPS on Simulated Toy Data
We first give a walkthrough of the package features using a simple, simulated data set. In later sections we provide two example workflows on real data sets.
Import the CoGAPS library with the following command:
library(CoGAPS)To ensure CoGAPS is working properly, we will first load in the simulated toy data for a test run.
Single-cell data will be loaded later in this file.
load('../data/modsimdata.rda')
# input to CoGAPS
modsimdata## V1 V2 V3 V4 V5 V6 V7 V8 V9
## 1 0.077764 0.94742 4.2487 7.0608 4.8730 4.2687 9.1061 12.6020 9.0283
## 2 0.081467 0.99253 4.4507 7.3906 5.0387 4.1205 8.5843 11.8690 8.5029
## 3 0.085170 1.03760 4.6527 7.7204 5.2044 3.9723 8.0626 11.1360 7.9775
## 4 0.088873 1.08270 4.8547 8.0502 5.3700 3.8241 7.5408 10.4030 7.4521
## 5 0.092576 1.12790 5.0567 8.3800 5.5357 3.6759 7.0190 9.6695 6.9266
## 6 0.096279 1.17300 5.2587 8.7098 5.7014 3.5277 6.4973 8.9362 6.4012
## 7 0.099982 1.21810 5.4607 9.0396 5.8670 3.3795 5.9755 8.2030 5.8758
## 8 0.103680 1.26320 5.6627 9.3694 6.0327 3.2313 5.4538 7.4698 5.3503
## 9 0.107390 1.30830 5.8647 9.6992 6.1984 3.0831 4.9320 6.7366 4.8249
## 10 0.111090 1.35340 6.0667 10.0290 6.3640 2.9349 4.4103 6.0034 4.2995
## 11 0.044437 0.54138 2.4277 4.0319 2.7547 2.2811 4.7735 6.6014 4.7299
## 12 0.055810 0.67994 3.0488 5.0588 3.4079 2.5904 5.2490 7.2493 5.1939
## 13 0.067184 0.81850 3.6700 6.0857 4.0611 2.8996 5.7244 7.8973 5.6579
## 14 0.078557 0.95707 4.2911 7.1127 4.7144 3.2089 6.1998 8.5453 6.1219
## 15 0.089931 1.09560 4.9122 8.1396 5.3676 3.5182 6.6752 9.1932 6.5859
## 16 0.101300 1.23420 5.5333 9.1665 6.0208 3.8274 7.1506 9.8412 7.0500
## 17 0.112680 1.37280 6.1545 10.1930 6.6740 4.1367 7.6260 10.4890 7.5140
## 18 0.124050 1.51130 6.7756 11.2200 7.3272 4.4460 8.1014 11.1370 7.9780
## 19 0.135420 1.64990 7.3967 12.2470 7.9804 4.7552 8.5768 11.7850 8.4420
## 20 0.146800 1.78840 8.0179 13.2740 8.6337 5.0645 9.0523 12.4330 8.9060
## 21 0.158170 1.92700 8.6390 14.3010 9.2869 5.3738 9.5277 13.0810 9.3700
## 22 0.169550 2.06560 9.2601 15.3280 9.9401 5.6830 10.0030 13.7290 9.8341
## 23 0.180920 2.20410 9.8812 16.3550 10.5930 5.9923 10.4780 14.3770 10.2980
## 24 0.192290 2.34270 10.5020 17.3820 11.2470 6.3016 10.9540 15.0250 10.7620
## 25 0.203670 2.48120 11.1230 18.4090 11.9000 6.6108 11.4290 15.6730 11.2260
## V10 V11 V12 V13 V14 V15 V16 V17 V18
## 1 3.3217 0.63098 0.081912 0.076605 0.15584 0.2000 0.15576 0.073576 0.021080
## 2 3.1288 0.59813 0.099451 0.150000 0.31159 0.4000 0.31152 0.147150 0.042160
## 3 2.9359 0.56529 0.116990 0.223400 0.46735 0.6000 0.46728 0.220730 0.063240
## 4 2.7430 0.53244 0.134530 0.296800 0.62310 0.8000 0.62304 0.294300 0.084319
## 5 2.5500 0.49959 0.152070 0.370200 0.77886 1.0000 0.77880 0.367880 0.105400
## 6 2.3571 0.46674 0.169610 0.443600 0.93462 1.2000 0.93456 0.441460 0.126480
## 7 2.1642 0.43390 0.187150 0.517000 1.09040 1.4000 1.09030 0.515030 0.147560
## 8 1.9713 0.40105 0.204690 0.590400 1.24610 1.6000 1.24610 0.588610 0.168640
## 9 1.7784 0.36820 0.222230 0.663800 1.40190 1.8000 1.40180 0.662180 0.189720
## 10 1.5854 0.33535 0.239770 0.737200 1.55760 2.0000 1.55760 0.735760 0.210800
## 11 1.7517 0.44215 0.685340 2.282400 4.82860 6.2000 4.82860 2.280900 0.653480
## 12 1.9220 0.47021 0.664380 2.198500 4.65060 5.9714 4.65060 2.196800 0.629380
## 13 2.0922 0.49826 0.643410 2.114600 4.47260 5.7429 4.47250 2.112700 0.605290
## 14 2.2625 0.52632 0.622450 2.030600 4.29460 5.5143 4.29450 2.028600 0.581200
## 15 2.4328 0.55438 0.601480 1.946700 4.11660 5.2857 4.11650 1.944500 0.557110
## 16 2.6031 0.58243 0.580520 1.862800 3.93860 5.0571 3.93850 1.860400 0.533020
## 17 2.7733 0.61049 0.559550 1.778900 3.76060 4.8286 3.76050 1.776300 0.508930
## 18 2.9436 0.63855 0.538590 1.694900 3.58260 4.6000 3.58250 1.692200 0.484840
## 19 3.1139 0.66660 0.517620 1.611000 3.40450 4.3714 3.40450 1.608200 0.460750
## 20 3.2841 0.69466 0.496660 1.527100 3.22650 4.1429 3.22650 1.524100 0.436650
## 21 3.4544 0.72272 0.475690 1.443100 3.04850 3.9143 3.04840 1.440000 0.412560
## 22 3.6247 0.75077 0.454730 1.359200 2.87050 3.6857 2.87040 1.355900 0.388470
## 23 3.7949 0.77883 0.433760 1.275300 2.69250 3.4571 2.69240 1.271800 0.364380
## 24 3.9652 0.80689 0.412800 1.191300 2.51450 3.2286 2.51440 1.187700 0.340290
## 25 4.1355 0.83494 0.391840 1.107400 2.33650 3.0000 2.33640 1.103600 0.316200
## V19 V20
## 1 0.0036631 0.00038609
## 2 0.0073263 0.00077218
## 3 0.0109890 0.00115830
## 4 0.0146530 0.00154440
## 5 0.0183160 0.00193050
## 6 0.0219790 0.00231650
## 7 0.0256420 0.00270260
## 8 0.0293050 0.00308870
## 9 0.0329680 0.00347480
## 10 0.0366310 0.00386090
## 11 0.1135600 0.01196900
## 12 0.1093700 0.01152800
## 13 0.1051800 0.01108600
## 14 0.1010000 0.01064500
## 15 0.0968110 0.01020400
## 16 0.0926250 0.00976260
## 17 0.0884380 0.00932130
## 18 0.0842520 0.00888010
## 19 0.0800660 0.00843880
## 20 0.0758790 0.00799760
## 21 0.0716930 0.00755630
## 22 0.0675060 0.00711510
## 23 0.0633200 0.00667390
## 24 0.0591330 0.00623260
## 25 0.0549470 0.00579140Next, we will set the parameters to be used by CoGAPS. First, we will create a CogapsParams object, then set parameters with the setParam function.
# create new parameters object
params <- new("CogapsParams")
# view all parameters
params## -- Standard Parameters --
## nPatterns 7
## nIterations 50000
## seed 292
## sparseOptimization FALSE
##
## -- Sparsity Parameters --
## alpha 0.01
## maxGibbsMass 100# get the value for a specific parameter
getParam(params, "nPatterns")## [1] 7# set the value for a specific parameter
params <- setParam(params, "nPatterns", 3)
getParam(params, "nPatterns")## [1] 3Run CoGAPS on the ModSim data.
Since this is a small dataset, the expected runtime is only about 5-10 seconds.
The only required argument to CoGAPS is the data set. This can be a
matrix, data.frame, SummarizedExperiment, SingleCellExperiment
or the path of a file (tsv, csv, mtx, gct) containing the data.
# run CoGAPS with specified parameters
cogapsresult <- CoGAPS(modsimdata, params, outputFrequency = 10000)##
## This is CoGAPS version 3.22.0
## Running Standard CoGAPS on modsimdata (25 genes and 20 samples) with parameters:
##
## -- Standard Parameters --
## nPatterns 3
## nIterations 50000
## seed 292
## sparseOptimization FALSE
##
## -- Sparsity Parameters --
## alpha 0.01
## maxGibbsMass 100cogapsresult## [1] "CogapsResult object with 25 features and 20 samples"
## [1] "3 patterns were learned"Verify that this output appears:
This is CoGAPS version 3.19.1
Running Standard CoGAPS on modsimdata (25 genes and 20 samples) with parameters:
-- Standard Parameters --
nPatterns 3
nIterations 50000
seed 622
sparseOptimization FALSE
-- Sparsity Parameters --
alpha 0.01
maxGibbsMass 100
Data Model: Dense, Normal
Sampler Type: Sequential
Loading Data...Done! (00:00:00)
-- Equilibration Phase --
10000 of 50000, Atoms: 59(A), 49(P), ChiSq: 245, Time: 00:00:00 / 00:00:00
20000 of 50000, Atoms: 68(A), 46(P), ChiSq: 188, Time: 00:00:00 / 00:00:00
30000 of 50000, Atoms: 80(A), 47(P), ChiSq: 134, Time: 00:00:00 / 00:00:00
40000 of 50000, Atoms: 69(A), 46(P), ChiSq: 101, Time: 00:00:00 / 00:00:00
50000 of 50000, Atoms: 76(A), 53(P), ChiSq: 132, Time: 00:00:00 / 00:00:00
-- Sampling Phase --
10000 of 50000, Atoms: 82(A), 52(P), ChiSq: 94, Time: 00:00:00 / 00:00:00
20000 of 50000, Atoms: 74(A), 54(P), ChiSq: 144, Time: 00:00:01 / 00:00:01
30000 of 50000, Atoms: 79(A), 47(P), ChiSq: 116, Time: 00:00:01 / 00:00:01
40000 of 50000, Atoms: 79(A), 46(P), ChiSq: 132, Time: 00:00:01 / 00:00:01
50000 of 50000, Atoms: 76(A), 48(P), ChiSq: 124, Time: 00:00:01 / 00:00:01
This means that the underlying C++ library has run correctly, and everything is installed how it should be.
We now examine the result object.
4.1 Analyzing the Toy Data CoGAPS result
CoGAPS returns a object of the class CogapsResult which inherits from
LinearEmbeddingMatrix (defined in the SingleCellExperiment package).
CoGAPS stores the lower dimensional representation of the samples (P
matrix) in the sampleFactors slot and the weight of the features (A
matrix) in the featureLoadings slot. CogapsResult also adds two of
its own slots - factorStdDev and loadingStdDev which contain the
standard deviation across sample points for each matrix.
There is also some information in the metadata slot such as the
original parameters and value for the Chi-Sq statistic. In general, the
metadata will vary depending on how CoGAPS was called in the first
place. The package provides these functions for querying the metadata in
a safe manner:
cogapsresult## [1] "CogapsResult object with 25 features and 20 samples"
## [1] "3 patterns were learned"cogapsresult@sampleFactors## Pattern_1 Pattern_2 Pattern_3
## V1 1.087933e-02 0.0003873799 0.0004527280
## V2 1.348153e-01 0.0003543354 0.0003608713
## V3 6.038909e-01 0.0014517390 0.0019288781
## V4 1.000000e+00 0.0021916586 0.0035907668
## V5 6.564594e-01 0.0017131811 0.0105322916
## V6 3.602804e-01 0.0015527669 0.2594192326
## V7 6.150563e-01 0.0044945534 0.7219751477
## V8 8.429935e-01 0.0049213646 0.9993809462
## V9 6.036290e-01 0.0042433301 0.7225041986
## V10 2.224598e-01 0.0017103030 0.2669574320
## V11 4.499433e-02 0.0090177897 0.0515765958
## V12 1.470349e-03 0.1136490554 0.0009290584
## V13 3.465668e-04 0.3692411184 0.0003694981
## V14 6.355364e-04 0.7796748281 0.0005511328
## V15 7.223710e-04 1.0000000000 0.0020751585
## V16 5.909408e-04 0.7800748348 0.0005938309
## V17 2.867557e-04 0.3685609400 0.0005282166
## V18 1.718689e-04 0.1054713875 0.0002792724
## V19 7.885735e-04 0.0148373963 0.0005396038
## V20 6.458124e-05 0.0001650290 0.0002596512cogapsresult@featureLoadings## Pattern_1 Pattern_2 Pattern_3
## Gene_1 7.140285 0.1665337 6.4039182663
## Gene_2 7.448377 0.3885588 5.4444108009
## Gene_3 7.774792 0.5884004 4.4480547905
## Gene_4 8.085073 0.7907643 3.4823195934
## Gene_5 8.393320 0.9907878 2.5145618916
## Gene_6 8.812235 1.1922625 1.3271282911
## Gene_7 9.215579 1.3912370 0.2088903189
## Gene_8 9.036409 1.5905225 0.0153642362
## Gene_9 8.625849 1.7899834 0.0024186834
## Gene_10 8.072262 1.9887595 0.0008760362
## Gene_11 4.054945 6.1431718 3.1409521103
## Gene_12 5.079877 5.9229212 2.9222431183
## Gene_13 6.097011 5.6985765 2.7133290768
## Gene_14 7.120383 5.4746556 2.4991726875
## Gene_15 8.145170 5.2496295 2.2770845890
## Gene_16 9.197388 5.0248389 2.0023994446
## Gene_17 10.271322 4.7990499 1.6821743250
## Gene_18 11.409943 4.5738611 1.2456048727
## Gene_19 12.510637 4.3517332 0.9027723670
## Gene_20 13.598970 4.1213160 0.5810650587
## Gene_21 14.623000 3.8964021 0.3594548106
## Gene_22 15.565862 3.6694975 0.2576346695
## Gene_23 16.517967 3.4397173 0.1672194302
## Gene_24 17.413399 3.2097712 0.1317380965
## Gene_25 18.325840 2.9828455 0.0834344402# check reference result:
load('../data/modsimresult.rda')If both matrices–sampleFactors and featureLoadings–have reasonable values (small, nonnegative, somewhat random-seeming), it is an indication that CoGAPS is working as expected.
We now continue with single-cell analysis.
5 Single-cell CoGAPS
# OPTION: download data object from Zenodo
options(timeout=50000) # adjust this if you're getting timeout downloading the file
url = "https://zenodo.org/record/7709664/files/inputdata.Rds"
download.file(url,"inputdata_download.Rds", mode="wb")
pdac_data <- readRDS("inputdata_download.Rds")
pdac_data## An object of class Seurat
## 15184 features across 25442 samples within 2 assays
## Active assay: originalexp (15176 features, 2000 variable features)
## 1 other assay present: CoGAPS
## 5 dimensional reductions calculated: PCA, Aligned, UMAP, pca, umappdac_data An object of class Seurat 15184 features across 25442 samples within 2 assays Active assay: originalexp (15176 features, 2000 variable features) 1 other assay present: CoGAPS 5 dimensional reductions calculated: PCA, Aligned, UMAP, pca, umap
We also want to extract the counts matrix to provide directly to CoGAPS
pdac_epi_counts <- as.matrix(pdac_data@assays$originalexp@counts)
norm_pdac_epi_counts <- log1p(pdac_epi_counts)
head(pdac_epi_counts, n=c(5L, 2L))
head(norm_pdac_epi_counts, n=c(5L, 2L))Most of the time we will set some parameters before running CoGAPS. Parameters are managed with a CogapsParams object. This object will store all parameters needed to run CoGAPS and provides a simple interface for viewing and setting the parameter values.
library(CoGAPS)
pdac_params <- CogapsParams(nIterations=50000, # 50000 iterations
seed=42, # for consistency across stochastic runs
nPatterns=8, # each thread will learn 8 patterns
sparseOptimization=TRUE, # optimize for sparse data
distributed="genome-wide") # parallelize across sets
pdac_params## -- Standard Parameters --
## nPatterns 8
## nIterations 50000
## seed 42
## sparseOptimization TRUE
## distributed genome-wide
##
## -- Sparsity Parameters --
## alpha 0.01
## maxGibbsMass 100
##
## -- Distributed CoGAPS Parameters --
## nSets 4
## cut 7
## minNS 2
## maxNS 6If you wish to run distributed CoGAPS, which is recommended to improve the computational efficiency for most large datasets, you must also call the setDistributedParams function. For a complete description of the parallelization strategy used in distributed CoGAPS, please refer to our preprint: https://www.biorxiv.org/content/10.1101/2022.07.09.499398v1
pdac_params <- setDistributedParams(pdac_params, nSets=7)## setting distributed parameters - call this again if you change nPatternspdac_params## -- Standard Parameters --
## nPatterns 8
## nIterations 50000
## seed 42
## sparseOptimization TRUE
## distributed genome-wide
##
## -- Sparsity Parameters --
## alpha 0.01
## maxGibbsMass 100
##
## -- Distributed CoGAPS Parameters --
## nSets 7
## cut 8
## minNS 4
## maxNS 11With all parameters set, we are now ready to run CoGAPS. Please note that this is the most time-consuming step of the procedure. Timing can take several hours and scales nlog(n) based on dataset size, as well as the parameter values set for ‘nPatterns’ and ‘nIterations’. Time is increased when learning more patterns, when running more iterations, and when running a larger dataset, with iterations having the largest variable impact on the runtime of the NMF function.
startTime <- Sys.time()
pdac_epi_result <- CoGAPS(pdac_epi_counts, pdac_params)
endTime <- Sys.time()
saveRDS(pdac_epi_result, "../data/pdac_epi_cogaps_result.Rds")
# To save as a .csv file, use the following line:
toCSV(pdac_epi_result, "../data")6 Analyzing the CoGAPS result
Now that the CoGAPS run is complete, learned patterns can be investigated. Due to the stochastic nature of the MCMC sampling in CoGAPS and long run time, it is generally a good idea to immediately save your CoGAPS result object to a file to have (Box 17), then read it in for downstream analysis.
If you wish to load and examine a precomputed result object, please do so by:
# OPTION: download precomputed CoGAPS result object from Zenodo
# Bioc vignette uses this
options(timeout=50000) # adjust this if you're getting timeout downloading the file
url = "https://zenodo.org/record/7709664/files/cogapsresult.Rds?download=1"
download.file(url,"cogapsresult_download.Rds", mode="wb")
cogapsresult <- readRDS("cogapsresult_download.Rds")To load your own result, simply edit the file path:
library(CoGAPS)
cogapsresult <- readRDS("../data/pdac_epi_cogaps_result.Rds")It is recommended to immediately visualize pattern weights on a UMAP because you will immediately see whether they are showing strong signal and make common sense.
Since pattern weights are all continuous and nonnegative, they can be used to color a UMAP in the same way as one would color by gene expression. The sampleFactors matrix is essentially just nPatterns different annotations for each cell, and featureLoadings is likewise just nPatterns annotations for each gene. This makes it very simple to incorporate pattern data into any data structure and workflow.
6.1 Load CoGAPS pattern information into Seurat object
To store CoGAPS patterns as an Assay within a Seurat object (recommended):
library(Seurat)
# make sure pattern matrix is in same order as the input data
patterns_in_order <-t(cogapsresult@sampleFactors[colnames(pdac_data),])
# add CoGAPS patterns as an assay
pdac_data[["CoGAPS"]] <- CreateAssayObject(counts = patterns_in_order)6.2 Plot patterns on an embedding
With the help of Seurat’s FeaturePlot function, we generate a UMAP embedding of the cells colored by the intensity of each pattern.
DefaultAssay(pdac_data) <- "CoGAPS"
pattern_names = rownames(pdac_data@assays$CoGAPS)
library(viridis)
color_palette <- viridis(n=10)
FeaturePlot(pdac_data, pattern_names, cols=color_palette, reduction = "umap") & NoLegend()7 Pattern Markers
To assess pattern marker genes, we provide a patternMarkers() CoGAPS function to find genes associated with each pattern and returns a dictionary of information containing lists of marker genes, their ranking, and their “score” for each pattern. This is vital because genes are often associated with multiple patterns.
patternMarkers can run in two modes, depending on the “threshold” parameter
If threshold=“all”, each gene is treated as a marker of one pattern (whichever it is most strongly associated with). The number of marker genes will always equal the number of input genes. If threshold=“cut”, a gene is considered a marker of a pattern if and only if it is less significant to at least one other pattern. Counterintuitively, this results in much shorter lists of patternMarkers and is a more convenient statistic to use when functionally annotating patterns.
The three components of the returned dictionary pm are:
PatternMarkers:
A list of marker genes for each pattern
Can be determined using two threshold metrics (cut/all)
PatternMarkerRank:
Each marker gene ranked by association for each pattern
Whole natural numbers, assigning each marker gene a place in the rank for each pattern.
Lower rank indicates higher association and vice versa.
PatternMarkerScores:
Scores describing how strongly a marker gene is associated with a pattern.
A higher score value indicates the marker gene is more associated with the pattern, and vice versa.
Scores have nonnegative values mostly falling between 0 and 2
pm <- patternMarkers(cogapsresult, threshold="cut")## Warning in sweep(As, 2, pscale, FUN = "*"): STATS is longer than the extent of
## 'dim(x)[MARGIN]'8 Pattern GSEA
One way to explore and use CoGAPS patterns is to conduct gene set enrichment analysis by functionally annotating the genes which are significant for each pattern. The getPatternHallmarks function provides a wrapper around the fgsea fora method and associates each pattern with msigDB hallmark pathway annotations using the list of marker genes attained from the patternMarkers statistic.
To perform gene set analysis on pattern markers, please run:
hallmarks <- getPatternHallmarks(cogapsresult)## Warning in sweep(As, 2, pscale, FUN = "*"): STATS is longer than the extent of
## 'dim(x)[MARGIN]'hallmarks is a list of data frames, each containing hallmark overrepresentation statistics corresponding to one pattern.
To generate a barchart of the most significant hallmarks for any given pattern, please run:
pl_pattern7 <- plotPatternHallmarks(cogapsresult, hallmarks, whichpattern = 7)
pl_pattern7
To generate statistics on the association between certain sample groups and patterns, we provide a wrapper function, called MANOVA.This will allow us to explore if the patterns we have discovered lend to statistically significant differences in the sample groups. We will first load in the original data (if not already done earlier).
Then, create a new matrix called “interestedVariables” consisting of the metadata variables of interest in conducting analysis on. Lastly, call the wrapper function, passing in the result object as well.
# create dataframe of interested variables
interestedVariables <- cbind(pdac_data@meta.data[["nCount_RNA"]], pdac_data@meta.data[["nFeature_RNA"]])
# call cogaps manova wrapper
manova_results <- MANOVA(interestedVariables, cogapsresult)## [1] "Pattern_1"
## Df Pillai approx F num Df den Df Pr(>F)
## pattern_column 1 0.46053 10858 2 25439 < 2.2e-16 ***
## Residuals 25440
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "Pattern_2"
## Df Pillai approx F num Df den Df Pr(>F)
## pattern_column 1 0.14815 2212.2 2 25439 < 2.2e-16 ***
## Residuals 25440
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "Pattern_3"
## Df Pillai approx F num Df den Df Pr(>F)
## pattern_column 1 0.46173 10911 2 25439 < 2.2e-16 ***
## Residuals 25440
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "Pattern_4"
## Df Pillai approx F num Df den Df Pr(>F)
## pattern_column 1 0.31354 5809.5 2 25439 < 2.2e-16 ***
## Residuals 25440
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "Pattern_5"
## Df Pillai approx F num Df den Df Pr(>F)
## pattern_column 1 0.16056 2432.8 2 25439 < 2.2e-16 ***
## Residuals 25440
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "Pattern_6"
## Df Pillai approx F num Df den Df Pr(>F)
## pattern_column 1 0.19702 3120.9 2 25439 < 2.2e-16 ***
## Residuals 25440
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "Pattern_7"
## Df Pillai approx F num Df den Df Pr(>F)
## pattern_column 1 0.18574 2901.5 2 25439 < 2.2e-16 ***
## Residuals 25440
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "Pattern_8"
## Df Pillai approx F num Df den Df Pr(>F)
## pattern_column 1 0.11419 1639.7 2 25439 < 2.2e-16 ***
## Residuals 25440
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The function will print out the MANOVA results for each pattern learned based on the variables of interest. From the output, we can observe that all p-values have a value of 0.0, indicating that differences observed in the sample groups based on the patterns are statistically significant.
9 Citing CoGAPS
If you use the CoGAPS package for your analysis, please cite Fertig et al. (2010)
If you use the gene set statistic, please cite Ochs et al. (2009)
References
Fertig, Elana J., Jie Ding, Alexander V. Favorov, Giovanni Parmigiani, and Michael F. Ochs. 2010. “CoGAPS: An R/C++ Package to Identify Patterns and Biological Process Activity in Transcriptomic Data.” Bioinformatics 26 (21): 2792–3. https://doi.org/10.1093/bioinformatics/btq503.
Ochs, Michael F., Lori Rink, Chi Tarn, Sarah Mburu, Takahiro Taguchi, Burton Eisenberg, and Andrew K. Godwin. 2009. “Detection of Treatment-Induced Changes in Signaling Pathways in Gastrointestinal Stromal Tumors Using Transcriptomic Data.” Cancer Research 69 (23): 9125–32. https://doi.org/10.1158/0008-5472.CAN-09-1709.
Seung, Sebastian, and Daniel D. Lee. 1999. “Learning the Parts of Objects by Non-Negative Matrix Factorization.” Nature 401 (6755): 788–91. https://doi.org/10.1038/44565.