Authors: Meelad Amouzgar and David Glass
Bendall lab @ Stanford University
This repository is still under development.
Linear Discriminant Analysis (LDA) is a classification algorithm that we’ve repurposed for supervised dimensionality reduction of single-cell data. LDA identifies linear combinations of predictors that optimally separate a priori labels, enabling users to tailor visualizations to separate specific aspects of cellular heterogeneity. We implement LDA with feature selection by Hybrid Subset Selection (HSS) in this R package, called hsslda.
If you use our package, please cite our manuscript:
https://doi-org.stanford.idm.oclc.org/10.1016/j.patter.2022.100536
Amouzgar M, Glass DR, Baskar R, Averbukh I, Kimmey SC, Tsai AG, Hartmann FJ, Bendall SC. Supervised dimensionality reduction for exploration of single-cell data by HSS-LDA. Patterns (N Y). 2022 Jun 24;3(8):100536. doi: 10.1016/j.patter.2022.100536. PMID: 36033591; PMCID: PMC9403402.
You can install hsslda using:
remotes::install_github("mamouzgar/hsslda", build_vignettes = FALSE)You may need to install the 'entropy' package first.
The github page includes an introduction to the package.
library(hsslda)Here we read-in the example data
data(TcellHartmann2020_sampleData)colnames(TcellHartmann2020_sampleData)## [1] "GLUT1" "HK2" "GAPDH" "LDHA" "MCT1" "PFKFB4"
## [7] "IDH2" "CyclinB1" "GLUD12" "CS" "OGDH" "CytC"
## [13] "ATP5A" "S6_p" "HIF1A" "labels"
head(TcellHartmann2020_sampleData,3)## GLUT1 HK2 GAPDH LDHA MCT1 PFKFB4 IDH2
## 1 0.03409762 0.00000000 0.3481982 0.4066992 0.06882467 0.1601350 0.5051168
## 2 0.25528617 0.06572665 0.3005934 0.5078840 0.01220142 0.0241186 0.6933922
## 3 0.14032230 0.00000000 0.1665477 0.1122911 0.12135540 0.1192041 0.4822793
## CyclinB1 GLUD12 CS OGDH CytC ATP5A S6_p
## 1 0.063481520 0.4324707 0.5296415 0.5315838 0.20964937 0.3771783 0.03704562
## 2 0.102636694 0.4726154 0.5879990 0.4161547 0.02309679 0.6053693 0.16939760
## 3 0.007619569 0.3998965 0.4228455 0.1749531 0.08402797 0.2401586 0.03365913
## HIF1A labels
## 1 0.02346801 day0
## 2 0.08144526 day0
## 3 0.09690983 day0
You can run hybrid subset selection on a dataset using runHSS().
runHSS takes 3 inputs:
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x: a dataframe of cells (rows) and markers/genes (columns)
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y: a vector of your class labels of interest.
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score.method: A scoring metric to use for feature selection, which can include: ‘euclidean’, ‘silhouette’, ‘pixel.entropy’, ‘pixel.density’, or ‘custom’
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(optional) downsample: Boolean, defaults to TRUE. Downsamples data to improve runtime. Set to FALSE to use all input data.
Here we will run HSS using the default scoring method: euclidean distance.Note that scoring metrics like silhouette or pixel class entropy (PCE) score will require additional package dependencies.
channels = c('GLUT1', 'HK2', 'GAPDH', 'LDHA', 'MCT1', 'PFKFB4', 'IDH2', 'CyclinB1', 'GLUD12', 'CS', 'OGDH', 'CytC', 'ATP5A', 'S6_p', 'HIF1A')
train.x = TcellHartmann2020_sampleData[channels]
train.y = TcellHartmann2020_sampleData[['labels']]
hss.result = runHSS(x = train.x, y = train.y, score.method = 'euclidean', downsample = FALSE)## Using all input cells for HSS-LDA...
## Optimizing dimensionality reduction using euclidean metric...
## Number of markers: 2
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The final hss.result object outputted from runHSS contains a few elements, the most important ones are highlighted below:
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HSSscores: a table of all scores for each subsetted model.
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ElbowPlot: visualizes the elbow plot and calculated elbow point for the optimal feature set.
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HSS-LDA-model: The final LDA model using the optimal feature set.
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HSS-LDA-result: The final result table containing all initially inputted markers, class labels, and linear discriminants from the opimal model.
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downsampled.cells.included.in.analysis: A boolean vector of rows included in the downsampling analysis. If downsampling was not performed, all values are TRUE. The final output results includes all data projected onto the HSS-LD axes.
You can visualize the elbow plot, which is ggplot configurable:
hss.result$ElbowPlot
The final output object contains a merged dataframe of your markers, class labels, and newly generated LD axes
lda.df = hss.result$`HSS-LDA-result`
head(lda.df, 3)## GLUT1 HK2 GAPDH LDHA MCT1 PFKFB4 IDH2
## 1 0.03409762 0.00000000 0.3481982 0.4066992 0.06882467 0.1601350 0.5051168
## 2 0.25528617 0.06572665 0.3005934 0.5078840 0.01220142 0.0241186 0.6933922
## 3 0.14032230 0.00000000 0.1665477 0.1122911 0.12135540 0.1192041 0.4822793
## CyclinB1 GLUD12 CS OGDH CytC ATP5A S6_p
## 1 0.063481520 0.4324707 0.5296415 0.5315838 0.20964937 0.3771783 0.03704562
## 2 0.102636694 0.4726154 0.5879990 0.4161547 0.02309679 0.6053693 0.16939760
## 3 0.007619569 0.3998965 0.4228455 0.1749531 0.08402797 0.2401586 0.03365913
## HIF1A LD1 LD2 LD3 LD4 LD5 labels
## 1 0.02346801 0.1824071 -1.505745 4.121023 3.561247 0.17292992 day0
## 2 0.08144526 -1.4912720 -1.858684 4.190646 4.693052 -2.52678835 day0
## 3 0.09690983 -1.0026704 -2.758428 2.453262 3.370301 0.09091075 day0
ggplot2::ggplot(lda.df,ggplot2::aes(x = HSS_LD1, y = HSS_LD2, color = labels)) +
ggplot2::geom_point() 
The final HSS-LDA model is also saved, and can be used like any R model.
hss.result$`HSS-LDA-model`## Call:
## lda(y ~ ., data = x[, markers])
##
## Prior probabilities of groups:
## day0 day1 day2 day3 day4 day5
## 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##
## Group means:
## GLUT1 HK2 IDH2 CyclinB1 GLUD12 CS OGDH
## day0 0.1686856 0.04104809 0.6052301 0.06537171 0.4897904 0.5299507 0.3292659
## day1 0.2953167 0.21629789 0.5935709 0.06965901 0.4730912 0.5417745 0.3906114
## day2 0.5763669 0.55772316 0.6680269 0.23513566 0.5277285 0.7177145 0.5890289
## day3 0.7184115 0.55541671 0.7248705 0.35324105 0.5967461 0.7861387 0.6456323
## day4 0.7027508 0.41256773 0.7639317 0.31064447 0.6161448 0.7786976 0.5322304
## day5 0.7213829 0.31763930 0.7655344 0.25145793 0.6068985 0.7636594 0.4400868
## CytC ATP5A HIF1A
## day0 0.1369610 0.4328304 0.1148124
## day1 0.1670760 0.5025277 0.2048914
## day2 0.2500147 0.6946313 0.2941883
## day3 0.3662381 0.7670108 0.3772618
## day4 0.3900886 0.7277347 0.2854079
## day5 0.4314735 0.6504328 0.2555777
##
## Coefficients of linear discriminants:
## LD1 LD2 LD3 LD4 LD5
## GLUT1 -9.3286320 -2.42021822 -4.2104736 -2.427140 0.5830266
## HK2 0.4317694 3.60630945 -1.9692387 2.802069 1.0771403
## IDH2 0.9131571 -6.23232819 0.2676104 6.611837 -2.5128133
## CyclinB1 0.4159760 0.89607252 3.3770898 -1.120539 0.9637185
## GLUD12 3.2002486 0.08886794 1.2587234 -2.408197 2.8570995
## CS -4.3611705 -2.34919265 3.6521969 6.055976 4.8876598
## OGDH 1.2117074 2.79674730 0.5939495 -1.434667 3.1181463
## CytC -0.8575323 -2.13438292 -0.2152454 -1.984046 0.1923797
## ATP5A 1.2688525 4.81834552 3.0803171 -1.425575 -11.1020405
## HIF1A -0.1810920 0.73022516 0.1653555 -3.167533 1.1239380
##
## Proportion of trace:
## LD1 LD2 LD3 LD4 LD5
## 0.7906 0.1890 0.0115 0.0066 0.0023
You can use this final model to apply the same dimensionality reduction to new data using makeAxes.
lda.df.newData = makeAxes(df = newdata, co =hss.result$`HSS-LDA-model`$scaling)To run LDA without HSS, you can use the MASS package in R, then use makeAxes to generate your LD axes or apply it to a new dataset.
lda.res = MASS::lda(x = train.x, grouping = train.y)
lda.df = makeAxes(df = train.x, co =lda.res$scaling)
You can also add your own custom separation metric to perform feature selection with by changing score.method = ‘custom’ and adding custom function. The custom function must take in as input:
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x: dataframe of all your data.
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y: vector of class labels matching training data rows.
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custom.score.method: the function for your custom separation metric.
You can then input your custom function into the hsslda::runHSS() function as an argument into custom.score.method, and indicate score.method = ‘custom’
hss.resultCustom = runHSS(x = train.x, y = train.y, score.method = 'custom', custom.score.method = myCustomFunction)And that’s how you use LDA with Hybrid Subset Selection!
Questions, comments, or general feedback: