denoisePCA: Denoise expression with PCA
In scran: Methods for Single-Cell RNA-Seq Data Analysis

Description Usage Arguments Details Value Effects of gene selection Caveats with interpretation Author(s) References See Also Examples

View source: R/denoisePCA.R

Denoise log-expression data by removing principal components corresponding to technical noise.

getDenoisedPCs(x, ...)

## S4 method for signature 'ANY'
getDenoisedPCs(
  x,
  technical,
  subset.row = NULL,
  min.rank = 5,
  max.rank = 50,
  fill.missing = FALSE,
  BSPARAM = bsparam(),
  BPPARAM = SerialParam()
)

## S4 method for signature 'SummarizedExperiment'
getDenoisedPCs(x, ..., assay.type = "logcounts")

denoisePCA(x, ..., value = c("pca", "lowrank"), assay.type = "logcounts")

denoisePCANumber(var.exp, var.tech, var.total)

`x`	For `getDenoisedPCs`, a numeric matrix of log-expression values, where rows are genes and columns are cells. Alternatively, a SummarizedExperiment object containing such a matrix. For `denoisePCA`, a SingleCellExperiment object containing a log-expression amtrix.
`...`	For the `getDenoisedPCs` generic, further arguments to pass to specific methods. For the SingleCellExperiment method, further arguments to pass to the ANY method. For the `denoisePCA` function, further arguments to pass to the `getDenoisedPCs` function.
`technical`	An object containing the technical components of variation for each gene in `x`. This can be: a function that computes the technical component of the variance for a gene with a given mean log-expression, as generated by `fitTrendVar`. a numeric vector of length equal to the number of rows in `x`, containing the technical component for each gene. a DataFrame of variance decomposition results generated by `modelGeneVarWithSpikes` or related functions.
`subset.row`	See `?"scran-gene-selection"`.
`min.rank, max.rank`	Integer scalars specifying the minimum and maximum number of PCs to retain.
`fill.missing`	Logical scalar indicating whether entries in the rotation matrix should be imputed for genes that were not used in the PCA.
`BSPARAM`	A BiocSingularParam object specifying the algorithm to use for PCA.
`BPPARAM`	A BiocParallelParam object to use for parallel processing.
`assay.type`	A string specifying which assay values to use.
`value`	String specifying the type of value to return. `"pca"` will return the PCs, `"n"` will return the number of retained components, and `"lowrank"` will return a low-rank approximation.
`var.exp`	A numeric vector of the variances explained by successive PCs, starting from the first (but not necessarily containing all PCs).
`var.tech`	A numeric scalar containing the variance attributable to technical noise.
`var.total`	A numeric scalar containing the total variance in the data.

This function performs a principal components analysis to eliminate random technical noise in the data. Random noise is uncorrelated across genes and should be captured by later PCs, as the variance in the data explained by any single gene is low. In contrast, biological processes should be captured by earlier PCs as more variance can be explained by the correlated behavior of sets of genes in a particular pathway. The idea is to discard later PCs to remove noise and improve resolution of population structure. This also has the benefit of reducing computational work for downstream steps.

The choice of the number of PCs to discard is based on the estimates of technical variance in technical. This argument accepts a number of different values, depending on how the technical noise is calculated - this generally involves functions such as modelGeneVarWithSpikes or modelGeneVarByPoisson. The percentage of variance explained by technical noise is estimated by summing the technical components across genes and dividing by the summed total variance. Genes with negative biological components are ignored during downstream analyses to ensure that the total variance is greater than the overall technical estimate.

Now, consider the retention of the first d PCs. For a given value of d, we compute the variance explained by all of the later PCs. We aim to find the smallest value of d such that the sum of variances explained by the later PCs is still less than the variance attributable to technical noise. This choice of d represents a lower bound on the number of PCs that can be retained before biological variation is definitely lost. We use this value to obtain a “reasonable” dimensionality for the PCA output.

Note that d will be coerced to lie between min.rank and max.rank. This mitigates the effect of occasional extreme results when the percentage of noise is very high or low.

For getDenoisedPCs, a list is returned containing:

components, a numeric matrix containing the selected PCs (columns) for all cells (rows). This has number of columns between min.rank and max.rank inclusive.
rotation, a numeric matrix containing rotation vectors (columns) for all genes (rows). This has number of columns between min.rank and max.rank inclusive.
percent.var, a numeric vector containing the percentage of variance explained by the first max.rank PCs.

denoisePCA will return a modified x with:

the PC results stored in the reducedDims as a "PCA" entry, if type="pca".
a low-rank approximation stored as a new "lowrank" assay, if type="lowrank".

denoisePCANumber will return an integer scalar specifying the number of PCs to retain. This is equivalent to the output from getDenoisedPCs after setting value="n", but ignoring any setting of min.rank or max.rank.

We can use subset.row to perform the PCA on a subset of genes, e.g., HVGs. This can be used to only perform the PCA on genes with the largest biological components, thus increasing the signal-to-noise ratio of downstream analyses. Note that only rows with positive components are actually used in the PCA, even if we explicitly specified them in subset.row.

If fill.missing=TRUE, entries of the rotation matrix are imputed for all genes in x. This includes “unselected” genes, i.e., with negative biological components or that were not selected with subset.row. Rotation vectors are extrapolated to these genes by projecting their expression profiles into the low-dimensional space defined by the SVD on the selected genes. This is useful for guaranteeing that any low-rank approximation has the same dimensions as the input x. For example, denoisePCA will only ever use fill.missing=TRUE when value="lowrank".

The function's choice of d is only optimal if the early PCs capture all the biological variation with minimal noise. This is unlikely to be true as the PCA cannot distinguish between technical noise and weak biological signal in the later PCs. In practice, the chosen d can only be treated as a lower bound for the retention of signal, and it is debatable whether this has any particular relation to the “best” choice of the number of PCs. For example, many aspects of biological variation are not that interesting (e.g., transcriptional bursting, metabolic fluctuations) and it is often the case that we do not need to retain this signal, in which case the chosen d - despite being a lower bound - may actually be higher than necessary.

Interpretation of the choice of d is even more complex if technical was generated with modelGeneVar rather than modelGeneVarWithSpikes or modelGeneVarByPoisson. The former includes “uninteresting” biological variation in its technical component estimates, increasing the proportion of variance attributed to technical noise and yielding a lower value of d. Indeed, use of results from modelGeneVar often results in d being set to to min.rank, which can be problematic if secondary factors of biological variation are discarded.

Aaron Lun

Lun ATL (2018). Discussion of PC selection methods for scRNA-seq data. https://github.com/LTLA/PCSelection2018

modelGeneVarWithSpikes and modelGeneVarByPoisson, for methods of computing technical components.

runSVD, for the underlying SVD algorithm(s).

library(scuttle)
sce <- mockSCE()
sce <- logNormCounts(sce)

# Modelling the variance:
var.stats <- modelGeneVar(sce)

# Denoising:
pcs <- getDenoisedPCs(sce, technical=var.stats)
head(pcs$components)
head(pcs$rotation)
head(pcs$percent.var)

# Automatically storing the results.
sce <- denoisePCA(sce, technical=var.stats)
reducedDimNames(sce)