Select Principal Components

Purpose

Choosing the number of principal components is a key step before graph construction, clustering, UMAP, or t-SNE.

The chosen dimension range usually appears as:

dims <- 1:30

Common starting values are:

Workflow	Common starting dims
Classic log-normalized workflow	1:30
SCT workflow	1:40
Integrated assay PCA	1:30 or 1:40
Harmony reduction	use the selected PCA dimensions, often 1:30 or 1:40

These values are starting points, not rules. SCT workflows often use more PCs than the classic workflow because SCT normalization can preserve more biological signal in higher PCs.

This value should still be checked from the data. Do not copy 1:30 or 1:40 blindly.

Where PCs Are Used

PC selection affects downstream steps such as:

seu <- Seurat::FindNeighbors(
  object = seu,
  reduction = "pca",
  dims = dims
)

seu <- Seurat::FindClusters(seu)

seu <- Seurat::RunUMAP(
  object = seu,
  reduction = "pca",
  dims = dims
)

For Harmony integration, the same idea applies, but the reduction is usually harmony:

seu <- Seurat::FindNeighbors(
  object = seu,
  reduction = "harmony",
  dims = dims
)

seu <- Seurat::RunUMAP(
  object = seu,
  reduction = "harmony",
  dims = dims
)

Main Approaches

Seurat workflows commonly use several complementary approaches.

Approach	Use
Biological inspection	Check PC loadings, marker genes, pathway signals, and known metadata
Elbow plot	Look for where additional PCs add much less variation
Variance heuristic	Use explained variance rules for automated or batch workflows

These approaches should be treated as guidance, not as absolute rules.

Elbow Plot

Use ElbowPlot() to inspect how quickly the standard deviation drops across PCs:

p_elbow <- Seurat::ElbowPlot(
  object = seu,
  reduction = "pca",
  ndims = 50
) +
  ggplot2::labs(title = "Elbow Plot of PCA")

p_elbow

The elbow is the point where additional PCs start contributing less new structure.

For Harmony, inspect the original PCA before Harmony and then use the selected dimension range for the Harmony reduction.

Inspect PC Loadings

PCs should also make biological sense.

Check genes driving selected PCs:

print(
  x = seu[["pca"]],
  dims = 1:10,
  nfeatures = 10
)

Visualize loadings:

Seurat::VizDimLoadings(
  object = seu,
  dims = 1:5,
  reduction = "pca"
)

Heatmap selected PCs:

Seurat::DimHeatmap(
  object = seu,
  dims = 1:10,
  cells = 500,
  balanced = TRUE
)

PCs dominated by technical effects, stress genes, mitochondrial genes, or sample-specific artifacts should be interpreted carefully.

Variance-Based Heuristic

The PCA reduction stores stdev for each PC. The variance explained by each PC is based on squared standard deviation:

stdev <- seu[["pca"]]@stdev
variance <- stdev^2
var_ratio <- variance / sum(variance) * 100
cum_var <- cumsum(var_ratio)

Do not compute variance explained directly from stdev. Use stdev^2.

Check the first few PCs:

head(var_ratio, 10)
head(cum_var, 10)

var_ratio is the percentage of variance explained by each PC. cum_var is the cumulative percentage explained by the first k PCs.

Cutoff 1

The first cutoff asks for the first PC where:

• cumulative variance is greater than 90%
• the current PC explains less than 5% of variance

pc_cutoff_1 <- which(cum_var > 90 & var_ratio < 5)[1]

pc_cutoff_1

This rule tries to avoid selecting too few PCs. It keeps enough PCs to cover most of the variation, while also requiring the current PC to no longer be a dominant axis.

In words:

Use enough PCs to explain most variation, but stop after individual PCs are no longer very large.

Cutoff 2

The second cutoff approximates the elbow point by looking at the drop in explained variance between adjacent PCs:

var_diff <- head(var_ratio, -1) - tail(var_ratio, -1)

head(var_diff, 10)

Then find the last PC where the drop is still greater than 0.1%:

pc_cutoff_2 <- if (any(var_diff > 0.1)) {
  max(which(var_diff > 0.1)) + 1
} else {
  NA_integer_
}

pc_cutoff_2

This rule asks where the variance curve is still dropping meaningfully. After that point, additional PCs contribute less extra structure and are more likely to add noise or weak technical signal.

In words:

Keep PCs until the explained variance curve has mostly flattened.

Suggested PCs

Use the smaller of the two cutoffs as a conservative suggestion:

n_pcs <- min(pc_cutoff_1, pc_cutoff_2, na.rm = TRUE)

if (!is.finite(n_pcs)) {
  n_pcs <- length(stdev)
}

dims <- 1:n_pcs

n_pcs
dims

The two cutoffs capture different ideas:

Cutoff	Meaning
pc_cutoff_1	enough cumulative variance has been captured
pc_cutoff_2	the elbow-like drop in variance has mostly flattened

This is only a heuristic. Compare the result with ElbowPlot(), PC loadings, and biological interpretation.

Practical Rule

For routine analysis, start by computing more PCs than expected:

seu <- Seurat::RunPCA(
  object = seu,
  npcs = 50,
  verbose = TRUE
)

Then inspect the elbow plot, PC loadings, and the variance heuristic. Use the selected dims consistently in FindNeighbors(), RunUMAP(), and RunTSNE().

Note

PC selection is not specific to SCT. It applies after classic PCA, SCT PCA, integrated assay PCA, and Harmony-based workflows.

The final choice should balance statistical signal, biological interpretability, and downstream clustering stability.