Calculate Categorization Entropy

This function takes a matrix of category scores (cell type by cells) and calculates the entropy of the category probabilities for each cell. This gives a sense of how confident the cell type assignments are. High entropy = lots of plausible category assignments = low confidence. Low entropy = only one or two plausible categories = high confidence. This is confidence in the vernacular sense, not in the "confidence interval" statistical sense. Also note that the entropy tells you nothing about whether or not the assignments are correct – see the other functionality in the package for that. This functionality can be used for assessing how comparatively confident different sets of assignments are (given that the number of categories is the same).

calculateCategorizationEntropy(
  X,
  inverse_normal_transform = FALSE,
  plot = TRUE,
  verbose = TRUE
)

Arguments

X

A matrix of category scores.

inverse_normal_transform

If TRUE, apply inverse normal transformation to X. Default is FALSE.

plot

If TRUE, plot a histogram of the entropies. Default is TRUE.

verbose

If TRUE, display messages about the calculations. Default is TRUE.

Value

A vector of entropy values for each column in X.

Details

The function checks if X is already on the probability scale. Otherwise, it applies softmax columnwise.

You can think about entropies on a scale from 0 to a maximum that depends on the number of categories. This is the function for entropy (minus input checking): entropy(p) = -sum(p*log(p)) . If that input vector p is a uniform distribution over the length(p) categories, the entropy will be a high as possible.

Author

Andrew Ghazi, andrew_ghazi@hms.harvard.edu

Examples

# Simulate 500 cells with scores on 4 possible cell types
X <- rnorm(500 * 4) |> matrix(nrow = 4)
X[1, 1:250] <- X[1, 1:250] + 5 # Make the first category highly scored in the first 250 cells

# The function will issue a message about softmaxing the scores, and the entropy histogram will be
# bimodal since we made half of the cells clearly category 1 while the other half are roughly even.
entropy_scores <- calculateCategorizationEntropy(X)
#> X doesn't seem to be on the probability scale, applying column-wise softmax.
#> Max possible entropy given 4 categories: 1.39