Compute Second-Order Similarity Scores

This function calculates the second order similarity between two similarity vectors derived from a provided distance function applied to matrix X and a reference similarity matrix S. The calculation takes into account a blocking variable to exclude comparisons within the same block.

Usage

second_order_similarity(
  dist_fun,
  X,
  D,
  block,
  method = c("pearson", "spearman")
)

Arguments

dist_fun

A distance function object or a character string specifying the method used for distance computation. This function should be capable of processing the matrix X to produce a distance matrix.

X

A numeric matrix where each row is an observation and columns are features. Distances will be computed pairwise between rows of this matrix.

D

A numeric matrix, typically a predefined dissimilarity matrix that serves as a reference to compare against the computed distances from X.

block

A vector (numeric or factor) indicating the block or group for each row in X and S. Comparisons are only made between elements of different blocks.

method

The method used for computing correlation between similarity vectors. Defaults to "pearson", but "spearman" or "kendall" could also be used.

Value

A numeric vector of similarity scores, one for each observation in X, representing the correlation between distance vectors derived from X and the corresponding vectors in S for non-matching blocks.

Details

The function computes a distance matrix for X using the specified `dist_fun`. It then compares these distances with the entries in S for each observation, excluding comparisons within the same block as defined by the `block` argument. This is useful for evaluating how well the distances within X align with an external similarity standard, adjusting for within-block dependencies.

Examples

# Assuming X and S are numeric matrices and block is a factor or numeric vector
dist_fun <- "euclidean"  # This should be defined or loaded from your package/environment
X <- matrix(rnorm(100), ncol=10)
D <- matrix(rnorm(100), ncol=10)
block <- rep(1:5, each=20)
scores <- second_order_similarity(dist_fun, X, D, block, method = "pearson")
#> Error in pairwise_dist.default(dist_fun, X): pairwise_dist not implemented for objects of class matrix