If any edge are dropped, the MST are pruned. This generate a two subgraphs. So, it makes a tree graphs and tree dissimilarity values are computed, one for each graph. The dissimilarity is the sum over sqared differences between the observactions in the nodes and mean vector of observations in the graph. The dissimilarity of original graph and the sum of dissimilarity of subgraphs are returned.

prunecost(edges, data, method = c("euclidean", "maximum", "manhattan",
"canberra", "binary", "minkowski", "mahalanobis"),
p = 2, cov, inverted = FALSE)

## Arguments

edges

A matrix with 2 colums with each row is one edge

data

A data.frame with observations in the nodes.

method

Character or function to declare distance method. If method is character, method must be "mahalanobis" or "euclidean", "maximum", "manhattan", "canberra", "binary" or "minkowisk". If method is one of "euclidean", "maximum", "manhattan", "canberra", "binary" or "minkowisk", see dist for details, because this function as used to compute the distance. If method="mahalanobis", the mahalanobis distance is computed between neighbour areas. If method is a function, this function is used to compute the distance.

p

The power of the Minkowski distance.

cov

The covariance matrix used to compute the mahalanobis distance.

inverted

logical. If 'TRUE', 'cov' is supposed to contain the inverse of the covariance matrix.

## Value

A vector with the differences between the dissimilarity of all nodes and the dissimilarity sum of all subgraphs obtained by pruning one edge each time.

## Author

Elias T. Krainski and Renato M. Assuncao

See Also as prunemst

## Examples

d <- data.frame(a=-2:2, b=runif(5))
e <- matrix(c(1,2, 2,3, 3,4, 4,5), ncol=2, byrow=TRUE)

sum(sweep(d, 2, colMeans(d))^2)
#> [1] 10.35574

prunecost(e, d)
#> [1] 2.138259 2.875555 2.820048 2.169740