find_kmedoids_weights: Optimise Gower's weights for K-medoids clustering

In Jeroentjeh/opthierarch: Hiearchical clustering with optimised Gower's metric's weights

Description

Uses the limited memory BFGS algorithm with bounds from optim to optimise the weights of a K-medoids clustering with the goal of maximising the cophenetic correlation coefficient.

Usage

find_kmedoids_weights(data, k, start_values = rep(1 / ncol(data), ncol(data) - 1),
                        n_iterate = 10, minimal_memory_mode = T,
                        bounds=c(1 / (3 * ncol(data)),
                        1 - (ncol(data) - 1) / (3 * ncol(data))))
                        

Arguments

data	the data that needs to be clustered, provided as a dataframe or (numeric) matrix. It is assumed that rows correspond to instances and columns correspond to features.
start_values	a vector containing the initial values of the weights. Defaults to 1/ncol(data) for all variables. They must not be negative. Furthermore, 1 - sum(start_values) >= bounds[1] must hold. Due to the way the algorithm is programmed, you only have to supply values for the first ncol(data) - 1 variables!
k	the number of clusters, the K in K-medoids.
n_iterate	the maximum number of iterations used by the quasi-newton method optim. Defaults to 10.
minimal_memory_mode	logical that determines whether the algorithm calculates the differences for each instance and each variables beforehand or calculates them live each time. The first will be chosen when this variable is FALSE, the second one will be chosen when this variable is TRUE. Note that this requires k vectors of size n(n-1)/2 to be stored, where k is the number of columns and n the number of rows. If you have the required memory, setting this to FALSE is definitely worth the speed increase, which seems to be a factor of something between 2 and 3.
bounds	a vector of size 2 containing the lower and upper bound in position 1 and 2 respectively. The lower bound must not be lower than 0 and not higher than 1/ncol(data). The upper bound will be set to the minimum of its current value and 1-(ncol(data)-1)*bounds[1]. For more information, see details.

Details

Contrary to intuition, the start_values vector should not be equal to the number of columns in data. It should have one weights less (the weight for the last variable). The reason for this is that we set the sum of all weights to equal a constant (1 in this case), allowing us to not have to set a weight for one variable. This allows us to skip the calculations for that variable, saving some time. The weight for this variable should of course still abide the given bounds!

Value

The result is the output of optim.

par	The best set of parameters found.
value	The value of fn corresponding to par.
counts	A two-element integer vector giving the number of calls to fn and gr respectively. This excludes those calls needed to compute the Hessian, if requested, and any calls to fn to compute a finite-difference approximation to the gradient.
convergence	An integer code. 0 indicates successful completion (which is always the case for "SANN" and "Brent"). Possible error codes are noted in the optim documentation

Note

This package requires the cluster package.

Author(s)

Jeroen van den Hoven

References

Clustering with optimised weights for Gower's metric: Using hierarchical clustering and Quasi-Newton methods to maximise the cophenetic correlation coefficient, Jeroen van den Hoven.

Examples

## Basic example
data(mtcars)
find_kmedoids_weights(mtcars, k = 3)

## Using custom bounds
find_kmedoids_weights(mtcars, k = 3, bounds = c(0, 1))

Jeroentjeh/opthierarch documentation built on May 26, 2019, 7:28 a.m.