Whclust {WCluster}

Hierarchical Clustering with observational weights

Description

This function produces the hierarchical tree for observations with weights, by agglomerative hierarchical clustering based on Ward's method considering observational weights.

Usage

Whclust(x,w)

Arguments

x

A data matrix (of class matrix, data.frame, or data.table) containing only entries of class numeric.

w

Vector of length nrow(x) of weights for each observation in the dataset. Must be of class numeric or integer. If NULL, the default value is a vector of 1 with length nrow(x), i.e., weights equal 1 for all observations.

Details

Agglomerative hierarchical clustering based on Ward's method considering observational weights are used to generate the hierarchical tree. Based on the Ward method, the distance between two clusters is the increase of sum of squares after merging them, which is the merging cost of combining two clusters. This function computes the merging costs for each pair of clusters for a data set with observational weights. During the process of agglomerative hierarchical clustering, the sums of squares are calculated with observational weights, and the pair of clusters with minimal distance is merged at each step.

Value

An object of class hclust which describes the tree produced by the clustering process. It's the same class of object as outputs from function hclust in the package stats. See details in hclust. There are print, plot, and cutree methods for hclust objects.

Author(s)

Javier Cabrera, Yajie Duan, Ge Cheng

References

Cherasia, K. E., Cabrera, J., Fernholz, L. T., & Fernholz, R. (2022). Data Nuggets in Supervised Learning. In Robust and Multivariate Statistical Methods: Festschrift in Honor of David E. Tyler (pp. 429-449). Cham: Springer International Publishing.

Beavers, T., Cheng, G., Duan, Y., Cabrera, J., Lubomirski, M., Amaratunga, D., Teigler, J. (2023). Data Nuggets: A Method for Reducing Big Data While Preserving Data Structure (Submitted for Publication)

See Also

hclust, distw

Examples

    require(cluster)
      t1 = Sys.time()

    # The Ruspini data set from the package "cluster""
    x = as.matrix(ruspini)

    # assign random weights to observations
    w = sample(1:20,nrow(x),replace = TRUE)

    # hierarchical clustering with observational weights
    h = Whclust(x,w)

    #print the hclust object
    print(h)

    #plot the hierarchical tree
    plot(h)

    #cut the hierarchical tree to get 4 clusters
    k4 = cutree(h,4)
    table(k4)

    #plot the clustering result
    plot(x,cex = log(w),pch = 16,col = k4)
      t2 = Sys.time()