Last updated: 2024-08-16

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Rmd cf1ff46 Dave Tang 2024-08-16 k-methods clustering

The Partitioning Around Medoids (PAM) methods is as follows:

  1. Start from a matrix of \(p\) features measured on a set of \(n\) observations.
  2. Randomly pick \(k\) distinct cluster centers out of the \(n\) observations (“seeds”).
  3. Assign each of the remaining observations to the group to whose center it is the closest.
  4. For each group, choose a new center from the observations in the group, such that the sum of the distances of group members to the center is minimal; this is called the medoid.
  5. Repeat Steps 3 and 4 until the groups stabilise.

Each time the algorithm is run, different initial seeds will be picked in Step 2, and in general, this can lead to different final results. A popular implementation is the pam() function in the {cluster} package.

A slight variation of the method replaces the medoids by the arithematic means (centers of gravity) of the clusters and is called k-means. Whereas in PAM the centers are observations, this is not, in general, the case with k-means. The function kmeans() comes with base R via the {stats} package.

These so-called k-methods are the most common off-the-shelf methods for clustering; they work particularly well when the clusters are of comparable size and convex (blob-shaped). On the other hand, if the true clusters are very different in size, the larger ones will tend to be broken up; the same is true for groups that have pronounced non-spherical or non-elliptical shapes.

There are clever schemes that repeat the process many times using different initial centers or resampled datasets. Repeating a clustering procedure multiple times on the same data but with different starting points creates strong forms. Repeatedly subsampling the dataset and applying a clustering method will result in groups of observations that are “almost always” grouped together; these are called tight clusters. The study of strong forms or tight clusters facilitates the choice of the number of clusters. The {clusterExperiment} package can combine and compare the output from many different clusterings.


sessionInfo()
R version 4.4.0 (2024-04-24)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 22.04.4 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.20.so;  LAPACK version 3.10.0

locale:
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 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
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[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

time zone: Etc/UTC
tzcode source: system (glibc)

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
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 [5] purrr_1.0.2     readr_2.1.5     tidyr_1.3.1     tibble_3.2.1   
 [9] ggplot2_3.5.1   tidyverse_2.0.0 workflowr_1.7.1

loaded via a namespace (and not attached):
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[13] jsonlite_1.8.8    processx_3.8.4    whisker_0.4.1     ps_1.7.6         
[17] promises_1.3.0    httr_1.4.7        fansi_1.0.6       scales_1.3.0     
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[25] withr_3.0.0       cachem_1.1.0      yaml_2.3.8        tools_4.4.0      
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[41] later_1.3.2       gtable_0.3.5      glue_1.7.0        Rcpp_1.0.12      
[45] xfun_0.44         tidyselect_1.2.1  rstudioapi_0.16.0 knitr_1.47       
[49] htmltools_0.5.8.1 rmarkdown_2.27    compiler_4.4.0    getPass_0.2-4