gt_cluster_pca_best_k.RdThis function selects the best k value based on a chosen metric and criterion.
It is equivalent to plotting the metric against the k values, and selecting
the k that fulfils a given criterion (see details for an explanation of
each criterion). This function simply adds an element 'best_k' to the
gt_cluster_pca returned by gt_cluster_pca(). The choice can be
over-ridden simply by assigning a different value to that element (e.g.
for an object x and a desired k of 8, simply use x$best_k <- 8)
a gt_cluster_pca object obtained with gt_cluster_pca()
a statistics, one of "BIC", "AIC" or "WSS"
one of "diffNgroup", "min", "goesup", "smoothNgoesup", "goodfit", see details for a discussion of each approach.
boolean on whether to silence outputting information to the screen (defaults to FALSE)
a 'gt_cluster_pca' object with an added element 'best_k'
The analysis of data simulated under various population genetics models (see reference) suggested an ad-hoc rule for the selection of the optimal number of clusters. First important result is that BIC seems more efficient than AIC and WSS to select the appropriate number of clusters (see example). The rule of thumb consists in increasing K until it no longer leads to an appreciable improvement of fit (i.e., to a decrease of BIC). In the most simple models (island models), BIC decreases until it reaches the optimal K, and then increases. In these cases, the best rule amounts to choosing the lowest K. In other models such as stepping stones, the decrease of BIC often continues after the optimal K, but is much less steep, so a change in slope can be taken as an indication of where the best k lies.
This function provides a programmatic way to select k. Note that it is highly recommended to look at the graph of BIC versus the numbers of clusters, to understand and validate the programmatic selection. The criteria available in this function are:
"diffNgroup": differences between successive values of the summary statistics (by default, BIC) are split into two groups using a Ward's clustering method (see ?hclust), to differentiate sharp decrease from mild decreases or increases. The retained K is the one before the first group switch. This criterion appears to work well for island/hierarchical models, and decently for isolation by distance models, albeit with some unstability. It can be confounded by an initial, very sharp decrease of the test statistics. IF UNSURE ABOUT THE CRITERION TO USE, USE THIS ONE.
"min": the model with the minimum summary statistics (as specified by stat argument, BIC by default) is retained. Is likely to work for simple island model, using BIC. It is likely to fail in models relating to stepping stones, where the BIC always decreases (albeit by a small amount) as K increases. In general, this approach tends to over-estimate the number of clusters.
"goesup": the selected model is the K after which increasing the number of clusters leads to increasing the summary statistics. Suffers from inaccuracy, since i) a steep decrease might follow a small 'bump' of increase of the statistics, and ii) increase might never happen, or happen after negligible decreases. Is likely to work only for clear-cut island models.
"smoothNgoesup": a variant of "goesup", in which the summary statistics is first smoothed using a lowess approach. Is meant to be more accurate than "goesup" as it is less prone to stopping to small 'bumps' in the decrease of the statistics.
"goodfit": another criterion seeking a good fit with a minimum number of clusters. This approach does not rely on differences between successive statistics, but on absolute fit. It selects the model with the smallest K so that the overall fit is above a given threshold.
Jombart T, Devillard S and Balloux F (2010) Discriminant analysis of principal components: a new method for the analysis of genetically structured populations. BMC Genetics 11:94. doi:10.1186/1471-2156-11-94