K-means Clustering 86 Single Malt Scotch Whiskies
blog.revolutionanalytics.com
blog.revolutionanalytics.com
-High dimensional dataset, probably some redundant dimension are being "counting twice". Solution PCA your data first.
-sampling artefacts. Run the k-nearest algorithm lots of times and average
If the data points were lower dimension, the clusters would be able to cover the space better. Bowmore is a smoky whisky (score 3), but it has enough interesting other characteristics that means it does not align with the obvious "Islay" cluster (smoky centre of 2.8). I think it's in the wrong cluster, due to redundant fields having too much power.
On your point, turns out PCA alone doesn't tend to help with Bowmore (or the similar Highland Park). The first component you get is basically medicinal-and-smoky, and these two only score 1 for medicinal. They're also probably a bit too honeyed or floral for cluster 4. But clustering on the components and tweaking the starting values can draw Isle of Jura, Oban, Old Pulteney and occasionally Glen Garioch into the smoky cluster. On the other hand, looking at a biplot of the first two components your could argue for two clusters - the six in OP's original cluster 4 vs. the rest.
The most important thing is that this work led OP to Talisker - result. But I suspect a definitive clustering will require more features - so, sadly, someone needs to taste them all again...
Anyway a few "next thing to try" suggestions from a machine learning perspective:
The model selection process used here is by its own admission quite ad-hoc, based on a gut feel about diminishing returns. There are various more principled methods you can use to find the sweet spot between over- and under-fitting with these kind of models, a lot of them based on held-out validation data.
One way to do this would be leave-one-out cross validation (LOO-CV): hold out one whisky, fit the model, and see how 'surprised' the model is by the held-out whisky, repeat for the next whisky and average over all the folds. Because the dataset is tiny this should be quite feasible.
To measure 'surprisal' you could e.g. look at the distance from the held-out data point to the nearest cluster, although something better motivated would be if you switched to a probabilistic model and used likelihood of the held-out data. Probably the simplest next thing you could try in that direction would be a Gaussian mixture model (GMM) trained using EM. K-means is actually a degenerate limiting case of this.
A probabilistic model would also allow you to use Bayesian model selection criteria, which can get quite interesting (and might lead you eventually to things like Dirichlet process mixture models).
It would make it easier to compare the model's explanatory power with other unsupervised probabilistic models. For example some kind of latent factor model like Factor analysis or pPCA would be quite interesting to investigate too, whether taken alone or in combination with clustering as a dimensionality reduction step as tlarkworthy is suggesting.
Also concur that doing multiple runs with different randomised initialization is generally a good idea for k-means or EM, since they can get stuck in poor local minima. Perhaps more common practise to pick the best of multiple runs than to average them though.
A Classification of Pure Malt Scotch Whiskies
Lapointe and Legendre
Appl. Statist. (1994) 43, No. 1, pp. 237-257
http://www.albany.edu/psychology/bcd/share/scotch_classifica...
It would be interesting to compare their results with the OP.
http://kilchomandistillery.com/
... also the bewildering array sold by the others, particularly Bruichladdich, and the ridiculously expensive remaining stock of the defunct Port Ellen:
http://www.theguardian.com/lifeandstyle/2013/oct/26/scotch-w...
edit: on the post. Very curious to see your thoughts on Talisker and whether it fits the profile the results gave it.
I study food, fragrance, software and other types of product preferences. In the studies I've done, often people's very subjective preferences (or so we assume) turn out to be highly clustered into just one or two clusters of highly similarly-preferenced people. Sometimes when you'd assume there would be total disagreement, there's actually total preference agreement.
Ardbeg: 55ppm (this has changed over time)
Lagavulin: 40-45ppm
Laphroaig: 40ppm
however, it's important to distinguish between standard levels and novelty bottlings. the Ardbeg Supernova is peated to over 100ppm, twice the usual level. Bruichladdich, which is a relatively lightly-peated malt, produces the highly-peated Port Charlotte line, as well as the Octomore, peated to about 170ppm.
so, unless you're talking about the standard line, you can't simply talk about the peating level of Ardbeg.
finally, since all single malts are aged in a charred oak cask which acts as a filter over time, in general, the older the malt, the less smoky it will taste. compare a Laphroaig 10yo cask strength to a Laphroaig 18yo, and/or 25yo, if you're ever lucky enough to do so.