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    <p>A simple cluster measure:<br> 1) draw "sunburst" rays from each point to its nearest cluster centre,<br> 2) look at the lengths &mdash; distance( point, centre, metric=... ) &mdash; of all the rays. </p> <p>For <code>metric="sqeuclidean"</code> and 1 cluster, the average length-squared is the total variance <code>X.var()</code>; for 2 clusters, it's less ... down to N clusters, lengths all 0. "Percent of variance explained" is 100 % - this average.</p> <p>Code for this, under <a href="https://stackoverflow.com/questions/5529625/is-it-possible-to-specify-your-own-distance-function-using-scikits-learn-k-means">is-it-possible-to-specify-your-own-distance-function-using-scikits-learn-k-means</a>:</p> <pre><code>def distancestocentres( X, centres, metric="euclidean", p=2 ): """ all distances X -&gt; nearest centre, any metric euclidean2 (~ withinss) is more sensitive to outliers, cityblock (manhattan, L1) less sensitive """ D = cdist( X, centres, metric=metric, p=p ) # |X| x |centres| return D.min(axis=1) # all the distances </code></pre> <p>Like any long list of numbers, these distances can be looked at in various ways: np.mean(), np.histogram() ... Plotting, visualization, is not easy.<br> See also <a href="https://stats.stackexchange.com/questions/tagged/clustering">stats.stackexchange.com/questions/tagged/clustering</a>, in particular<br> <a href="https://stats.stackexchange.com/questions/11691/how-to-tell-if-data-is-clustered-enough-for-clustering-algorithms-to-produce-me">How to tell if data is “clustered” enough for clustering algorithms to produce meaningful results?</a></p>
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    1. POCalculating the percentage of variance measure for k-means?
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    1. CO+1 Thank you for your time and explanation! I made an attempt at coding what you explained in your post and added it at the end of my question. Could you please take a look at it when you have some spare time?
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    2. COSure, good enough. The real question is, how does that vary with k for your real data -- numbers please ? If k = say 5 and 6 are close, move on.
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    3. COI am guessing there is something wrong in my function. I have posted the observed values in my question below the function under EDIT 1. The percentages I am getting are exceeding 100% and going to thousands. I guess now I am pretty sure my implementation is wrong.
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