tag:blogger.com,1999:blog-6555947.post8817573263920494125..comments2021-04-01T03:55:55.200-06:00Comments on The Geomblog: Axioms of ClusteringSuresh Venkatasubramanianhttp://www.blogger.com/profile/15898357513326041822noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-6555947.post-21521002104104854082011-07-20T10:57:24.487-06:002011-07-20T10:57:24.487-06:00I'm not an expert here but you may want to con...I'm not an expert here but you may want to consider level set clustering http://bit.ly/oJ8C2x<br />Its satisfying two of the axioms (consistency and richness)..scale would need change of parameters. <br />This is also another simpler algorithm it satisfies the two conditions:<br />http://bit.ly/nPl72WHasannoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-48990845815675518712011-07-19T16:48:37.027-06:002011-07-19T16:48:37.027-06:00In my opinion, there is a simple reason why the ri...In my opinion, there is a simple reason why the richness axiom should be modified. Namely, I see no intuitive reason why <i>both</i> the partition that lumps everything into a single cluster <i>and</i> the partition that puts everything into a singleton cluster of its own should be realized. Both of these are basically "failure modes" where the verdict is that there is no natural clustering. If we simply pick one of these two clusterings to represent our failure mode, and forbid the other one, then the inconsistency among the axioms disappears. Conversely, if you insist on richness as standardly defined, it's not really surprising that if you start with everything in a single cluster and then dilate everything, then there's no principled way to decide when you should shatter into singletonsâ€”and yet the axioms say you must.Timothy Chowhttp://alum.mit.edu/www/tchownoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-66042546131674622342011-07-18T13:09:22.101-06:002011-07-18T13:09:22.101-06:00All three axioms, while they may seem natural at f...All three axioms, while they may seem natural at first, are ultimately questionable.<br /><br />For example, almost any real life clustering problem has an implicit notion of unit distance built into it. <br /><br />Say, if we are tracking human diseases and you have a four point quadrangular configuration a few city blocks apart, this clearly forms a cluster. Now scale up the square so that the corners lie one each in North America, South America, Europe and Africa. Clearly, the new configuration does not form a cluster. Out goes Scale invariance.<br /><br />Richness is perhaps the most unnatural of the axioms. If you are given two points, and yourclustering algorithm is scale and rotation invariant it is not possible to achieve all partitions of the input set. There is nothing wrong with this, yet it violates the richness axiom.Alex Lopez-Ortiznoreply@blogger.com