I am going to try out a tentative clustering of some feature vectors. The range of values spanned by the three items making up the features vector is quite different: Item-1 goes roughly from 70 to 525 (integer numbers only) Item-2 is in-between 0 and 1 (all real numbers between 0 and 1) Item-3 goes from 1 to 10 (integer numbers only) In order to spread out Item-2 even further I might try to replace Item-2 with Log10(Item-2). My concern is that, regardless the distance measure used, the item whose order of magnitude is the highest may carry the highest weight in the process of calculating the similarity matrix therefore fading out the influence of the items with smaller variation in the resulting clusters. Should I normalize all feature vector elements to 1 in advance of generating the similarity matrix ? Thank you so much. Maura tutti i telefonini TIM! [[alternative HTML version deleted]]
Generally, how to scale different variables when aggregating them in a dissimilarity measure is strongly dependent on the subject matter, what the aim of clustering and your "cluster comncept" is. This cannot be answered properly on such a mailing list. A standard transformation before computing dissimilarities would be to scale all variables to variance 1 by dividing by their standard deviations. This gives in some well defined sense all variables the same weight (which may be somewhat affected by outliers, heavy tails, skewness; note, however, that normalising to the same range shares the same problems more severly). Regards, Christian On Mon, 26 Jan 2009, mauede at alice.it wrote:> I am going to try out a tentative clustering of some feature vectors. > The range of values spanned by the three items making up the features vector is quite different: > > Item-1 goes roughly from 70 to 525 (integer numbers only) > Item-2 is in-between 0 and 1 (all real numbers between 0 and 1) > Item-3 goes from 1 to 10 (integer numbers only) > > In order to spread out Item-2 even further I might try to replace Item-2 with Log10(Item-2). > > My concern is that, regardless the distance measure used, the item whose order of magnitude is the highest may carry the highest weight in the process of calculating the similarity matrix therefore fading out the influence of the items with smaller variation in the resulting clusters. > Should I normalize all feature vector elements to 1 in advance of generating the similarity matrix ? > > Thank you so much. > Maura > > > > > > > > tutti i telefonini TIM! > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. >*** --- *** Christian Hennig University College London, Department of Statistical Science Gower St., London WC1E 6BT, phone +44 207 679 1698 chrish at stats.ucl.ac.uk, www.homepages.ucl.ac.uk/~ucakche
Have you tried using the cosine of the angle between two observations as the similarity measure? If you want to account for magnitudes, there is something called the jaccard coefficient (if I remember correctly) that can be used. Darin On Mon, Jan 26, 2009 at 10:41:40AM +0100, mauede at alice.it wrote:> I am going to try out a tentative clustering of some feature vectors. > The range of values spanned by the three items making up the features vector is quite different: > > Item-1 goes roughly from 70 to 525 (integer numbers only) > Item-2 is in-between 0 and 1 (all real numbers between 0 and 1) > Item-3 goes from 1 to 10 (integer numbers only) > > In order to spread out Item-2 even further I might try to replace Item-2 with Log10(Item-2). > > My concern is that, regardless the distance measure used, the item whose order of magnitude is the highest may carry the highest weight in the process of calculating the similarity matrix therefore fading out the influence of the items with smaller variation in the resulting clusters. > Should I normalize all feature vector elements to 1 in advance of generating the similarity matrix ? > > Thank you so much. > Maura > > > > > > > > tutti i telefonini TIM! > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code.