Re: cluster analysis in one-dimensional "circular" space
Since clustering methods begin with pairwise distances among observations, why not measure these distances as minimum arc-lengths along the best-fitting circle (or min chord lengths, or min angular deviations with respect to the centroid, etc)? This is how geographic distances are measured (in 2 dimensions, rather than one) and clustered, and also how distances are measured among observations in Kendall's shape spaces (e.g., Procrustes distances), so there's a well established literature. Rich Strauss At 05:32 PM 4/14/00 +0200, you wrote: >Hi everybody. >I face the problem of clustering one-dimensional data that can range in a >circular way. Does anybody knows the best way to solve this problem with no >aid of an additional variable ? Using a well-suitable trigonometric >transform ? Using an ad-hoc metric ? >Thanks. > >Carl > > > > >=== >This list is open to everyone. Occasionally, less thoughtful >people send inappropriate messages. Please DO NOT COMPLAIN TO >THE POSTMASTER about these messages because the postmaster has no >way of controlling them, and excessive complaints will result in >termination of the list. > >For information about this list, including information about the >problem of inappropriate messages and information about how to >unsubscribe, please see the web page at >http://jse.stat.ncsu.edu/ >=== > Dr Richard E Strauss Biological Sciences Texas Tech University Lubbock TX 79409-3131 Email: [EMAIL PROTECTED] Phone: 806-742-2719 Fax: 806-742-2963 === This list is open to everyone. Occasionally, less thoughtful people send inappropriate messages. Please DO NOT COMPLAIN TO THE POSTMASTER about these messages because the postmaster has no way of controlling them, and excessive complaints will result in termination of the list. For information about this list, including information about the problem of inappropriate messages and information about how to unsubscribe, please see the web page at http://jse.stat.ncsu.edu/ ===
Re: cluster analysis in one-dimensional "circular" space
In article <[EMAIL PROTECTED]>, Donald F. Burrill <[EMAIL PROTECTED]> wrote: >On Fri, 14 Apr 2000, Carl Frelicot wrote: >> I face the problem of clustering one-dimensional data that can range in a >> circular way. Does anybody knows the best way to solve this problem with no >> aid of an additional variable ? Using a well-suitable trigonometric >> transform ? Using an ad-hoc metric ? >> Thanks. >If you mean that data are constrained to lie on a circle of fixed radius, >you could consider substituting the distance of each point from the next >one (in one direction or the other). This would provide global >information (sorry -- pun unintentional) about the existence of >clustering. Plotting this against, say, angular dispacement would give >information about the location(s) of cluster(s). This is a poor procedure, even with a fair amount of clustering. Clustering is a poorly defined concept in the first place. But a linear procedure, with some care not to split the circle in the "middle" of a cluster, should do just about as well. This is not the same as finding a combination of normal or near-normal distributions; a relatively flat stretch with drops at the edges is going to require many of them with a fairly large sample size, although it looks like one cluster. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 === This list is open to everyone. Occasionally, less thoughtful people send inappropriate messages. Please DO NOT COMPLAIN TO THE POSTMASTER about these messages because the postmaster has no way of controlling them, and excessive complaints will result in termination of the list. For information about this list, including information about the problem of inappropriate messages and information about how to unsubscribe, please see the web page at http://jse.stat.ncsu.edu/ ===
Re: cluster analysis in one-dimensional "circular" space
On Fri, 14 Apr 2000, Carl Frelicot wrote: > I face the problem of clustering one-dimensional data that can range in a > circular way. Does anybody knows the best way to solve this problem with no > aid of an additional variable ? Using a well-suitable trigonometric > transform ? Using an ad-hoc metric ? > Thanks. If you mean that data are constrained to lie on a circle of fixed radius, you could consider substituting the distance of each point from the next one (in one direction or the other). This would provide global information (sorry -- pun unintentional) about the existence of clustering. Plotting this against, say, angular dispacement would give information about the location(s) of cluster(s). -- DFB. Donald F. Burrill [EMAIL PROTECTED] 348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED] MSC #29, Plymouth, NH 03264 603-535-2597 184 Nashua Road, Bedford, NH 03110 603-471-7128 === This list is open to everyone. Occasionally, less thoughtful people send inappropriate messages. Please DO NOT COMPLAIN TO THE POSTMASTER about these messages because the postmaster has no way of controlling them, and excessive complaints will result in termination of the list. For information about this list, including information about the problem of inappropriate messages and information about how to unsubscribe, please see the web page at http://jse.stat.ncsu.edu/ ===
Re: cluster analysis in one-dimensional "circular" space
If your data can be "cut" and unrolled at a specific boundry then you can rotate/translate the data away from the boundry. For example if your data crosses the 0 degree boundry but not the -180/+180 boundry then you don't need to do anything, if it crosses the -180/+180 boundry but not the 0 degree boundry then you can translate the data for that cluster/variable with the following: if old >= 0 then new := old - 180 else if old < 0 then new := old + 180. and then translate the results back when you are finished. This allows you to compute the means of the data correctly. You only need to do this for data clusters that cross the 180 degree boundry. If however your data is actually distributed entirely on a circular range, I don't think this technique will work as it will artifically increase the distance between elements that were previously close. -Jason "Carl Frelicot" <[EMAIL PROTECTED]> writes: >I face the problem of clustering one-dimensional data that can range in a >circular way. Does anybody knows the best way to solve this problem with no >aid of an additional variable ? Using a well-suitable trigonometric >transform ? Using an ad-hoc metric ? >Thanks. -- --- J. [EMAIL PROTECTED] http://www.cs.ubc.ca/~harrison Graduate Motto: Free-time with guilt. ftp://ftp.cs.ubc.ca/pub/local/quotes === This list is open to everyone. Occasionally, less thoughtful people send inappropriate messages. Please DO NOT COMPLAIN TO THE POSTMASTER about these messages because the postmaster has no way of controlling them, and excessive complaints will result in termination of the list. For information about this list, including information about the problem of inappropriate messages and information about how to unsubscribe, please see the web page at http://jse.stat.ncsu.edu/ ===
