Sep
29
Cluster Analysis by B. Everitt et al, from Victor Niederhoffer
September 29, 2010 |
One of the most useful things that humans can do when making decisions about life or market is to form objects into groups. The caveman must have had to decide which animals were dangerous and which foods were edible, and the investor must decide between value stocks and fundamental socks, or between utilities and industrials, the canals versus the railroads, the nifty fifty versus the old favorites, the stocks that old man sage buys versus the ones that the Druck likes to buy after hearing a technology conference, the stocks touted by the wildman, or those in group 1 in value 1 etc., the stocks when bonds are up et al.
Methods for grouping data are given in the Excellent book Cluster Analysis by Brian Everitt, et al of which I have the fourth edition from 2000. It's the very model of a modern book with a list of software to do all the things for free and price enhanced graphs showing all the things that the programs do, and examples from all fields ranging from biology, genetics, pol science, taxonomy, astronomy, psychology, et al.
It's a lot easier to visualize a cluster then to find one. The basic idea is to find objects that are pretty homogeneous within themselves but disparate among the others. That's a lot easier said then done.
First you have to measure the distance between the objects. The usual measures are squared distance, city block distance, generalized Minkowski distance which is the same as the usual geometric distance but scaled to the third or fourth power instead of the second, or Pearson correlations themselves between the values of the variables for just two objects.
Then you have to form the groups. The usual method is to start with the nearest two, then to build up from there. That's called an agglomeration method. Compare this to the divisive methods which starts with the largest group, and then successively removes the ones that are furthest away. One of the thorniest problems is how to handle more than one variable. Methods based on scaling from the extremes then the standardized values are recommended.
A section that shows how to fit the data based on kernel estimates using kernel function for each pair of observations based on a rectangular, triangular or gaussian distribution is particularly helpful. Also interesting is the preliminary methods for discovering groups using one dimensional and two dimensional histograms. A nice section using factor analysis and principal components analysis, and a related method I've never come across in all my years of reading statistics books called projection pursuit is recommended as a way to reduce the number of variables to a manageable and non-correlated set is also given.
Indeed the book is filled with everything you could ever want to know about grouping data, including multidimensional scaling, similarity measures, weighting techniques, standardization procedures, missing value treatments, mixture models.
Everything is there in a fairly accessible form except how all these methods relate to the current worthless non-predictive fad of artificial intelligence relating to neural networks and its extension. Doubtless the current work in the field has shown how these methods converge to the usual clustering methods based on such things as clustering with constraints, or fuzzy clustering.
Much of the work in clustering comes from such institutes as the Rotterdam Institute of Agriculture and the institute of psychiatry at Kings College in London so it's not surprising that no examples are given from our own field, where grouping is so helpful and necessary. How often do we look at a scatter diagram of two variables, and note that there are two modes in the data, or that two regression lines would fit the data much better than one. If only we knew which of the two groups that the various observations belonged to. And if we only knew how to scale such things as currencies and gold to each other in considering the similarities.
Let's take our own humble attempts to group clusters where we put the four comoves and counter moves of bonds and stocks into four colors yellow for stocks up bonds down, blue for stocks down and bonds up, and green for both up, and red for both down. Haven't seen any reds recently until today. And the colors themselves are just one of the many ways of handling binary splits.
Here are some data to practice clustering on from the real world.
date stocks bonds
Sep 28 4.0 0.28
Sep 27 -5.5 1.2
Sep 24 22.8 -1.0
Sep 23 -9.4 0.01
Sep 22 -4.9 0.2
Sep 21 -1.9 1.1
Sep 20 16.0 0.17
The rest of data for the last 9 months is on our site. It's a good exercise to form groups from such data and maybe even to come up with something useful from it.
Comments
WordPress database error: [Table './dailyspeculations_com_@002d_dailywordpress/wp_comments' is marked as crashed and last (automatic?) repair failed]
SELECT * FROM wp_comments WHERE comment_post_ID = '5323' AND comment_approved = '1' ORDER BY comment_date
Archives
- January 2021
- December 2020
- November 2020
- October 2020
- September 2020
- August 2020
- July 2020
- June 2020
- May 2020
- April 2020
- March 2020
- February 2020
- January 2020
- December 2019
- November 2019
- October 2019
- September 2019
- August 2019
- July 2019
- June 2019
- May 2019
- April 2019
- March 2019
- February 2019
- January 2019
- December 2018
- November 2018
- October 2018
- September 2018
- August 2018
- July 2018
- June 2018
- May 2018
- April 2018
- March 2018
- February 2018
- January 2018
- December 2017
- November 2017
- October 2017
- September 2017
- August 2017
- July 2017
- June 2017
- May 2017
- April 2017
- March 2017
- February 2017
- January 2017
- December 2016
- November 2016
- October 2016
- September 2016
- August 2016
- July 2016
- June 2016
- May 2016
- April 2016
- March 2016
- February 2016
- January 2016
- December 2015
- November 2015
- October 2015
- September 2015
- August 2015
- July 2015
- June 2015
- May 2015
- April 2015
- March 2015
- February 2015
- January 2015
- December 2014
- November 2014
- October 2014
- September 2014
- August 2014
- July 2014
- June 2014
- May 2014
- April 2014
- March 2014
- February 2014
- January 2014
- December 2013
- November 2013
- October 2013
- September 2013
- August 2013
- July 2013
- June 2013
- May 2013
- April 2013
- March 2013
- February 2013
- January 2013
- December 2012
- November 2012
- October 2012
- September 2012
- August 2012
- July 2012
- June 2012
- May 2012
- April 2012
- March 2012
- February 2012
- January 2012
- December 2011
- November 2011
- October 2011
- September 2011
- August 2011
- July 2011
- June 2011
- May 2011
- April 2011
- March 2011
- February 2011
- January 2011
- December 2010
- November 2010
- October 2010
- September 2010
- August 2010
- July 2010
- June 2010
- May 2010
- April 2010
- March 2010
- February 2010
- January 2010
- December 2009
- November 2009
- October 2009
- September 2009
- August 2009
- July 2009
- June 2009
- May 2009
- April 2009
- March 2009
- February 2009
- January 2009
- December 2008
- November 2008
- October 2008
- September 2008
- August 2008
- July 2008
- June 2008
- May 2008
- April 2008
- March 2008
- February 2008
- January 2008
- December 2007
- November 2007
- October 2007
- September 2007
- August 2007
- July 2007
- June 2007
- May 2007
- April 2007
- March 2007
- February 2007
- January 2007
- December 2006
- November 2006
- October 2006
- September 2006
- August 2006
- Older Archives
Resources & Links
- The Letters Prize
- Pre-2007 Victor Niederhoffer Posts
- Vic’s NYC Junto
- Reading List
- Programming in 60 Seconds
- The Objectivist Center
- Foundation for Economic Education
- Tigerchess
- Dick Sears' G.T. Index
- Pre-2007 Daily Speculations
- Laurel & Vics' Worldly Investor Articles