History

Pythias Consulting, LLC, is a small software and consulting company owned and run by Mark H. Moulton, Ph.D., with his wife, Christine, in Sunnyvale, California.  Currently, it owns the Damon copyrights.  These will be transitioned to a nonprofit organization if a community develops.

Pythias was founded in 2008 to fill a gap opened up when a previous venture, The Andrea O'Brennan Foundation (AOB), closed.  AOB partners included Roger Deming, a bay area hacker, and Howard Silsdorf, an aerospace engineer.  It was Howard who, in collaboration with Moulton from 1999 - 2003, worked out the core Damon algorithm, privately dubbed the "Silsdorf decomposition".  It was later realized that the Silsdorf decomposition is in fact a rediscovery of what has been known since at least the 1990's as the "alternating least squares" algorithm.  (Rediscovering the wheel is endemic in data analysis, but no less valuable for all that.)  The decomposition algorithm behind Damon is distinguished from other alternating least squares algorithms by how it assesses dimensionality and avoids degenerate solutions, by its generality, and by its insistence on the objectivity criterion.

The Silsdorf decomposition was not the first matrix analysis algorithm to come out of this work.  It arose as a response to an earlier algorithm worked out and published as Moulton's doctoral dissertation in 1996 called the "n-Dimensional Replacement Model" and later dubbed NOUS when Roger Deming and Mark Moulton began programming it.  Here is how it was described by Ben Wright, Moulton's dissertation advisor at the University of Chicago and founding father of the Rasch Model in the United States:

As his work took shape, Mark concentrated on the problem of analyzing data sets of ambiguous or indeterminate dimensionality. As the Rasch Model restricts itself to predominantly unidimensional data, I was concerned he might lose himself in an intellectual cul-de-sac. Nonetheless, within two years he had succeeded using an innovative and startling combination of geometry and basic statistics, derived in his dissertation. By viewing each person as a point in n-dimensional space, each item as a line drawn through that space, and each rating as a projection of a point onto a line, he was able to extend the basic form of the Rasch Model (G[ni] = b[n] - d[i] — a person’s performance G[ni] specified as his ability b[n] minus the difficulty of the item d[i]) into a non-unidimensional space, i.e., a space in which the items are not constrained to a single dimension. His model, called the n-Dimensional Replacement Model because it replaces each rating with an estimate culled from the remainder of an n-dimensional data matrix, follows the Rasch Model in its insistence on reproducibility as a condition of fit. With it, he was able successfully to predict, among other things, responses of educational leaders to policy questions in his work with the Chicago school system, a data set that proved too thorny for other methodologies to cope with.

The Deming-Moulton algorithm was (and is) quite interesting and had many data-mining and psychometric applications.  Of particular note, it completely avoided the problem of determining dimensionality and used no linear algebra.  However, it was unduly complex and computationally expensive.  After studying it, Howard Silsdorf felt sure that he could reproduce it using simpler methods derived only from linear algebra.  After three years of hard work, he succeeded.  Moulton felt that the new Silsdorf decomposition was superior to his own algorithm and made it the focus of his work.  He kept the name NOUS to describe the underlying mathematical paradigm -- objects as points floating in space -- which is behind both the original n-Dimensional Replacement Model and the Silsdorf decomposition.  In 2008, Moulton taught himself Python and re-programmed the Silsdorf decomposition from scratch, adding many new mathematical features along the way.  This software is called Damon.

A history of Damon is not complete without mentioning the company that made it possible -- Educational Data Systems (EDS), located in Morgan Hill, California, where Moulton has worked as lead psychometrician since 2003 (www.eddata.com).  In addition to his regular duties, EDS CEO Caroline Fahmy encouraged Moulton to apply NOUS to psychometric problems in the field of educational measurement.  By 2006, Moulton had created an algorithm for EDS called EdScale which makes it possible for school districts to report scale scores in the metric of the state-wide California Standards Test (CST) using only locally developed and administered benchmark tests.  In other words, EdScale gets students onto the common scale score metric used throughout the state of California even though the tests used to generate those scores have no items in common with the CST's, or with any other test.  This product serves a huge need which has only begun to be realized.  

The psychometric engine under the hood of EdScale is Damon.  As a public service, EDS has kindly allowed Moulton to develop and release Damon independently of EDS as an all-purpose open-source project under Pythias.  Meanwhile, it retains ownership of the EdScale product built on top of Damon.  This business model has been pursued successfully with other Pythias clients.

Whether Damon will be adopted in any significant way in the fields of psychometrics and data mining remains to be seen.  In data mining, especially, the past two decades have seen the development of stunningly powerful algorithms used in brilliant ways, as evidenced by the amazing Netflix Prize competition (www.netflixprize.com) and other competitions such as those sponsored by the Knowledge Discovery and Data Mining special interest group -- ACM SIGKDD.  Damon exists as a free, light-weight, practical alternative for individuals and entrepreneurs who need access to this kind of technology without becoming expert coders and statisticians themselves.