DCA

[James Lyons-Weiler]

On Tue, 20 Aug 1996, Richard Jensen wrote:

> Regarding the effect of input order on the results of various analyses:
>
> I don't see how the order would have any effect on an eigenanalysis of a
> covariance or correlation matrix, as typically used for PCA, or on
> eigenanalysis of a dissimilarity matrix as typically used for PCOR.  And,
> unless there are programming errors, order of input will have no effect
> on the calculation of pairwise similarities or distances.

Entry order will have no influence on simple units solved with
deterministic algorithms (e.g., pairwise distances).  If, however,
approximation alogorithms are employed, entry order can easily influence
the "optimal" solution found by that non-deterministic algorithm.  The
severity of the problem will vary from data set to data set.
>
> Order can have an effect on the results of cluster analysis of a
> similarity or dissimilarity matrix.  The effect will be a function of how
> ties are resolved.  One way around this is to use a program, such as
> NTSYS-pc, that will allow the user to find all ties and all solutions -
> this can result in many different phenograms for the same data set, just
> as there may be many alternative equally parsimonious trees for a data set.

People seeking the influence of entry order on finding the mpt quite often
search for multiple islands of shortest tree, as prescribed by Maddison in
1991? (reference not to hand). Showing that there may be multiple classes
of equally parsimonious trees (note the difference between finding > 1 mpt
and islands of mpts) tells the researcher that entry order sensitivity is
problem for their data.  Solutions to this type of problem can only be
found if more time is put into developing deterministic, polynomial-time
solutions, which for some problems are thought (perhaps erroneously) to be
impossible.  The fact that eigenvalues are approximated causes entry order
problems in ordination methods as well.

James


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