Re: VMs: Overfitting the Data

[Koontz John E <John.Koontz@xxxxxxxxxxxx>]

On Mon, 31 Jan 2005, Dennis wrote:
> 	But this leaves out the constraint imposed by the grill
> overlays.  These block out some potential pairs; thus the
> output of a Rugg grill is a subset of the prefix-root-suffix
> paradigm.

Agreed about the subsetting.  But think about it.  For simplicity consider
a matrix with one set of three adjacent columns (prefix, midfix, suffix).
Now consider one grill.  Its windows constrain which fix triplets you can
extract from the matrix - the subsetting you refer to.  Say your grill has
windows at prefix row 4, midfix row 2, and suffix row 3.  Again, for
simplicity let's assume all windows have to read within the matrix.  This
means you can select combinations P3-M1-S2, P4-M2-S3, P5-M3-S4, etc.,
until you run into the end of the matrix.  This is the same as sliding the
midfix column down 2 rows, and the suffix column down 1 row and reading
across complete rows.  If your columns are transformed into rings the main
difference is that you get a few extra rows at the overlap, e.g.,
P1-M(n-1)-S(n).

So, modulo small edge effects, sliding the fix columns up and down and
requiring readouts to be across columns on the same row is the same as
using a grill, and, again modulo small edge effects, using sliding columns
is the same as using sliding rings in a wheel.  Presumably matrices are
large relative to the difference in the row indices imposed by grills, so
edge effects are small.  You can eliminate the edge effects in various
ways, anyway.

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