General Logic Diagrams

General Logic Diagrams (GLDs) are graphical projections of multi-dimensional discrete spaces onto two dimensions. They are similar to Karnaugh maps, but are generalized to non Boolean inputs and outputs. A GLD provides a way of displaying up to about ten dimensions in a graphical representation that can be understood by humans. GLDs were described in gld-michalski and later used in org-monk-diagrammatic. They were used in monks-problems-short and in wnek-michalski-aq17 to compare algorithms. GLDs have a long history and have been rediscovered many times. They are sometimes called Dimensional Stacking [].

Each possible instance in the space defines exactly one box in the GLD. The GLD utility has the following display options (GLD_SET):

Test

Show the test set instances with their classes.

Overlay

Show the test set instances. The display shows correct or incorrect prediction by the categorizer.

Predicted Train

Show the full predicted space and overlay the training set classes. You must have a color/grey-scale display.

Predicted Test

Show the full predicted space and overlay the test set instances, showing the mistakes as X's. You must have a color/grey-scale display.

The output of the GLD utility can either be an X window popup or a file that can be read using Xfig. The main advantage of the Xfig output is that the attribute names and other comments may be added and then inserted into a document. There are currently only eight colors and they begin to cycle if there are more classes.

[General Logic Diagrams]

We now show the four different sets displayable in the GLD. The four GLDs are shown in Figures 6 and 7.

   setenv INDUCER ID3
   setenv DATAFILE monk1
   setenv GLD_MANAGER xfig
   setenv GLD_OUTFILE monk1-GLD-test.fig
   setenv GLD_SET test
   GLD
   setenv GLD_OUTFILE monk1-GLD-overlay.fig
   setenv GLD_SET overlay
   GLD
   setenv GLD_OUTFILE monk1-GLD-predTrain.fig
   setenv GLD_SET predictedTrain
   GLD
   setenv GLD_OUTFILE monk1-GLD-predTest.fig
   setenv GLD_SET predictedTest
   GLD

   Generating GLD for monk1.data
   Classifying (% done): 10%  20%  30%  40%  50%  60%  70%  80%  90%  100%  done.
   Generating GLD for monk1.data
   Classifying (% done): 10%  20%  30%  40%  50%  60%  70%  80%  90%  100%  done.
   Generating GLD for monk1.data
   Classifying (% done): 10%  20%  30%  40%  50%  60%  70%  80%  90%  100%  done.
   Generating GLD for monk1.data
   Classifying (% done): 10%  20%  30%  40%  50%  60%  70%  80%  90%  100%  done.

  
Figure 6: GLD for ID3/monk1. Set=test on the top and Set=overlay on the bottom.

  
Figure 7: GLD for ID3/monk1. Set=predictedTrain on the top and Set=predictedTest on the bottom.