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Input attribute weightings

When the number of input dimensions is greater than one, a new issue arises. It is possible that each input should be treated differently when modeling the data. Some of them may be totally irrelevant while others can be treated more globally than others.

   figure315
Figure 13: A two dimensional contour plot of tex2html_wrap_inline1546 with an averaging local model

In the last example, the two input attributes were equally important to the output (in fact, their effect was identical). Next, we'll look at b2.mbl, which has two input attributes but the second one is completely irrelevant. This file was generated from the following equation: tex2html_wrap_inline1548

File -> Open -> b2.mbl
Edit -> Metacode -> Regression  A: Average
                    Localness   1: Super ultra local
                    Input Weights -> ``x2''  -: Ignore completely
Model -> Graph -> Dimensions  2
                  x attribute -> ``x1''
                  y attribute -> ``x2''
                  Graph

The contour plot (shown in fig. 13) shows how the second input attribute is ignored (as we requested by editing the Metacode appropriately). Even though we know the second input attribute wasn't used to generate the data, we can verify its irrelevance visually by looking at the 1-d plots against each input as done in the last subsection on graphing. In this case, the 1-d curve does fit the data when graphed along the first input while leaving the second fixed. When doing the opposite, however, the curve is a flat line and the data appears scattered randomly everywhere. As before, we could change the place the flat line appears by adjusting the query point.

Model -> Graph -> Dimensions  1
                  x attribute -> ``[All inputs]''
                  Graph

   figure323
Figure 14: A two dimensional contour plot of tex2html_wrap_inline1550 with a linear local model

Another common situation is that a certain input variable has a global effect on the output, rather than a complicated non-linear effect that must be modeled locally. This is the case with c2.mbl, which was generated by the following equation: tex2html_wrap_inline1552

File -> Open -> c2.mbl
Edit -> Metacode -> Regression  L: Linear
                    Localness   2: Ultra local
                    Input Weights -> ``x2''  0: Ignore in metric
Model -> Graph -> Dimensions  2
                  x attribute -> ``x1''
                  y attribute -> ``x2''
                  Graph

Using the label ``Ignore in metric'' means that input attribute will not be used when computing the distances between points (the same as saying the effect from that attribute is global), but it will be included in the regression equation. The contour plot (shown in fig. 14) shows how the fitted function varies non-linearly along the first attribute, but globally linearly along the second.



next up previous contents
Next: Classification Up: Multivariate Learning Previous: A note on graphing



Jeff Schneider
Fri Feb 7 18:00:08 EST 1997