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Multivariate Learning

Figure 12: A two dimensional contour plot of tex2html_wrap_inline1540 with a quadratic local model

All of the examples so far have been on one dimensional data sets, but all of the methods presented so far generalize easily to multivariate inputs and outputs. We can see the fits of two dimensional data with contour plots. a2.mbl is a data file containing 100 data points with two input dimensions and one output dimension. The data was generated with the following equation: tex2html_wrap_inline1542

File -> Open -> a2.mbl
Edit -> Metacode -> Localness   4: Very local
                    Regression  Q: Quadratic
Model -> Graph -> Dimensions  2

The graph is shown in fig. 12. The contours show the approximated function and have the expected shape of smooth peaks mixed between smooth valleys. The data points are also shown. It is no longer possible, however, to evaluate how well the function is approximated visually. The distribution of the data points in input space can be seen, but the height, or output value, of each data point is not represented in the plot.

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