INTERPRETINGAND EVALUATING TASK-BASED MLP MODELS in .NET

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INTERPRETINGAND EVALUATING TASK-BASED MLP MODELS
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The hierarchy of reduced models starting from mlp.6.15.6
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THE TASK-BASED MLP
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Table 6.9
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hidden-layer unit class
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109 120 0 0 0 121 120
121 121 5 0
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Table 6.10
The T matrix for model mlp.6.5.6.114
class
121 0
hiddei - laye 2 3 -0
121 121
Table 6.11
The T matrix for model mlp.6.6.6.n2
hidden-I;
UI - - __
6 121
106 0 120 6 114
Table 6.12
matrix for model mlp.6.5.6.n3
hidden-layer unit class
0 112 0 0
4 121 0 1 2
121 0 1
0 120
0 121 1 116
121 0 0 1 0
0 120
INTERPRETING N D EVALUATING TASK-BASED M L P MODELS A
unit number hidden unit 1 hidden unit 2 hidden unit 3 hidden unit 4 hidden unit 5 gives a
+ value for classes
pasture, salt bush and salt damage lupins and some wheat pasture lupins and salt damage pasture, salt bush and remnant vegetation n3 respectively and further training was conducted
and on these models.
Analysis of the
matrices
we consider the two pruned models, and to see if any further pruning or simplification is possible. The outputs of the hidden-layer units may be analyzed via one of two means. For the training data, we can take the raw outputs or the matrix simplification. Also, for the whole image, the hidden-layer outputs can themselves be interpreted as [0,1] greyscale images. Using the matrix as a guide, we can determine what the hidden-layer units are doing in terms of class separations. For two of the models and Tables 6.13 and 6.14 interpret the matrices (given, respectively, in Tables 6.15 and 6.16) to show which classes are on the side of the separating hyperplane.
After training,
Table
which classes are on the
f The action of the hidden units of the mlp.6.4.6.n3model in terms o + side of the separating hyperplanes.
As the next stage in the MLP model, the rows of the matrix indicate the linear combinations of the hidden-layer outputs (and thus of the columns of the matrices) that are important in determining the various class labels. However, an inspection of the matrix, for either model, indicates a complex pattern involving all of the hidden-layer units.
Weight simplification
I n order to improve the interpretability of the matrix, we have employed a weight elimination penalty term (see note 6, p. 64). This implementation, unlike the
THE TASK-BASED
Table
matrix for model mlp.6.4.6.n3
0 0 0 0
Table
The T matrix for model mlp.6.5.6.nl hidden-layer unit class 1 1 0 1 120 2
3 4 5 6 2 1 0 3 4 5 0 120 8 0 0 121 115 0
0 3 4 120 0 0 0 5 114 . 1
0 0 0
0 0 120 121 1 2 1 12 0
standard one, is only applied to the matrix, not to both matrices. Ideally, X should be chosen by cross-validation; however, we have simply set it to 0.01 on investigates this question and the basis of previous experience. Ripley (1996, suggests choosing X in the range 0.001 - 0.1 and comments that the value for X is not critical within a factor of 5. After weight elimination was carried out on the rnlp . 6 . 4 . 6 . model, the weights were simplified so that weights of magnitude less than 0.5 were fixed at 0, weights greater than 3 were set to and weights less than -3 were set to -4. This had no effect on the accuracy of the fit to the training data (see the classification matrix in Table 6.17) and gave the following R matrix:
-2.23 -4 --2.33 0 0 -1.78 4 -1.45 1.56 -4 1-1.72 0
0 4 0 -4 0 0
4 0 -4 -4 0 4
-4 -4
We selected two output units for analysis7. Output unit 5 (which detects remnant vegetation) is using minus the sum of hidden-layer units 1 and 4. An inspection of Table 6.14 reveals that these two units between them have all the classes except remnant vegetation on the "+" side of their hyperplanes. Hence remnant vegetation is the only class left on the "-" side; minus the sum of hidden units 1 and 5 thus isolates remnant vegetation on the side of output unit 5 .