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Note that many different choices of <math>g_i(x)</math> will yield the same decision rule, because we are interested in the order of values of <math>g_i(x)</math> for each x, and not their exact values. | Note that many different choices of <math>g_i(x)</math> will yield the same decision rule, because we are interested in the order of values of <math>g_i(x)</math> for each x, and not their exact values. | ||
| + | |||
| + | For example: | ||
| + | <math>g_i(x)</math> -> 2(<math>g_i(x)</math>) or <math>g_i(x)</math> -> ln(<math>g_i(x)</math>) | ||
Revision as of 14:30, 10 March 2008
LECTURE THEME : - Discriminant Functions
Discriminant Functions: one way of representing classifiers
Given the classes $ \omega_1, \cdots, \omega_k $
The discriminant functions $ g_1(x),\ldots, g_K(x) $ such that $ g_i(x) $ n-dim S space $ \rightarrow \Re $
which are used to make decisions as follows:
decide $ \omega_i $ if $ g_i(x) \ge g_j(x), \forall j $
Note that many different choices of $ g_i(x) $ will yield the same decision rule, because we are interested in the order of values of $ g_i(x) $ for each x, and not their exact values.
For example: $ g_i(x) $ -> 2($ g_i(x) $) or $ g_i(x) $ -> ln($ g_i(x) $)
