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The discriminant functions <math>g_1(x),\ldots, g_K(x)</math> such that <math>g_i(x)</math> n-dim ''S'' space | The discriminant functions <math>g_1(x),\ldots, g_K(x)</math> such that <math>g_i(x)</math> n-dim ''S'' space | ||
<math> \rightarrow \Re</math> | <math> \rightarrow \Re</math> | ||
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| + | which are used to make decisions as follows: | ||
| + | |||
| + | decide <math>\omega_i</math> if <math>g_i(x) \ge g_j(x), \forall j</math> | ||
| + | |||
| + | 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. | ||
Revision as of 15:26, 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.
