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I apply multi-class major voting scheme for three classes (all pairs classification). I try to understand how the confusion matrix should look like when two classes in a pair classification are not discriminated (chance level). Consider pathological case where classes 1,2 and 2,3 are classified with 100% and 1,3 are at chance level (50%). The confusion matrix I which get looks like: <br>
0.584 0.083 0.333<br>0 1 0<br>0.327 0.071 0.602<br><br>So, all of sudden it seems that classes 1 and 3 are discriminated. Isn't it paradoxical? <br><br>When I checked out how I get this result, I have found that it indeed makes sense. Consider class 1 as a correct label: <br>
pair 1: the classification of classes 1,2 always results in '1' (we are at 100%, by definition)<br>pair 2: the classification of classes 1,3 results in half trials in '1' and
other half in '3' (we are at chance by definition).<br>pair 3: the classification of classes 2,3 results in half trials in '2' and
other in '3' (in case that classes are unrelated, the classifier should
be at chance here).<br><br>The bottom line: since all (1) pairs and half (2) pairs results in '1', I am already at 50% hit rate for correct class. <br><br>What do you think about all this? Is there any flaw in my logic?<br>
If someone is interested, I can send my matlab simulation.<br>
<br>Thanks for help,<br>Vadim<br><br>
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