<div dir="ltr">Fine, thanks. <br>So, then, the interpretation of mutli-class confusion can be misleading. <br>I have one more related question:<br>Does it make sense to interpret the confusion matrix off-diagonal values as a tuning? For example, if my three classes are the circles of three different size. For the row of the large circle I get 0.6 classified as large (the correct one), 0.3 as a medium and 0.1 as a small. Can I say that I get sort of tuning to circle size?<br>
<br>Thanks again.<br><br><div style="visibility: hidden; display: inline;" id="avg_ls_inline_popup"></div><style type="text/css">#avg_ls_inline_popup { position:absolute; z-index:9999; padding: 0px 0px; margin-left: 0px; margin-top: 0px; width: 240px; overflow: hidden; word-wrap: break-word; color: black; font-size: 10px; text-align: left; line-height: 13px;}</style><br>
<div class="gmail_quote">On Fri, May 14, 2010 at 4:29 PM, <span dir="ltr"><<a href="mailto:josef.pktd@gmail.com">josef.pktd@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
<div><div></div><div class="h5">On Fri, May 14, 2010 at 9:20 AM, Vadim Axel <<a href="mailto:axel.vadim@gmail.com">axel.vadim@gmail.com</a>> wrote:<br>
> Hi guys,<br>
><br>
> I apply multi-class major voting scheme for three classes (all pairs<br>
> classification). I try to understand how the confusion matrix should look<br>
> like when two classes in a pair classification are not discriminated (chance<br>
> level). Consider pathological case where classes 1,2 and 2,3 are classified<br>
> with 100% and 1,3 are at chance level (50%). The confusion matrix I which<br>
> 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<br>
> paradoxical?<br>
><br>
> When I checked out how I get this result, I have found that it indeed makes<br>
> sense. Consider class 1 as a correct label:<br>
> pair 1: the classification of classes 1,2 always results in '1' (we are at<br>
> 100%, by definition)<br>
> pair 2: the classification of classes 1,3 results in half trials in '1' and<br>
> 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<br>
> other in '3' (in case that classes are unrelated, the classifier should be<br>
> at chance here).<br>
><br>
> The bottom line: since all (1) pairs and half (2) pairs results in '1', I am<br>
> 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>
</div></div>looks right to me if the tie-breaker is unbiased<br>
<br>
Probs if 1 is tru:<br>
<br>
>>> 0.5*0.5 + 0.5*0.5/3. # 3 wins, by majority and tie-breaker<br>
0.33333333333333331<br>
>>> 0.5*0.5/3. # 2 wins, by tie-breaker<br>
0.083333333333333329<br>
>>> 1-(0.5*0.5 + 0.5*0.5/3. + 0.5*0.5/3.) # 1 wins<br>
0.58333333333333337<br>
<br>
Josef<br>
<br>
><br>
> Thanks for help,<br>
> Vadim<br>
><br>
><br>
><br>
><br>
><br>
><br>
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</blockquote></div><br></div>