Convert Binary to Multi class, Winner takes all

I am using a Binary classification ,I have K classifiers and K classes using one-versus-all method ,looking for winner takes all algorithm or code or reference paper to get a multi-class recognition rate. Any hints will be appreciated. Thanks in advance , Elahe

P.S: this method has been used in Binary SVM

Answer 1

[Walter Roberson]

This problem can be also looked at as a question about finding the ultimate winner of a multi-candidate election by holding pair-wise votes on the candidates. Game Theory applied to voting has, however, proven that whenever there are 3 or more candidates, that there is no pairwise voting strategy that produces fair outcomes, and that instead the result depends upon the order of the votes.

Consider, for example, the old game of "Scissors, Paper, Rock", and suppose you have three classes, one of which classifies as "scissors", one as "paper", and one as "rock". Compare any two of them, then compare the third to the winner of those two, and you get a definite outcome -- but the loser of the first match would have been the ultimate winner if you had compared in a different order.

Pairwise classification cannot be reliably leveraged to "winner takes all".

Answer 2

[Elahe]

Thanks Walter for your detailed answer , but what I am looking for is one -versus -all according to my specific model, based on what I have read so far ,I should use something like: y*=arg max Wi^T.x

first I have to train all the classifiers then according to the confidence score for each test sample , assign a class to test ... which I do not know how to do.

I really appreciate any help :)

Answer 3

[Elahe]

By the way I am not using SVM for classification any simple classifier even 1-NN works in my case ... (for binary classification part) Do I need to move to SVM ?

[Walter Roberson]

SVM is restricted to pairwise classifications, which as I mentioned above cannot be reliably converted in to "winner takes all" classification.

Answer 4

[Walter Roberson]

I believe my group has done work on aggregating classifiers, but I haven't read the results myself. See for example http://www.cs.bham.ac.uk/~wbl/biblio/gp-html/BrionDolenko.html