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I'm reading Data mining with decision trees by Rokach, and i've got to a chapter about ensemble methods (using multiple classifiers) and this is where I can't wrap my head around this concept of Plurality Voting (PV).

$$\operatorname{class}(x) = \operatorname{argmax} \left (\sum g(y_k(x), c_i) \right)$$

Where $$g(y_k(x), c_i) = \begin{cases}1 &\text{if } y = c\\ 0 &\text{if } y \neq c\end{cases}$$

Most of the other metrics in the chapter weight classifiers, yet this seems to just essentially pick the one which has the highest chance of returning the class you want. Which seems useless? If thats the case how would this be helpful?

Martin Thoma
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Tony
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1 Answers1

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I can't explain those formulas without more details about the notation, but plurality voting is a method where the class with the most votes wins. It is one form of majority voting.

Formally, if $x$ is your pattern and $y_k(x) = 1$ for the true class $k$ of $x$ and otherwise $y_k(x) = 0$. $c_i(x, k)$ is the prediction of classifier $i$ that $x$ belongs to class $k$. Then plurality voting is

$$\operatorname{ensemle}(x) = \operatorname{argmax}_{k \in K} \left ( \sum_{i} \mathbb{1}_{ \operatorname{argmax}_{l \in K} c_i(x, l) = k} \right )$$

So every classifier gives exactly one vote. The class with most votes is the prediction of the ensemble.

Martin Thoma
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