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One-vs-all
This is probably the most common strategy and is widely adopted by scikit-learn for most of its algorithms. If there are n output classes, n classifiers will be trained in parallel considering there is always a separation between an actual class and the remaining ones. This approach is relatively lightweight (at most, n-1 checks are needed to find the right class, so it has an O(n) complexity) and, for this reason, it's normally the default choice and there's no need for further actions.