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I'm having my head buried in the AdaBoost.M1. Are there yet some variations of AdaBoost.M1? I ask this because I read variations of algorithm listing from different sources.

For example, the original paper Experiments with a New Boosting Algorithm gives the following algorithm listing (screenshot attached): enter image description here

In Chapter 10 of The Elements of Statistical Learning pp.339 the algorithm listing is gives as: enter image description here

Also reading through Zhi-Hua Zhou (2012). Ensemble Methods Foundations and Algorithms, the author has this about the algorithm (pp. 54):

AdaBoost.M1 [Freund and Schapire, 1997] is a very straightforward extension, which is the same as the algorithm shown in Figure 2.2 except that the base learners now are multiclass learners instead of binary classifiers.

And here's the listing in Figure 2.2 enter image description here

I have to admit, I'm confuse about this. Can someone explain this variations please?

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