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A question that has been bugging me recently is whether it is more correct to refer to the Random Forests Classifier as "Random Forests" or "Random Forest" (e.g. "We implemented a Random Forest classifier" or "We implemented a Random Forests classifier".) Which is more correct, or are both equally correct? Breiman in his classic paper https://www.stat.berkeley.edu/~breiman/randomforest2001.pdf seems to use both interchangeably, although most papers I have read refer to it as "Random Forests".

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If you go Breiman's page, you will find this statement about trademark.

Random Forests(tm) is a trademark of Leo Breiman and Adele Cutler and is licensed exclusively to Salford Systems for the commercial release of the software. Our trademarks also include RF(tm), RandomForests(tm), RandomForest(tm) and Random Forest(tm).

I would say, all of the are the same.

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Wikitionary defines a "forest" as

A dense collection of trees covering a relatively large area. Larger than woods.

Therefore, random forests would necessarily be two or more large collections of trees. Perhaps this could be the averaging of random forest fit more than once, using different hyperparameters or data.

We also have a new term: when doing exploratory analysis with ntree = small, we have a random wood

In case the above is insufficiently pedantic:

library(randomForest)
random_wood <- randomForest(Species ~ ., ntree = 50, data = iris)
random_forest_1 <- randomForest(Species ~ ., ntree = 200, data = iris, mtry = 2)
random_forest_2 <- randomForest(Species ~ ., ntree = 200, data = iris, mtry = 3)
random_forests <- combine(random_forest_1, random_forest_2)
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    $\begingroup$ I think you are missing the forest for the trees here. $\endgroup$ – C8H10N4O2 Dec 1 '18 at 2:08

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