Github user manishamde commented on a diff in the pull request:
https://github.com/apache/spark/pull/2063#discussion_r16505721
--- Diff: docs/mllib-decision-tree.md ---
@@ -77,33 +85,46 @@ bins if the condition is not satisfied.
**Categorical features**
-For `$M$` categorical feature values, one could come up with `$2^(M-1)-1$`
split candidates. For
-binary classification, we can reduce the number of split candidates to
`$M-1$` by ordering the
+For a categorical feature with `$M$` possible values (categories), one
could come up with
+`$2^{M-1}-1$` split candidates. For binary classification and regression,
+we can reduce the number of split candidates to `$M-1$` by ordering the
categorical feature values by the proportion of labels falling in one of
the two classes (see
Section 9.2.4 in
[Elements of Statistical Machine
Learning](http://statweb.stanford.edu/~tibs/ElemStatLearn/) for
details). For example, for a binary classification problem with one
categorical feature with three
-categories A, B and C with corresponding proportion of label 1 as 0.2, 0.6
and 0.4, the categorical
-features are ordered as A followed by C followed B or A, C, B. The two
split candidates are A \| C, B
+categories A, B and C whose corresponding proportions of label 1 are 0.2,
0.6 and 0.4, the categorical
+features are ordered as A, C, B. The two split candidates are A \| C, B
and A , C \| B where \| denotes the split. A similar heuristic is used for
multiclass classification
-when `$2^(M-1)-1$` is greater than the number of bins -- the impurity for
each categorical feature value
-is used for ordering.
+when `$2^{M-1}-1$` is greater than the `maxBins` parameter: the impurity
for each categorical feature value
+is used for ordering. In multiclass classification, all `$2^{M-1}-1$`
possible splits are used
+whenever possible.
+
+Note that the `maxBins` parameter must be at least `$M_{max}$`, the
maximum number of categories for
--- End diff --
Suggestion: M_{max} can be eliminated unless it's used elsewhere in the
document.
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