Does Gini index considers only a binary split for each attribute or can it have multi way spliting?

Question

Does Gini-index based classification split values for any attribute always as a binary split or can it split into more than $2$ branches (multi-way split)?

For more clarification, if a split on $A$ partitions $D$ into $D_1$ and $D_2$ , the Gini-index of $D$ given that partitioning is,

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This is actually a binary split. Can there be also $D_4, D_5$ etc... too if it is not a binary split so that the formula will be,

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i've just read all of https://en.wikipedia.org/wiki/Gini_coefficient and i can't find your function anywhere. do you have any references? — JMP, Sep 05 '15 at 07:42
both; is the 2nd equation inadmissible or something? it won't be a binary split:-) — JMP, Sep 05 '15 at 08:33
First one is there in a book I read. I am asking whether the 2nd one is correct — Samitha Chathuranga, Sep 05 '15 at 08:46
I asked myself the same question and thus stumbled upon this question here. Do not let yourself get confused, @JonMarkPerry Gini index is not the same as Gini coefficient. — Zelphir Kaltstahl, Dec 26 '16 at 13:35

score 0 · Answer 1 · answered Oct 30 '18 at 20:15

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Yes, Gini-index can be used for multi-way splitting, like entropy. And the second formula you mentioned is correct if the feature has 3 distinct value, i.e. It can be generalized for more than this if the number of distinct values is more.

answered Oct 30 '18 at 20:15

Youssef Yossry

1

Does Gini index considers only a binary split for each attribute or can it have multi way spliting?

1 Answers1