Github user myui commented on a diff in the pull request:
https://github.com/apache/incubator-hivemall/pull/107#discussion_r131559009
--- Diff: docs/gitbook/eval/multilabel_classification_measures.md ---
@@ -0,0 +1,148 @@
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+
+<!-- toc -->
+
+# Multi-label classification
+
+
+Multi-label classification problem is predicting the labels given
categorized dataset.
+Each sample $$i$$ has $$l_i$$ labels ($$0 \leq l_i \leq |L| $$ )
+, where $$L$$ is the number of unique labels in the geven dataset.
+
+This page focuses on evaluation of the results from such Multi-label
classification problems.
+
+# Examples
+
+For the metrics explanation, this page introduces toy example data and two
metrics.
+
+## Data
+
+The following table shows the sample of Multi-label classification's
prediction.
+Animal names represent the tags of blog post.
+Left column includes supervised labels,
+Right column includes are predicted labels by a Multi-label classifier.
+
+| truth labels| predicted labels |
+|:---:|:---:|
+|cat, dog | cat, bird |
+| cat, bird | cat, dog |
+| | cat |
+| bird | bird |
+| bird, cat | bird, cat |
+| cat, dog, bird | cat, dog |
+| dog | dog, bird|
+
+
+# Evaluation metrics for multi-label classification
+
+Hivemall provises micro F1-score and micro F-measure.
+
+Given $$N$$ blog posts, we uses
+
+Define $$L$$ is the set of the tag of blog posts, and
+$$l_i$$ is a tag set of $$i$$th document.
+In the same manner,
+$$p_i$$ is a predicted tag set of $$i$$th document.
+
+
+
+## Micro F1-score
+
+
+F1-score is the harmonic mean of recall and precision.
+
+The value is computed by the following equation:
+
+$$
+\mathrm{F}_1 = 2 \frac
+{\sum_i |l_i \cap p_i |}
+{ 2* \sum_i |l_i \cap p_i | + \sum_i |l_i - p_i | + \sum_i |p_i - l_i | }
+$$
+
+The Following query shows the example to obtain F1-score.
+
+```sql
+WITH data as (
+ select array("cat", "dog") as actual, array("cat", "bird") as
predicted
+union all
+ select array("cat", "bird") as actual, array("cat", "dog") as
predicted
+union all
+ select array() as actual, array("cat") as
predicted
+union all
+ select array("bird") as actual, array("bird") as
predicted
+union all
+ select array("bird", "cat") as actual, array("bird", "cat") as
predicted
+union all
+ select array("cat", "dog", "bird") as actual, array("cat", "dog") as
predicted
+union all
+ select array("dog") as actual, array("dog", "bird") as
predicted
+)
+select
+ f1score(actual, predicted)
--- End diff --
Could you change the optional third argument to take `const string options`
?
`-beta 1.0 (default)`
`-average [micro (default), macro]`
http://scikit-learn.org/stable/modules/generated/sklearn.metrics.f1_score.html#sklearn.metrics.f1_score
`f1score(actual, predicted)` equals to `fmeasure(actual, predicted, '-beta
1.0 -average micro')` .
See `UDFWithOptions` and it's usage.
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