Github user myui commented on a diff in the pull request:
https://github.com/apache/incubatorhivemall/pull/107#discussion_r131559068
 Diff: docs/gitbook/eval/multilabel_classification_measures.md 
@@ 0,0 +1,148 @@
+<!
+ Licensed to the Apache Software Foundation (ASF) under one
+ or more contributor license agreements. See the NOTICE file
+ distributed with this work for additional information
+ regarding copyright ownership. The ASF licenses this file
+ to you under the Apache License, Version 2.0 (the
+ "License"); you may not use this file except in compliance
+ with the License. You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE2.0
+
+ Unless required by applicable law or agreed to in writing,
+ software distributed under the License is distributed on an
+ "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ KIND, either express or implied. See the License for the
+ specific language governing permissions and limitations
+ under the License.
+>
+
+<! toc >
+
+# Multilabel classification
+
+
+Multilabel 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 Multilabel classification problems.
+
+# Examples
+
+For the metrics explanation, this page introduces toy example data and two metrics.
+
+## Data
+
+The following table shows the sample of Multilabel classification's prediction.
+Animal names represent the tags of blog post.
+Left column includes supervised labels,
+Right column includes are predicted labels by a Multilabel 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 multilabel classification
+
+Hivemall provises micro F1score and micro Fmeasure.
+
+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 F1score
+
+
+F1score 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 F1score.
+
+```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)
+from data
+;
+
+ 0.6956521739130435;
+```
+
+
+## Micro Fmeasure
+
+Fmeasure is generalized F1score and the weighted harmonic mean of recall and precision.
+
+$$\beta$$ is the parameter to determine the weight of precision.
+So, F1score is the special case of Fmeasure given $$\beta=1$$.
+
+If $$\beta$$ is larger positive value than `1.0`, Fmeasure reaches to micro recall.
+On the other hand,
+if $$\beta$$ is smaller positive value than `1.0`, Fmeasure reaches to micro precision.
+
+The following query shows the example to obtain Fmeasure with $$\beta=2$$.
+
+$$
+\mathrm{F}_{\beta} = (1+\beta^2) \frac
+{\sum_i l_i \cap p_i }
+{ \beta^2 (\sum_i l_i \cap p_i  + \sum_i p_i  l_i ) + \sum_i l_i \cap p_i  + \sum_i
l_i  p_i }
+$$
+
+
+```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
+ fmeasure(actual, predicted, 2)
 End diff 
`fmeasure(actual, predicted, 'beta 2.0 average macro')`

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