Github user takuti commented on a diff in the pull request:
https://github.com/apache/incubator-hivemall/pull/107#discussion_r135454567
--- Diff: docs/gitbook/eval/binary_classification_measures.md ---
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+ KIND, either express or implied. See the License for the
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+
+<!-- toc -->
+
+# Binary problems
+
+Binary classification problem is the task to predict the label of each
data given two categorized dataset.
+
+Hivemall provides some tutorials to deal with binary classification
problems as follows:
+
+- [Online advertisement click prediction](../binaryclass/general.html)
+- [News classification](../binaryclass/news20_dataset.html)
+
+This page focuses on the evaluation of the results from such binary
classification problems.
+If your classifier outputs probability rather than 0/1 label, evaluation
based on [Area Under the ROC Curve](./auc.md) would be more appropriate.
+
+
+# Example
+
+For the metrics explanation, this page introduces toy example data and two
metrics.
+
+## Data
+
+The following table shows the sample of binary classification's prediction.
+In this case, `1` means positive label and `0` means negative label.
+Left column includes supervised label data,
+and center column includes predicted label by a binary classifier.
+
+| truth label| predicted label | |
+|:---:|:---:|:---:|
+| 1 | 0 |False Negative|
+| 0 | 1 |False Positive|
+| 0 | 0 |True Negative|
+| 1 | 1 |True Positive|
+| 0 | 1 |False Positive|
+| 0 | 0 |True Negative|
+
+## Preliminary metrics
+
+Some evaluation metrics are calculated based on 4 values:
+
+- True Positive (TP): truth label is positive and predicted label is also
positive
+- True Negative (TN): truth label is negative and predicted label is also
negative
+- False Positive (FP): truth label is negative but predicted label is
positive
+- False Negative (FN): truth label is positive but predicted label is
negative
+
+`TR` and `TN` represent correct classification, and `FP` and `FN`
illustrate incorrect ones.
+
+In this example, we can obtain those values:
+
+- TP: 1
+- TN: 2
+- FP: 2
+- FN: 1
+
+if you want to know about those metrics, Wikipedia provides [more detail
information](https://en.wikipedia.org/wiki/Sensitivity_and_specificity).
+
+### Recall
+
+Recall indicates the true positive rate in truth positive labels.
+The value is computed by the following equation:
+
+$$
+\mathrm{recall} = \frac{\mathrm{\#TP}}{\mathrm{\#TP} + \mathrm{\#FN}}
+$$
+
+In the previous example, $$\mathrm{precision} = \frac{1}{2}$$.
+
+### Precision
+
+Precision indicates the true positive rate in positive predictive labels.
+The value is computed by the following equation:
+
+$$
+\mathrm{precision} = \frac{\mathrm{\#TP}}{\mathrm{\#TP} + \mathrm{\#FP}}
+$$
+
+In the previous example, $$\mathrm{precision} = \frac{1}{3}$$.
+
+# Metrics
+
+## F1-score
+
+F1-score is the harmonic mean of recall and precision.
+F1-score is computed by the following equation:
+
+$$
+\mathrm{F}_1 = 2 \frac{\mathrm{precision} *
\mathrm{recall}}{\mathrm{precision} + \mathrm{recall}}
+$$
+
+Hivemall's `fmeasure` function provides the option which can switch
`micro`(default) or `binary` by passing `average` argument.
+
+
+> #### Caution
+> Hivemall also provides `f1score` function, but it is old function to
obtain F1-score. The value of `f1score` is based on set operation. So, we
recommend to use `fmeasure` function to get F1-score based on this article.
+
+You can learn more about this from the following external resource:
+
+- [scikit-learn's
F1-score](http://scikit-learn.org/stable/modules/generated/sklearn.metrics.f1_score.html)
+
+
+### Micro average
+
+If `micro` is passed to `average`,
+recall and precision are modified to consider True Negative.
+So, micro f1score are calculated by those modified recall and precision.
+
+$$
+\mathrm{recall} = \frac{\mathrm{\#TP} + \mathrm{\#TN}}{\mathrm{\#TP} +
\mathrm{\#FN} + \mathrm{\#TN}}
+$$
+
+$$
+\mathrm{precision} = \frac{\mathrm{\#TP} + \mathrm{\#TN}}{\mathrm{\#TP} +
\mathrm{\#FP} + \mathrm{\#TN}}
+$$
+
+If `average` argument is omitted, `fmeasure` use default value: `'-average
micro'`.
+
+The following query shows the example to obtain F1-score.
+Each row value has the same type (`int` or `boolean`).
+If row value's type is `int`, `1` is considered as the positive label, and
`-1` or `0` is considered as the negative label.
+
+
+```sql
+WITH data as (
+ select 1 as truth, 0 as predicted
+union all
+ select 0 as truth, 1 as predicted
+union all
+ select 0 as truth, 0 as predicted
+union all
+ select 1 as truth, 1 as predicted
+union all
+ select 0 as truth, 1 as predicted
+union all
+ select 0 as truth, 0 as predicted
+)
+select
+ fmeasure(truth, predicted, '-average micro')
+from data
+;
+
+-- 0.5;
+```
+
--- End diff --
How about writing the difference between `f1score` and `fmeasure` here? It
could be helpful to understand the concept of `-average micro` and replace the
old `f1score` with `fmeasure`. For instance:
> It should be noted that, since the old `f1score(truth, predicted)`
function simply counts the number of "matched" elements between `truth` and
`predicted`, the above query is equivalent to:
```sql
WITH data as (
select 1 as truth, 0 as predicted
union all
select 0 as truth, 1 as predicted
union all
select 0 as truth, 0 as predicted
union all
select 1 as truth, 1 as predicted
union all
select 0 as truth, 1 as predicted
union all
select 0 as truth, 0 as predicted
)
select
f1score(array(truth), array(predicted))
from data
;
```
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