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From nzw0301 <...@git.apache.org>
Subject [GitHub] incubator-hivemall pull request #107: [HIVEMALL-132] Generalize f1score UDAF...
Date Mon, 28 Aug 2017 08:45:35 GMT
Github user nzw0301 commented on a diff in the pull request:

    https://github.com/apache/incubator-hivemall/pull/107#discussion_r135471771
  
    --- Diff: docs/gitbook/eval/binary_classification_measures.md ---
    @@ -0,0 +1,261 @@
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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 --
    
    Sounds good! thanks


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