贝叶斯分类器的PHP实现:将主题分配给文本

Question

在我的新闻页面项目中,我有一个具有以下结构的数据库表新闻:

 - id: [integer] unique number identifying the news entry, e.g.: *1983*
 - title: [string] title of the text, e.g.: *New Life in America No Longer Means a New Name*
 - topic: [string] category which should be chosen by the classificator, e.g: *Sports*

此外,还有一个表格托架,其中包含有关字频率的信息:

 - word: [string] a word which the frequencies are given for, e.g.: *real estate*
 - topic: [string] same content as "topic" field above, e.h. *Economics*
 - count: [integer] number of occurrences of "word" in "topic" (incremented when new documents go to "topic"), e.g: *100*

现在我希望我的PHP脚本对所有新闻条目进行分类,并为它们分配几个可能的类别(主题)之一.

这是正确的实施吗？你能提高吗？

<?php
include 'mysqlLogin.php';
$get1 = "SELECT id, title FROM ".$prefix."news WHERE topic = '' LIMIT 0, 150";
$get2 = mysql_abfrage($get1);
// pTOPICS BEGIN
$pTopics1 = "SELECT topic, SUM(count) AS count FROM ".$prefix."bayes WHERE topic != '' GROUP BY topic";
$pTopics2 = mysql_abfrage($pTopics1);
$pTopics = array();
while ($pTopics3 = mysql_fetch_assoc($pTopics2)) {
    $pTopics[$pTopics3['topic']] = $pTopics3['count'];
}
// pTOPICS END
// pWORDS BEGIN
$pWords1 = "SELECT word, topic, count FROM ".$prefix."bayes";
$pWords2 = mysql_abfrage($pWords1);
$pWords = array();
while ($pWords3 = mysql_fetch_assoc($pWords2)) {
    if (!isset($pWords[$pWords3['topic']])) {
        $pWords[$pWords3['topic']] = array();
    }
    $pWords[$pWords3['topic']][$pWords3['word']] = $pWords3['count'];
}
// pWORDS END
while ($get3 = mysql_fetch_assoc($get2)) {
    $pTextInTopics = array();
    $tokens = tokenizer($get3['title']);
    foreach ($pTopics as $topic=>$documentsInTopic) {
        if (!isset($pTextInTopics[$topic])) { $pTextInTopics[$topic] = 1; }
        foreach ($tokens as $token) {
            echo '....'.$token;
            if (isset($pWords[$topic][$token])) {
                $pTextInTopics[$topic] *= $pWords[$topic][$token]/array_sum($pWords[$topic]);
            }
        }
        $pTextInTopics[$topic] *= $pTopics[$topic]/array_sum($pTopics); // #documentsInTopic / #allDocuments
    }
    asort($pTextInTopics); // pick topic with lowest value
    if ($chosenTopic = each($pTextInTopics)) {
        echo '<p>The text belongs to topic '.$chosenTopic['key'].' with a likelihood of '.$chosenTopic['value'].'</p>';
    }
}
?>

培训是手动完成的,不包含在此代码中.如果文本"你可以赚钱,如果你出售房地产"被分配到类别/主题"经济学",那么所有单词(你,可以,制作,...)被插入表贝叶斯与"经济学"作为该专题和1个标准计数.如果该单词已经与同一主题组合在一起,则计数会递增.

样本学习数据:

单词主题计数

卡钦斯基政治1

索尼科技1

银行经济学1

手机技术1

索尼经济学3

爱立信科技2

样本输出/结果:

文字标题:手机测试索尼爱立信Aspen - 敏感的Winberry

政治

....电话....测试....索尼....爱立信....白杨....敏感.... winberry

技术

....手机发现....测试....索尼发现....爱立信发现....白杨....敏感.... winberry

经济学

....电话....测试....索尼发现....爱立信....白杨....敏感.... winberry

结果:该文本属于主题技术,可能性为0.013888888888889

非常感谢你提前!

Answer 1

看起来您的代码是正确的,但有一些简单的方法可以优化它.例如,您可以为每个单词动态计算p(单词|主题),同时您可以预先轻松计算这些值.(我假设你想在这里对多个文件进行分类,如果你只做一个文件,我认为这是可以的,因为你没有为文件中没有的文字计算它)

类似地,p(主题)的计算可以移动到循环之外.

最后,您不需要对整个数组进行排序以找到最大值.

所有小点!但这就是你要求的:)

我写了一些未经测试的PHP代码,显示我将如何实现以下内容:

<?php

// Get word counts from database
$nWordPerTopic = mystery_sql();

// Calculate p(word|topic) = nWord / sum(nWord for every word)
$nTopics = array();
$pWordPerTopic = array();
foreach($nWordPerTopic as $topic => $wordCounts)
{
    // Get total word count in topic
    $nTopic = array_sum($wordCounts);

    // Calculate p(word|topic)
    $pWordPerTopic[$topic] = array();
    foreach($wordCounts as $word => $count)
        $pWordPerTopic[$topic][$word] = $count / $nTopic;

    // Save $nTopic for next step
    $nTopics[$topic] = $nTopic;
}

// Calculate p(topic)
$nTotal = array_sum($nTopics);
$pTopics = array();
foreach($nTopics as $topic => $nTopic)
    $pTopics[$topic] = $nTopic / $nTotal;

// Classify
foreach($documents as $document)
{
    $title = $document['title'];
    $tokens = tokenizer($title);
    $pMax = -1;
    $selectedTopic = null;
    foreach($pTopics as $topic => $pTopic)
    {
        $p = $pTopic;
        foreach($tokens as $word)
        {
            if (!array_key_exists($word, $pWordPerTopic[$topic]))
                continue;
            $p *= $pWordPerTopic[$topic][$word];
        }

        if ($p > $pMax)
        {
            $selectedTopic = $topic;
            $pMax = $p;
        }
    }
} 
?>

至于数学......

你正试图最大化p(主题|单词),所以找到

arg max p(topic|words)

(IE是p(主题|单词)最高的论点主题)

贝叶斯定理说

                  p(topic)*p(words|topic)
p(topic|words) = -------------------------
                        p(words)

所以你在寻找

         p(topic)*p(words|topic)
arg max -------------------------
               p(words)

由于文档的p(单词)对于任何主题都是相同的,这与查找相同

arg max p(topic)*p(words|topic)

朴素的贝叶斯假设(这使得它成为一个朴素的贝叶斯分类器)就是这样

p(words|topic) = p(word1|topic) * p(word2|topic) * ...

所以使用这个,你需要找到

arg max p(topic) * p(word1|topic) * p(word2|topic) * ...

哪里

p(topic) = number of words in topic / number of words in total

和

                   p(word, topic)                         1
p(word | topic) = ---------------- = p(word, topic) * ----------
                      p(topic)                         p(topic)

      number of times word occurs in topic     number of words in total
   = -------------------------------------- * --------------------------
            number of words in total           number of words in topic

      number of times word occurs in topic 
   = --------------------------------------
            number of words in topic