PHP 中的字符串相似度：类似 levenshtein 的长字符串函数

Question

PHP 中的函数 levenshtein 适用于最大长度为 255 的字符串。在 PHP 中计算句子的相似度分数有哪些好的替代方法。

基本上我有一个句子数据库，我想找到近似的重复项。 similar_text 函数没有给我预期的结果。对我来说检测类似句子的最简单方法是什么：

$ss="Jack is a very nice boy, isn't he?";
$pp="jack is a very nice boy is he";

$ss=strtolower($ss);  // convert to lower case as we dont care about case
$pp=strtolower($pp);

$score=similar_text($ss, $pp);
echo "$score %\n";  // Outputs just 29 %

$score=levenshtein ( $ss, $pp );
echo "$score\n";  // Outputs '5', which indicates they are very similar. But, it does not work for more than 255 chars :(

Answer 1

levenshtein 算法的时间复杂度为 O(n*m)，其中 n 和 m 是长度两个输入字符串的。这是相当昂贵的，并且计算长字符串的这样的距离将需要很长时间。

对于整个句子，您可能需要使用 diff 算法，例如：在 PHP 中突出显示两个字符串之间的区别

话虽如此，PHP 还提供了 similar_text 函数的复杂度更差 (O(max(n,m)**3)) 但似乎适用于较长的字符串。

Answer 2

我发现 Smith Waterman Gotoh 是最佳算法比较句子。更多信息在此答案中。这是 PHP 代码示例：

class SmithWatermanGotoh 
{
    private $gapValue;
    private $substitution;

    /**
     * Constructs a new Smith Waterman metric.
     * 
     * @param gapValue
     *            a non-positive gap penalty
     * @param substitution
     *            a substitution function
     */
    public function __construct($gapValue=-0.5, 
                $substitution=null) 
    {
        if($gapValue > 0.0) throw new Exception("gapValue must be <= 0");
        //if(empty($substitution)) throw new Exception("substitution is required");
        if (empty($substitution)) $this->substitution = new SmithWatermanMatchMismatch(1.0, -2.0);
        else $this->substitution = $substitution;
        $this->gapValue = $gapValue;
    }

    public function compare($a, $b) 
    {
        if (empty($a) && empty($b)) {
            return 1.0;
        }

        if (empty($a) || empty($b)) {
            return 0.0;
        }

        $maxDistance = min(mb_strlen($a), mb_strlen($b))
                * max($this->substitution->max(), $this->gapValue);
        return $this->smithWatermanGotoh($a, $b) / $maxDistance;
    }

    private function smithWatermanGotoh($s, $t) 
    {   
        $v0 = [];
        $v1 = [];
        $t_len = mb_strlen($t);
        $max = $v0[0] = max(0, $this->gapValue, $this->substitution->compare($s, 0, $t, 0));

        for ($j = 1; $j < $t_len; $j++) {
            $v0[$j] = max(0, $v0[$j - 1] + $this->gapValue,
                    $this->substitution->compare($s, 0, $t, $j));

            $max = max($max, $v0[$j]);
        }

        // Find max
        for ($i = 1; $i < mb_strlen($s); $i++) {
            $v1[0] = max(0, $v0[0] + $this->gapValue, $this->substitution->compare($s, $i, $t, 0));

            $max = max($max, $v1[0]);

            for ($j = 1; $j < $t_len; $j++) {
                $v1[$j] = max(0, $v0[$j] + $this->gapValue, $v1[$j - 1] + $this->gapValue,
                        $v0[$j - 1] + $this->substitution->compare($s, $i, $t, $j));

                $max = max($max, $v1[$j]);
            }

            for ($j = 0; $j < $t_len; $j++) {
                $v0[$j] = $v1[$j];
            }
        }

        return $max;
    }
}

class SmithWatermanMatchMismatch
{
    private $matchValue;
    private $mismatchValue;

    /**
     * Constructs a new match-mismatch substitution function. When two
     * characters are equal a score of <code>matchValue</code> is assigned. In
     * case of a mismatch a score of <code>mismatchValue</code>. The
     * <code>matchValue</code> must be strictly greater then
     * <code>mismatchValue</code>
     * 
     * @param matchValue
     *            value when characters are equal
     * @param mismatchValue
     *            value when characters are not equal
     */
    public function __construct($matchValue, $mismatchValue) {
        if($matchValue <= $mismatchValue) throw new Exception("matchValue must be > matchValue");

        $this->matchValue = $matchValue;
        $this->mismatchValue = $mismatchValue;
    }

    public function compare($a, $aIndex, $b, $bIndex) {
        return ($a[$aIndex] === $b[$bIndex] ? $this->matchValue
                : $this->mismatchValue);
    }

    public function max() {
        return $this->matchValue;
    }

    public function min() {
        return $this->mismatchValue;
    }
}

$str1 = "Jack is a very nice boy, isn't he?";
$str2 = "jack is a very nice boy is he";
$o = new SmithWatermanGotoh();
echo $o->compare($str1, $str2);

Answer 3

您可以尝试使用similar_text。
如果有 20,000 多个字符（3-5 秒），它可能会变得相当慢，但你提到的示例仅使用句子，这对于这种用法来说效果很好。

需要注意的一件事是，在比较不同大小的字符串时，您不会得到 100% 的结果。例如，如果您将“he”与“head”进行比较，您只会得到 50% 的匹配度。