问题描述
我有一个函数，它接受两个数组包含两个文本的标记/单词，并给出余弦相似性值，显示两个文本之间的关系。
函数接受数组$ tokensA（0 => house，1 => bike，2 => man）和数组$ tokensB（0 => bike，1 => house，2 => car）作为浮点值。
通常可以索引具有任意维数的数据， MySQL 空间能力仅限于几何 c $ c> -dimensional 和，您可以对其进行规范化，然后执行以下操作：
- 符合你的差异的角度数量的两倍
- 找到与每个扇区中心具有给定余弦差的向量的 MBR li>
- 查找 MBR 中的所有向量
- 对精确的差异进行精细过滤。
然而，在这种情况下，最好只是预先计算值的角度，并用平滑的 B-Tree 索引。
I have a function which takes two arrays containing the tokens/words of two texts and gives out the cosine similarity value which shows the relationship between both texts.
The function takes an array $tokensA (0=>house, 1=>bike, 2=>man) and an array $tokensB (0=>bike, 1=>house, 2=>car) and calculates the similarity which is given back as a floating point value.
function cosineSimilarity($tokensA, $tokensB) {
$a = $b = $c = 0;
$uniqueTokensA = $uniqueTokensB = array();
$uniqueMergedTokens = array_unique(array_merge($tokensA, $tokensB));
foreach ($tokensA as $token) $uniqueTokensA[$token] = 0;
foreach ($tokensB as $token) $uniqueTokensB[$token] = 0;
foreach ($uniqueMergedTokens as $token) {
$x = isset($uniqueTokensA[$token]) ? 1 : 0;
$y = isset($uniqueTokensB[$token]) ? 1 : 0;
$a += $x * $y;
$b += $x;
$c += $y;
}
return $b * $c != 0 ? $a / sqrt($b * $c) : 0;
}
If I want to compare 75 texts with each other, I need to make 5,625 single comparisons to have all texts compared with each other.
Is it possible to use MySQL's spatial columns to reduce the number of comparisons?
I don't want to talk about my function or about ways to compare texts. Just about reducing the number of comparisons.
MySQL's spatial columns
- You create spatial columns with: CREATE TABLE abc (clmnName TYPE)
- possible types are listed here
- here is how I select the data later [e.g. MultiPointFromText() or AsText()]
- You insert values like this: INSERT INTO clmnName VALUES (GeomFromText('POINT(1 1)'))
But how do you use this for my problem?
PS: I'm looking for ways to reduce the number of comparisons with algorithms in this question. Vinko Vrsalovic told me that I should open another question for the spatial features.
While R-Trees in general can index data with arbitrary number of dimensions, MySQL spatial abilities are only limited to Geometry types (2 dimensions).
If your vectors are 2-dimensional and you can normalize them, then do the following:
- Split the circle into twice the number of angles which fit your differences
- Find the MBR of vectors with given cosine difference from the center of each sector
- Find all vectors within the MBR
- Do the fine filtering for exact difference.
In this case, however, it will be better just to precaculate the angle of the value and index it with a plain B-Tree index.
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