Find euclidean distance of two array of different length - php

Question

I want to find Euclidean distance to check similarity of strings.
From above image in a painting object field there are many image types in database. Images is displaying using this paining_object field. Now i want to show related images of one selected image by comparing strings from paining_object field. So i have used Euclidean distance method to find similarities of strings.
But i am facing issue with length. For ex. In first row from database there are four image types in paining_object field and in the second row there are more than four image types. So, how could i measure distance with this method for the arrays having unequal length.

Answer 1

non euclidean distances
The distance between two unordered arrays can be rephrased as distance between sets.
A quick lookup shows there exists several distances representing the similarity between sets such as
the Jaccard distance
d(a,b) = |a inter b| / |a union b|
the maximum difference metric
d(a,b) = 1 - |a inter b| / max(|a|, |b|)
there are more distances (for instance) on the paper Distances between sets on set commonality
still euclidean distance
You can still force it:
Get all your mangas as a vocabulary V, say size n.
Consider the set R^n.
A row of your table can be represented as a vector v of R^n:
if the row contains word i, put v[i] = 1, v[i]=0 otherwise
Finally the euclidean distance can trivially be applied on the vectors of same length.
distance thus be like
d(a,b) = || v_b - v_a ||_2 = sqrt( (v_b[0] - v_a[0])^2 + ... + (v_b[n-1] - v_a[n-1)^2)
Every square is equal to 1 iff v_b[i]!=v_a[i] that is you want to count the elements in a not in b U b not in a idem the symmetric difference of a and b.
You can thus rewrite your distance:
d(a,b) = sqrt(|a Δ b|)

Answer 2

I have did this by using Jaccard distance as below. First created two tables for unique object from where we can collect object from id and second where all object comes together seperated from (,)
1) image_sub_main Table
2) image_main Table
3) PHP file as Wordpress Way
global $wpdb;
$post_id = $wpdb->get_results("SELECT * FROM `image_main`");
$i=1;
$finimgarray = array();
$aa = array();
$bb = array();
$firstarray = array('similarity' =>100 , 'id' => $post_id[0]->id );
foreach($post_id as $key => $post){
if($i < count($post_id)){
$arraya =$post_id[0]->image_types;
$a = explode(",",$arraya);
$arrayb =$post_id[$i]->image_types;
$b = explode(",",$arrayb);
$array = array_unique (array_merge ($a, $b));
$result=array_intersect($a,$b);
$finalres = count($result) / count($array)*100 ;
$finimgarray[] = array('similarity' =>round($finalres, 2) , 'id' => $post_id[$i]->id );
}
$i++;
}
array_push($finimgarray, $firstarray);
arsort($finimgarray);
foreach($finimgarray as $findimgarr){
$id = $findimgarr['id'];
$image = $wpdb->get_row("SELECT * FROM `image_main` WHERE `id` = $id ");
echo "<img src='$image->image'/>";
}
Your output will compare images to first one image and show according to similarity %

Answer 3

We cannot apply Euclidean Distance here because:
The array lengths can be different
The order of strings should not be considered. For example, hellsing
can be at any index in the array. So, we should not compare the first element of the first array with the first element of the second array only.
Instead, we can define a similarity function which takes care of both the above problems - we can use the ratio of number of string matches to the total number of combinations as the similarity score.
// Assuming $firstArr and $secondArr are sets, i.e., don't contain duplicates
function similarityScore($firstArr, $secondArr) {
$matchCount = 0;
foreach ($firstArr as $first) {
foreach($secondArr as $second) {
if ($first == $second) {
$matchCount++;
}
}
}
return $matchCount/(count($firstArr)*count($secondArr));
}
This function returns a real number in the range [0,1] where higher value indicates greater similarity.