MySQL / PHP: Find similar / related items by tag / taxonomy

Question

I have a cities table which looks like this.

|id| Name    |
|1 | Paris   |
|2 | London  |
|3 | New York|

I have a tags table which looks li

Answer 1

Too late, but I think that none of answers are fully correct. I got the best part of each one and put all together to make my own answer:

• The Jaccard Index explanaiton of @m-khalid-junaid is very interesting and correct, but the implementation of (q.sets + q.parisset) AS union and (q.sets - q.parisset) AS intersect is very wrong.
• The version of @n-lx is the way, but needs the Jaccard Index, this is very important, if a city have 2 tags and matches two tags of another city with 3 tags, the result will be the same of the matches on another city with only the same two tags. I think the full matches is most related.

My answer:

cities table like this.

| id | Name      |
| 1  | Paris     |
| 2  | Florence  |
| 3  | New York  |
| 4  | São Paulo |
| 5  | London    |

cities_tag table like this.

| city_id | tag_id |
| 1       | 1      | 
| 1       | 3      | 
| 2       | 1      |
| 2       | 3      | 
| 3       | 1      |     
| 3       | 2      |
| 4       | 2      |     
| 5       | 1      |
| 5       | 2      |
| 5       | 3      |

With this sample data, Florence have a full matches with Paris, New York matches one tag, São Paulo have no tags matches and London matches two tags and have another one. I think the Jaccard Index of this sample is:

Florence: 1.000 (2/2)

London: 0.666 (2/3)

New York: 0.333 (1/3)

São Paulo: 0.000 (0/3)

My query is like this:

select jaccard.city, 
       jaccard.intersect, 
       jaccard.union, 
       jaccard.intersect/jaccard.union as 'jaccard index'
from 
(select
    c2.name as city
    ,count(ct2.tag_id) as 'intersect' 
    ,(select count(distinct ct3.tag_id) 
      from cities_tags ct3 
      where ct3.city_id in(c1.id, c2.id)) as 'union'
from
    cities as c1
    inner join cities as c2 on c1.id != c2.id
    left join cities_tags as ct1 on ct1.city_id = c1.id
    left join cities_tags as ct2 on ct2.city_id = c2.id and ct1.tag_id = ct2.tag_id
where c1.id = 1
group by c1.id, c2.id) as jaccard
order by jaccard.intersect/jaccard.union desc

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