# tf\_feature\_self\_similarity

Given a query input of entity keys/IDs (for example, airplane tail numbers), a set of feature columns (for example, airports visited), and a metric column (for example number of times each airport was visited), scores each pair of entities based on their similarity. The score is computed as the cosine similarity of the feature column(s) between each entity pair, which can optionally be TF/IDF weighted.

```
select * from table(
  tf_feature_self_similarity(
    primary_features => cursor(
      select
        primary_key,
        pivot_features,
        metric
      from
        table
      group by
        primary_key,
        pivot_features
    ),
    use_tf_idf => <boolean>))
```

#### Input Arguments

| Parameter        | Description                                                                                                                                                                                                                                                                                                                                                                                                               | Data Type                                    |
| ---------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | -------------------------------------------- |
| `primary_key`    | Column containing keys/entity IDs that can be used to uniquely identify the entities for which the function computes co-similarity. Examples include countries, census block groups, user IDs of website visitors, and aircraft callsigns.                                                                                                                                                                                | Column\<TEXT ENCODING DICT \| INT \| BIGINT> |
| `pivot_features` | One or more columns constituting a compound feature. For example, two columns of visit hour and census block group would compare entities specified by `primary_key` based on whether they visited the same census block group in the same hour. If a single census block group feature column is used, the `primary_key` entities would be compared only by the census block groups visited, regardless of time overlap. | Column\<TEXT ENCODING DICT \| INT \| BIGINT> |
| `metric`         | Column denoting the values used as input for the cosine similarity metric computation. In many cases, this is `COUNT(*)` such that feature overlaps are weighted by the number of co-occurrences.                                                                                                                                                                                                                         | Column\<INT \| BIGINT \| FLOAT \| DOUBLE>    |
| `use_tf_idf`     | Boolean constant denoting whether [TF-IDF](https://en.wikipedia.org/wiki/Tf%E2%80%93idf) weighting should be used in the cosine similarity score computation.                                                                                                                                                                                                                                                             | BOOLEAN                                      |

#### Output Columns

<table>
  <thead><tr><th width="195.7006867662056">Name</th><th>Description</th><th>Data Types</th></tr></thead>

  <tbody><tr><td><code>class1</code></td><td>ID of the first <code>primary key</code> in the pair-wise comparison.</td><td>Column<TEXT ENCODING DICT | INT | BIGINT> (type is the same of <code>primary_key</code> input column)</td></tr><tr><td><code>class2</code></td><td>ID of the second <code>primary key</code> in the pair-wise comparison. Because the computed similarity score for a pair of <code>primary keys</code> is order-invariant, results are output only for ordering such that <code>class1</code> <= <code>class2</code>. For primary keys of type <code>TextEncodingDict</code>, the order is based on the internal integer IDs for each string value and not lexicographic ordering.</td><td>Column<TEXT ENCODING DICT | INT | BIGINT> (type is the same of <code>primary_key</code> input column)</td></tr><tr><td><code>similarity_score</code></td><td>Computed cosine similarity score between each <code>primary_key</code> pair, with values falling between 0 (completely dissimilar) and 1 (completely similar).</td><td>Column<Float></td></tr></tbody>
</table>

**Example**

```
/* Compute similarity of airlines by the airports they fly from */

select
  *
from
  table(
    tf_feature_self_similarity(
      primary_features => cursor(
        select
          carrier_name,
          origin,
          count(*) as num_flights
        from
          flights_2008
        group by
          carrier_name,
          origin
      ),
      use_tf_idf => false
    )
  )
where
  similarity_score <= 0.99
order by
  similarity_score desc
limit
  20;
  
class1|class2|similarity_score
Expressjet Airlines|Continental Air Lines|0.9564615
Delta Air Lines|Atlantic Southeast Airlines|0.9436753
Delta Air Lines|AirTran Airways Corporation|0.9379856
Atlantic Southeast Airlines|AirTran Airways Corporation|0.9326661
American Eagle Airlines|American Airlines|0.8906327
Northwest Airlines|Pinnacle Airlines|0.8222722
Skywest Airlines|United Air Lines|0.6857293
Mesa Airlines|US Airways|0.6116939
United Air Lines|Frontier Airlines|0.5921053
Mesa Airlines|United Air Lines|0.5686765
United Air Lines|American Eagle Airlines|0.5272493
Skywest Airlines|Frontier Airlines|0.4684323
Southwest Airlines|US Airways|0.4166781
United Air Lines|American Airlines|0.397027
Comair|JetBlue Airways|0.3631534
Mesa Airlines|American Eagle Airlines|0.3379275
Skywest Airlines|American Eagle Airlines|0.3331468
Mesa Airlines|Skywest Airlines|0.3235496
Comair|Delta Air Lines|0.3075919
Southwest Airlines|Mesa Airlines|0.2901711

/* Compute the similarity of US States by the TF-IDF
 weighted cosine similarity of the words tweeted in each state */
 
 select
  *
from
  table(
    tf_feature_self_similarity(
      primary_features => cursor(
        select
          state_abbr,
          unnest(tweet_tokens),
          count(*)
        from
          tweets_2022_06
        where country = 'US'
        group by
          state_abbr,
          unnest(tweet_tokens)
      ),
      use_tf_idf => TRUE
    )
  )
where
  class1 <> class2
order by
  similarity_score desc;
  
TX|GA|0.9928479
IL|TN|0.9920474
IL|NC|0.9920027
TX|IL|0.9917723
IN|OH|0.9916649
TN|NC|0.9915619
CA|TX|0.9910875
IN|VA|0.9909871
CA|IL|0.9909689
IL|OH|0.9909481
TX|NC|0.9908867
IL|MO|0.9907863
IN|MI|0.990751
TN|OH|0.9907123
IL|MD|0.9907106
OH|NC|0.9905779
VA|OH|0.990536
IN|IL|0.9904549
IN|MO|0.9903805
TX|TN|0.9903381
```

![Computed similarity score for US airlines for 2008, where similarity is computed by the cosine similarity of the airports each airline departs from, weighted by the number of flights from that airport (using the first example query above, sans LIMIT). Dataset courtesy of the FAA.](https://files.buildwithfern.com/heavyai.docs.buildwithfern.com/heavyai/331d95b59fb9ec85aebc38f524c05e68d9d1cae9b74808b1785b719571e2c08c/docs/assets/airline_similarity.png)