# NAME Text::Sorensen

Calculate the Sorensen-Dice or Jaccard similarity coefficient.

# SYNOPSIS

```
use Text::Sorensen :sorensen;
# test a word against a small list
say sorensen('compition', 'completion', 'competition');
# ([0.777778 competition] [0.705882 completion])
# or against a large one
my %hash = './unixdict.txt'.IO.slurp.words.race.map: { $_ => .&bi-gram };
.say for sorensen('compition', %hash).head(5);
# [0.777778 competition]
# [0.777778 compilation]
# [0.777778 composition]
# [0.705882 completion]
# [0.7 decomposition]
use Text::Sorensen :jaccard;
.say for jaccard('compition', %hash).head(5);
# [0.636364 competition]
# [0.636364 compilation]
# [0.636364 composition]
# [0.545455 completion]
# [0.538462 decomposition]
```

# DESCRIPTION

Both Sorensen-Dice and Jaccard calculate a "similarity" between two tokenized groups of items. They can be used to compare many different types of tokenized objects; this module is optimized to do a text similarity calculation.

Both methods use a similar algorithm and, though they assign different weights, return nearly identical relative coefficients, and may be readily converted from one to the other.

You can easily convert back and forth:

```
# J (Jaccard index)
# SDI (Sorensen-Dice index)
J = SDI / (2 - SDI)
SDI = 2 * J / (1 + J)
```

For both operations, each word / phrase is broken up into tokens for the comparison. The most typical tokenizing scheme for text is to break the words up into bi-grams: groups of two consecutive letters. For instance, the word 'differ' would be tokenized to the group:

```
'di', 'if', 'ff', 'fe', 'er'
```

This tokenized word is then compared to another tokenized word to calculate the similarity.

The bi-gram routine case-folds the words before tokenizing so the comparison routines ignore case differences.

A great deal of the work is spent in tokenizing the words. If you plan to do multiple comparisons to a large group of words, it may be worthwhile to pre-tokenize the word list to reduce the working time.

When using the module, you must specify which similarity routine(s) you want to import. There are the two basic similarity algorithms and several built-in, exported-on-demand aliases available.

Optionally exported similarity routines:

```
:sorensen --> sub sorensen() # traditional spelling
:sorenson --> sub sorenson() # alternate spelling
:sdi --> sub sdi() # Sorensen-Dice index
:dice --> sub dice() # let Dice have top billing for once
:dsc --> sub dsc() # Dice similarity coefficient
# All point to exactly the same routines behind the scenes.
:jaccard --> sub jaccard() # Jaccard index
```

You'll need to import at least one similarity routine, or some combination, or :ALL.

Always exported helper routine:

```
sub bi-gram() # tokenize a word into a Bag of bi-grams
```

### Sorensen-Dice

```
use Text::Sorensen :sorensen; # or some other alias
```

Sorensen-Dice, named after botanists Thorvald Sørensen and Lee Raymond Dice, measures the similarity of two groups by dividing twice the intersection token count by the total token count of both groups.

```
2 * +(@a ∩ @b) / (@a ⊎ @b)
```

The index is known by several names, Sorensen-Dice index is probably most common, though Sorensen index and Dice's coefficient are also popular. Other variations include the "similarity coefficient" or "index", such as Dice similarity coefficient (DSC).

The module provides multi subs for different use cases.

For a one-off or low memory case, use:

```
sorensen($word, @list, :$ge)
```

Where $word is the word to be compared against, @list is a list or array of words to compare with $word, and :$ge is the minimum for the returned coefficients (default .5). (It's the coefficients **greater than or equal to** .5).

The list of words will be tokenized, the coefficient calculated, entries with coefficients lower than the :$ge threshold filtered out and the remaining list sorted and returned. If you want all values to be returned, even ones that don't match at all, you'll need to specify :ge(0). It's a little unintuitive at first but can seriously reduce memory and time consumption for the common use case.

Each word comparison will return a 2 element array consisting of:

the SDC from the :ge threshold (default .5) to 1 (identical).

the word that was checked.

That works well but retokenizes the list every time it is invoked.

If you want to reuse a list several times to check against mutiple words, it may be better to pre-tokenize the list and pass that to the coefficient function.

Use the module supplied, always exported, sub bi-gram() on each element to pre-tokenize the list.

```
# returns the tokenized word as a Bag
my $tokens = bi-gram($word);
```

Save the list as a hash of word / tokens pairs, then pass that into the coefficient function to avoid re-tokenizing every time. This is a nice parallelizable operation so .race can really speed it up.

```
my %hash = './unixdict.txt'.IO.slurp.words.race.map: { $_ => .&bi-gram };
sorensen($word, %hash)
```

The returned list has results less than the :ge threshold filtered out and is sorted by inverse coefficient (largest first) with a secondary alphabetical sort.

See the following. We compare the typo 'compition' against an entire dictionary, filter out everything lower than .6 coefficient and return the sorted list.

```
.say for sorensen('compition', %hash, :ge(.6));
# [0.777778 competition]
# [0.777778 compilation]
# [0.777778 composition]
# [0.705882 completion]
# [0.7 decomposition]
# [0.666667 compunction]
# [0.666667 computation]
```

### Jaccard

```
use Text::Sorensen :jaccard;
```

The Jaccard index (named for botanist Paul Jaccard) is calculated very similarly to the Sorensen-Dice index.

Instead of the intersection token count divided by the total token count, it is the intersection token count divided by the difference between the total token count and the intersection token count. (Intersection over difference rather than intersection over sum).

```
+(@a ∩ @b) / ( (@a ⊎ @b) - (@a ∩ @b) )
```

Jaccard coefficients tend to be even smaller than Sorensen-Dice but are similarly, a ratio between 0 and 1.

Again, multis are provided for a one-off list:

```
my @results = jaccard($word, @list, :$ge);
```

or a multi use hash.

```
my @results = jaccard($word, @hash, :$ge);
```

The exact same tokenizer is used for each, and the same efficiencies come into play by pre-tokenizing dictionaries for repeated use.

```
.say for jaccard('maintainence', %hash, :ge(.45));
# [0.636364 maintain]
# [0.615385 maintenance]
```

# AUTHOR

2019 Steve Schulze aka thundergnat

This package is free software and is provided "as is" without express or implied warranty. You can redistribute it and/or modify it under the same terms as Perl itself.

# LICENSE

Licensed under The Artistic 2.0; see LICENSE.