Similarity

Cosine similarity & Simhash implementation

Full documentation can be found at https://hexdocs.pm/similarity.

Installation

Add similarity to your list of dependencies in mix.exs:

def deps do
  [
    {:similarity, "~> 0.4"}
  ]
end

Cosine Similarity

Cosine similarity is not sensitive to the scale of the vector:

Similarity.cosine([1,2,3], [1,2,3])
1.0
Similarity.cosine([1,2,3], [2,4,6])
1.0

Module Similarity.Cosine takes care of building a struct and streaming similarities:
(It handles non matching attributes, elements added don’t have to have the exact attributes)

s = Similarity.Cosine.new()
s = s |> Similarity.Cosine.add("a", [{"bananas", 9}, {"hair_color_r", 124}, {"hair_color_g", 8}, {"hair_color_b", 122}])
s = s |> Similarity.Cosine.add("b", [{"bananas", 19}, {"hair_color_r", 124}, {"hair_color_g", 8}, {"hair_color_b", 122}])
s = s |> Similarity.Cosine.add("c", [{"bananas", 9}, {"hair_color_r", 124}])
s |> Similarity.Cosine.stream |> Enum.to_list
[
  {"a", "b", 1.9967471152702767},
  {"a", "c", 1.4142135623730951},
  {"b", "c", 1.409736747211141}
]
s |> Similarity.Cosine.between("a", "b")
1.9967471152702767

Similarity.cosine_srol/2
Cosine similarity between two vectors, multiplied by the square root of the length of the vectors.
(In my experience, where the number of common attributes doesn’t match between some vectors, this gives a better value.)

a = [1,2,3,4]
b = [1,2,3]
c = [1,2,3,4]
Similarity.cosine_srol(a |> Enum.take(3), b)
1.7320508075688772
Similarity.cosine_srol(a, c)
2.0

Above even though the first 3 elements of a match with b, just like a with c,
the a & c cosine similarity returns higher value due to more elements matching.
In real world scenario I suggest using this if compared vectors aren’t the same length.

Simhash

left = "pork belly jerky brisket tenderloin shank kevin spare ribs"
right = "porchetta pork loin. Leberkas ball tip biltong, beef ribs"
Similarity.simhash(left, right, ngram_size: 3)
0.484375

Performance

Similarity.simhash is 2x faster than simhash-ex v1.1.0 package.

Benchmark suite executing with the following configuration:
warmup: 2 s
time: 5 s
memory time: 0 ns
parallel: 1
inputs: none specified
Estimated total run time: 14 s
Benchmarking simhash-ex...
Benchmarking similarity.simhash...
Name                         ips        average  deviation         median         99th %
similarity.simhash        3.67 K      272.69 μs     ±6.50%      267.84 μs      353.05 μs
simhash-ex                1.75 K      572.14 μs    ±12.31%      552.22 μs      781.02 μs
Comparison:
similarity.simhash        3.67 K
simhash-ex                1.75 K - 2.10x slower +299.46 μs

License

Similarity is MIT licensed.