Add Hamming Distance (#58)

.formatter.exs

@@ -1,4 +1,5 @@
 # Used by "mix format"
 [
+  import_deps: [:nx],
   inputs: ["{mix,.formatter}.exs", "{config,lib,test}/**/*.{ex,exs}"]
 ]

lib/scholar/metrics/distance.ex

@@ -407,4 +407,68 @@ defmodule Scholar.Metrics.Distance do
     res = Nx.select(one_zero?, 0.0, res)
     1.0 - Nx.select(both_zero?, 1.0, res)
   end
+
+  @doc """
+  Hamming distance.
+
+  $$
+  hamming(x ,y) = \frac{\#\{x_{i, j...} \neq y_{i, j, ...}\}}{\#x_{i, j, ...}}$, where $i, j, ...$ are the aggregation axes
+  $$
+
+  ## Options
+
+  #{NimbleOptions.docs(@general_schema)}
+
+  ## Examples
+
+      iex> x = Nx.tensor([1, 0, 0])
+      iex> y = Nx.tensor([0, 1, 0])
+      iex> Scholar.Metrics.Distance.hamming(x, y)
+      #Nx.Tensor<
+        f32
+        0.6666666865348816
+      >
+      iex> weights = Nx.tensor([1, 0.5, 0.5])
+      iex> Scholar.Metrics.Distance.hamming(x, y, weights)
+      #Nx.Tensor<
+        f32
+        0.75
+      >
+
+      iex> x = Nx.tensor([1, 2])
+      iex> y = Nx.tensor([1, 2, 3])
+      iex> Scholar.Metrics.Distance.hamming(x, y)
+      ** (ArgumentError) expected tensor to have shape {2}, got tensor with shape {3}
+
+      iex> x = Nx.tensor([[1, 2, 3], [0, 0, 0], [5, 2, 4]])
+      iex> y = Nx.tensor([[1, 5, 2], [2, 4, 1], [0, 0, 0]])
+      iex> Scholar.Metrics.Distance.hamming(x, y, axes: [1])
+      #Nx.Tensor<
+        f32[3]
+        [0.6666666865348816, 1.0, 1.0]
+      >
+  """
+  deftransform hamming(x, y), do: hamming_unweighted(x, y)
+
+  deftransform hamming(x, y, opts) when is_list(opts) do
+    NimbleOptions.validate!(opts, @general_schema)
+    hamming_unweighted(x, y, opts)
+  end
+
+  deftransform hamming(x, y, w), do: hamming_weighted(x, y, w)
+
+  deftransform hamming(x, y, w, opts) when is_list(opts) do
+    NimbleOptions.validate!(opts, @general_schema)
+    hamming_weighted(x, y, w, opts)
+  end
+
+  defnp hamming_unweighted(x, y, opts \\ []) do
+    assert_same_shape!(x, y)
+    (x != y) |> Nx.mean(axes: opts[:axes])
+  end
+
+  defnp hamming_weighted(x, y, w, opts \\ []) do
+    assert_same_shape!(x, y)
+    (x != y) |> Nx.weighted_mean(w, axes: opts[:axes])
+  end
 end

test/scholar/metrics/distance_test.exs

@@ -52,4 +52,18 @@ defmodule Scholar.Metrics.DistanceTest do
   test "cosine matches scipy" do
     assert_all_close(Distance.cosine(@x, @y), Nx.tensor(0.7650632810164779))
   end
+
+  test "hamming matches scipy" do
+    assert Distance.hamming(Nx.tensor([1, 0, 0]), Nx.tensor([0, 1, 0])) ==
+             Nx.tensor(0.6666666865348816)
+
+    assert Distance.hamming(Nx.tensor([1, 0, 0]), Nx.tensor([1, 1, 0])) ==
+             Nx.tensor(0.3333333432674408)
+
+    assert Distance.hamming(Nx.tensor([1, 0, 0]), Nx.tensor([2, 0, 0])) ==
+             Nx.tensor(0.3333333432674408)
+
+    assert Distance.hamming(Nx.tensor([1, 0, 0]), Nx.tensor([3, 0, 0])) ==
+             Nx.tensor(0.3333333432674408)
+  end
 end