Brute k-NN

lib/scholar/neighbors/brute_knn.ex

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+defmodule Scholar.Neighbors.BruteKNN do
+  @moduledoc """
+  Brute-Force k-Nearest Neighbor Search Algorithm.
+
+  In order to find the k-nearest neighbors the algorithm calculates
+  the distance between the query point and each of the data samples.
+  Therefore, its time complexity is $O(MN)$ for $N$ samples and $M$ query points.
+  It uses $O(BN)$ memory for batch size $B$.
+  Larger batch sizes will lead to faster predictions, but will consume more memory.
+  """
+  import Nx.Defn
+  import Scholar.Shared
+  require Nx
+
+  @derive {Nx.Container, keep: [:num_neighbors, :metric, :batch_size], containers: [:data]}
+  defstruct [:num_neighbors, :metric, :data, :batch_size]
+
+  opts = [
+    num_neighbors: [
+      required: true,
+      type: :pos_integer,
+      doc: "The number of nearest neighbors."
+    ],
+    metric: [
+      type: {:or, [{:custom, Scholar.Options, :metric, []}, {:fun, 2}]},
+      default: {:minkowski, 2},
+      doc: ~S"""
+      The function that measures distance between two points. Possible values:
+
+      * `{:minkowski, p}` - Minkowski metric. By changing value of `p` parameter (a positive number or `:infinity`)
+      we can set Manhattan (`1`), Euclidean (`2`), Chebyshev (`:infinity`), or any arbitrary $L_p$ metric.
+
+      * `:cosine` - Cosine metric.
+
+      * Anonymous function of arity 2 that takes two rank-1 tensors of same dimension and returns a scalar.
+      """
+    ],
+    batch_size: [
+      type: :pos_integer,
+      doc: "The number of samples in a batch."
+    ]
+  ]
+
+  @opts_schema NimbleOptions.new!(opts)
+
+  @doc """
+  Fits a brute-force k-NN model.
+
+  ## Options
+
+  #{NimbleOptions.docs(@opts_schema)}
+
+  ## Examples
+
+      iex> data = Nx.tensor([[1, 2], [2, 3], [3, 4], [4, 5], [5, 6]])
+      iex> model = Scholar.Neighbors.BruteKNN.fit(data, num_neighbors: 2)
+      iex> model.num_neighbors
+      2
+      iex> model.data
+      #Nx.Tensor<
+        s64[5][2]
+        [
+          [1, 2],
+          [2, 3],
+          [3, 4],
+          [4, 5],
+          [5, 6]
+        ]
+      >
+  """
+  deftransform fit(data, opts) do
+    if Nx.rank(data) != 2 do
+      raise ArgumentError,
+            "expected input tensor to have shape {num_samples, num_features},
+             got tensor with shape: #{inspect(Nx.shape(data))}"
+    end
+
+    opts = NimbleOptions.validate!(opts, @opts_schema)
+    k = opts[:num_neighbors]
+
+    if k > Nx.axis_size(data, 0) do
+      raise ArgumentError,
+            """
+            expected num_neighbors to be less than or equal to \
+            num_samples = #{Nx.axis_size(data, 0)}, got: #{k}
+            """
+    end
+
+    metric =
+      case opts[:metric] do
+        {:minkowski, p} ->
+          &Scholar.Metrics.Distance.minkowski(&1, &2, p: p)
+
+        :cosine ->
+          &Scholar.Metrics.Distance.cosine/2
+
+        fun when is_function(fun, 2) ->
+          fun
+      end
+
+    %__MODULE__{
+      num_neighbors: k,
+      metric: metric,
+      data: data,
+      batch_size: opts[:batch_size]
+    }
+  end
+
+  @doc """
+  Computes nearest neighbors of query tensor using brute-force search.
+  Returns the neighbors indices and distances from query points.
+
+  ## Examples
+
+      iex> data = Nx.tensor([[1, 2], [2, 3], [3, 4], [4, 5], [5, 6]])
+      iex> model = Scholar.Neighbors.BruteKNN.fit(data, num_neighbors: 2)
+      iex> query = Nx.tensor([[1, 3], [4, 2], [3, 6]])
+      iex> {neighbors, distances} = Scholar.Neighbors.BruteKNN.predict(model, query)
+      iex> neighbors
+      #Nx.Tensor<
+        u64[3][2]
+        [
+          [0, 1],
+          [1, 2],
+          [3, 2]
+        ]
+      >
+      iex> distances
+      #Nx.Tensor<
+        f32[3][2]
+        [
+          [1.0, 1.0],
+          [2.2360680103302, 2.2360680103302],
+          [1.4142135381698608, 2.0]
+        ]
+      >
+  """
+  deftransform predict(%__MODULE__{} = model, query) do
+    if Nx.rank(query) != 2 do
+      raise ArgumentError,
+            "expected query tensor to have shape {num_queries, num_features},
+             got tensor with shape: #{inspect(Nx.shape(query))}"
+    end
+
+    if Nx.axis_size(model.data, 1) != Nx.axis_size(query, 1) do
+      raise ArgumentError,
+            """
+            expected query tensor to have the same dimension as tensor used for fitting the model, \
+            got #{inspect(Nx.axis_size(model.data, 1))} \
+            and #{inspect(Nx.axis_size(query, 1))}
+            """
+    end
+
+    predict_n(model, query)
+  end
+
+  defn predict_n(%__MODULE__{} = model, query) do
+    k = model.num_neighbors
+    metric = model.metric
+    data = model.data
+    type = Nx.Type.merge(to_float_type(data), to_float_type(query))
+    query_size = Nx.axis_size(query, 0)
+
+    batch_size =
+      case model.batch_size do
+        nil -> query_size
+        _ -> min(model.batch_size, query_size)
+      end
+
+    {batches, leftover} = get_batches(query, batch_size: batch_size)
+    num_batches = Nx.axis_size(batches, 0)
+
+    {neighbor_indices, neighbor_distances, _} =
+      while {
+              neighbor_indices = Nx.broadcast(Nx.u64(0), {query_size, k}),
+              neighbor_distances =
+                Nx.broadcast(Nx.as_type(:nan, type), {query_size, k}),
+              {
+                data,
+                batches,
+                i = Nx.u64(0)
+              }
+            },
+            i < num_batches do
+        batch = batches[i]
+
+        {batch_indices, batch_distances} =
+          brute_force_search(data, batch, num_neighbors: k, metric: metric)
+
+        neighbor_indices = Nx.put_slice(neighbor_indices, [i * batch_size, 0], batch_indices)
+
+        neighbor_distances =
+          Nx.put_slice(neighbor_distances, [i * batch_size, 0], batch_distances)
+
+        {neighbor_indices, neighbor_distances, {data, batches, i + 1}}
+      end
+
+    {neighbor_indices, neighbor_distances} =
+      case leftover do
+        nil ->
+          {neighbor_indices, neighbor_distances}
+
+        _ ->
+          leftover_size = Nx.axis_size(leftover, 0)
+
+          leftover =
+            Nx.slice_along_axis(query, query_size - leftover_size, leftover_size, axis: 0)
+
+          {leftover_indices, leftover_distances} =
+            brute_force_search(data, leftover, num_neighbors: k, metric: metric)
+
+          neighbor_indices =
+            Nx.put_slice(neighbor_indices, [num_batches * batch_size, 0], leftover_indices)
+
+          neighbor_distances =
+            Nx.put_slice(neighbor_distances, [num_batches * batch_size, 0], leftover_distances)
+
+          {neighbor_indices, neighbor_distances}
+      end
+
+    {neighbor_indices, neighbor_distances}
+  end
+
+  defn get_batches(tensor, opts) do
+    {size, dim} = Nx.shape(tensor)
+    batch_size = opts[:batch_size]
+    num_batches = div(size, batch_size)
+    leftover_size = rem(size, batch_size)
+
+    batches =
+      tensor
+      |> Nx.slice_along_axis(0, num_batches * batch_size, axis: 0)
+      |> Nx.reshape({num_batches, batch_size, dim})
+
+    leftover =
+      if leftover_size > 0 do
+        Nx.slice_along_axis(tensor, num_batches * batch_size, leftover_size, axis: 0)
+      else
+        nil
+      end
+
+    {batches, leftover}
+  end
+
+  defnp brute_force_search(data, query, opts) do
+    k = opts[:num_neighbors]
+    metric = opts[:metric]
+    {m, d} = Nx.shape(data)
+    n = Nx.axis_size(query, 0)
+    x = query |> Nx.new_axis(1) |> Nx.broadcast({n, m, d}) |> Nx.vectorize([:query, :data])
+    y = data |> Nx.new_axis(0) |> Nx.broadcast({n, m, d}) |> Nx.vectorize([:query, :data])
+    distances = metric.(x, y) |> Nx.devectorize() |> Nx.rename(nil)
+
+    neighbor_indices =
+      Nx.argsort(distances, axis: 1, type: :u64) |> Nx.slice_along_axis(0, k, axis: 1)
+
+    neighbor_distances = Nx.take_along_axis(distances, neighbor_indices, axis: 1)
+    {neighbor_indices, neighbor_distances}
+  end
+end

test/scholar/neighbors/brute_knn_test.exs

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+defmodule Scholar.Neighbors.BruteKNNTest do
+  use ExUnit.Case, async: true
+  alias Scholar.Neighbors.BruteKNN
+  doctest BruteKNN
+
+  defp data do
+    Nx.tensor([
+      [10, 15],
+      [46, 63],
+      [68, 21],
+      [40, 33],
+      [25, 54],
+      [15, 43],
+      [44, 58],
+      [45, 40],
+      [62, 69],
+      [53, 67]
+    ])
+  end
+
+  defp query do
+    Nx.tensor([
+      [12, 23],
+      [55, 30],
+      [41, 57],
+      [64, 72],
+      [26, 39]
+    ])
+  end
+
+  defp result do
+    neighbor_indices =
+      Nx.tensor(
+        [
+          [0, 5, 3],
+          [7, 3, 2],
+          [6, 1, 9],
+          [8, 9, 1],
+          [5, 4, 3]
+        ],
+        type: :u64
+      )
+
+    neighbor_distances =
+      Nx.tensor([
+        [8.246211051940918, 20.2237491607666, 29.73213768005371],
+        [14.142135620117188, 15.29705810546875, 15.81138801574707],
+        [3.1622776985168457, 7.8102498054504395, 15.620499610900879],
+        [3.605551242828369, 12.083045959472656, 20.124610900878906],
+        [11.704699516296387, 15.033296585083008, 15.231546401977539]
+      ])
+
+    {neighbor_indices, neighbor_distances}
+  end
+
+  describe "fit" do
+    test "default" do
+      data = data()
+      k = 3
+      model = BruteKNN.fit(data, num_neighbors: k)
+      assert model.num_neighbors == 3
+      assert model.data == data
+      assert model.batch_size == nil
+    end
+
+    test "custom metric and batch_size" do
+      data = data()
+      k = 3
+      metric = &Scholar.Metrics.Distance.minkowski/2
+      batch_size = 2
+      model = BruteKNN.fit(data, num_neighbors: k, metric: metric, batch_size: batch_size)
+      assert model.num_neighbors == k
+      assert model.metric == metric
+      assert model.data == data
+      assert model.batch_size == batch_size
+    end
+  end
+
+  describe "predict" do
+    test "batch_size = 1" do
+      query = query()
+      k = 3
+      model = BruteKNN.fit(data(), num_neighbors: k, batch_size: 1)
+      {neighbors_true, distances_true} = result()
+      {neighbors_pred, distances_pred} = BruteKNN.predict(model, query)
+      assert neighbors_pred == neighbors_true
+      assert distances_pred == distances_true
+    end
+
+    test "batch_size = 2" do
+      query = query()
+      k = 3
+      model = BruteKNN.fit(data(), num_neighbors: k, batch_size: 2)
+      {neighbors_true, distances_true} = result()
+      {neighbors_pred, distances_pred} = BruteKNN.predict(model, query)
+      assert neighbors_pred == neighbors_true
+      assert distances_pred == distances_true
+    end
+
+    test "batch_size = 5" do
+      query = query()
+      k = 3
+      model = BruteKNN.fit(data(), num_neighbors: k, batch_size: 5)
+      {neighbors_true, distances_true} = result()
+      {neighbors_pred, distances_pred} = BruteKNN.predict(model, query)
+      assert neighbors_pred == neighbors_true
+      assert distances_pred == distances_true
+    end
+
+    test "batch_size = 10" do
+      query = query()
+      k = 3
+      model = BruteKNN.fit(data(), num_neighbors: k, batch_size: 10)
+      {neighbors_true, distances_true} = result()
+      {neighbors_pred, distances_pred} = BruteKNN.predict(model, query)
+
+      assert neighbors_pred ==
+               neighbors_true
+
+      assert distances_pred == distances_true
+    end
+  end
+end