Random Projection Forest

lib/scholar/neighbors/random_projection_forest.ex

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+defmodule Scholar.Neighbors.RandomProjectionForest do
+  @moduledoc """
+  Random Projection Forest.
+
+  Each tree in a forest is constructed using a divide and conquer approach.
+  We start with the entire dataset and at every node we project the data onto a random
+  hyperplane and split it in the following way: the points with the projection smaller
+  than or equal to the median are put into the left subtree and the points with projection
+  greater than the median are put into the right subtree. We then proceed
+  recursively with the left and right subtree.
+
+  In this implementation the trees are complete, i.e. there are 2^l nodes at level l.
+  The leaves of the trees are arranged as blocks in the field `indices`. We use the same
+  hyperplane for all nodes on the same level as in [2].
+
+  * [1] - Random projection trees and low dimensional manifolds
+  * [2] - Fast Nearest Neighbor Search through Sparse Random Projections and Voting
+  """
+
+  import Nx.Defn
+  import Scholar.Shared
+  require Nx
+
+  @derive {Nx.Container,
+           keep: [:depth, :leaf_size, :num_trees],
+           containers: [:indices, :data, :hyperplanes, :medians]}
+  @enforce_keys [:depth, :leaf_size, :num_trees, :indices, :data, :hyperplanes, :medians]
+  defstruct [:depth, :leaf_size, :num_trees, :indices, :data, :hyperplanes, :medians]
+
+  opts = [
+    num_trees: [
+      required: true,
+      type: :pos_integer,
+      doc: "The number of trees in the forest."
+    ],
+    min_leaf_size: [
+      required: true,
+      type: :pos_integer,
+      doc: "The minumum number of points in the leaf."
+    ],
+    key: [
+      type: {:custom, Scholar.Options, :key, []},
+      doc: """
+      Used for random number generation in hyperplane initialization.
+      If the key is not provided, it is set to `Nx.Random.key(System.system_time())`.
+      """
+    ]
+  ]
+
+  @opts_schema NimbleOptions.new!(opts)
+
+  @doc """
+  Grows a random projection forest.
+
+  ## Options
+
+  #{NimbleOptions.docs(@opts_schema)}
+
+  ## Examples
+
+      iex> key = Nx.Random.key(12)
+      iex> tensor = Nx.iota({5, 2})
+      iex> forest = Scholar.Neighbors.RandomProjectionForest.fit(tensor, num_trees: 3, min_leaf_size: 2, key: key)
+      iex> forest.indices
+      #Nx.Tensor<
+        u32[3][5]
+        [
+          [0, 1, 2, 3, 4],
+          [0, 1, 2, 3, 4],
+          [4, 3, 2, 1, 0]
+        ]
+      >
+  """
+  deftransform fit(tensor, opts) do
+    if Nx.rank(tensor) != 2 do
+      raise ArgumentError,
+            """
+            expected input tensor to have shape {num_samples, num_features}, \
+            got tensor with shape: #{inspect(Nx.shape(tensor))}\
+            """
+    end
+
+    opts = NimbleOptions.validate!(opts, @opts_schema)
+    min_leaf_size = opts[:min_leaf_size]
+    num_trees = opts[:num_trees]
+    key = Keyword.get_lazy(opts, :key, fn -> Nx.Random.key(System.system_time()) end)
+    size = Nx.axis_size(tensor, 0)
+    # TODO: Try calculating depth from tensor
+    # floor(log2(size / min_leaf_size)) might do the job!
+    {depth, leaf_size} = compute_depth_and_leaf_size(size, min_leaf_size, 0)
+
+    if depth == 0 do
+      raise ArgumentError,
+            """
+            expected num_samples to be at least twice \
+            min_leaf_size = #{inspect(min_leaf_size)}, got #{inspect(size)}
+            """
+    end
+
+    {indices, hyperplanes, medians} = fit_n(tensor, key, depth: depth, num_trees: num_trees)
+
+    %__MODULE__{
+      depth: depth,
+      leaf_size: leaf_size,
+      num_trees: num_trees,
+      indices: indices,
+      data: tensor,
+      hyperplanes: hyperplanes,
+      medians: medians
+    }
+  end
+
+  defp compute_depth_and_leaf_size(size, min_leaf_size, depth) do
+    right_size = div(size, 2)
+    left_size = right_size + rem(size, 2)
+
+    cond do
+      right_size < min_leaf_size ->
+        {depth, size}
+
+      right_size == min_leaf_size ->
+        {depth + 1, left_size}
+
+      true ->
+        new_size = if rem(left_size, 2) == 1, do: left_size, else: right_size
+        compute_depth_and_leaf_size(new_size, min_leaf_size, depth + 1)
+    end
+  end
+
+  defn fit_n(tensor, key, opts) do
+    depth = opts[:depth]
+    num_trees = opts[:num_trees]
+    type = to_float_type(tensor)
+    {size, dim} = Nx.shape(tensor)
+    num_nodes = 2 ** depth - 1
+
+    {hyperplanes, _key} =
+      Nx.Random.normal(key, type: type, shape: {num_trees, depth, dim})
+
+    {indices, medians, _} =
+      while {
+              indices = Nx.iota({num_trees, size}, axis: 1, type: :u32),
+              medians = Nx.broadcast(Nx.tensor(:nan, type: type), {num_trees, num_nodes}),
+              {
+                tensor,
+                hyperplanes,
+                level = Nx.u32(0),
+                pos = Nx.iota({size}, type: :u32),
+                cell_sizes = Nx.broadcast(Nx.u32(size), {size}),
+                tags = Nx.broadcast(Nx.u32(0), {size}),
+                nodes = Nx.iota({num_nodes}, type: :u32),
+                width = Nx.u32(1),
+                median_offset = Nx.u32(0)
+              }
+            },
+            level < depth do
+        level_proj =
+          Nx.dot(hyperplanes[[.., level]], [1], tensor, [1])
+          |> Nx.take_along_axis(indices, axis: 1)
+
+        level_indices = Nx.argsort(level_proj, axis: 1, type: :u32, stable: true)
+        orders = Nx.argsort(tags[level_indices], axis: 1, stable: true, type: :u32)
+        level_indices = Nx.take_along_axis(level_indices, orders, axis: 1)
+        indices = Nx.take_along_axis(indices, level_indices, axis: 1)
+        level_proj = Nx.take_along_axis(level_proj, level_indices, axis: 1)
+
+        right_sizes = Nx.quotient(cell_sizes, 2)
+        left_sizes = right_sizes + Nx.remainder(cell_sizes, 2)
+        cell_sizes = Nx.select(pos < left_sizes, left_sizes, right_sizes)
+        tags = 2 * tags + (pos >= cell_sizes)
+
+        medians =
+          update_medians(
+            pos,
+            left_sizes,
+            right_sizes,
+            level_proj,
+            nodes,
+            width,
+            median_offset,
+            medians
+          )
+
+        pos = Nx.remainder(pos, left_sizes)
+
+        {
+          indices,
+          medians,
+          {tensor, hyperplanes, level + 1, pos, cell_sizes, tags, nodes, 2 * width,
+           2 * median_offset + 1}
+        }
+      end
+
+    {indices, hyperplanes, medians}
+  end
+
+  defnp update_medians(
+          pos,
+          left_sizes,
+          right_sizes,
+          level_proj,
+          nodes,
+          width,
+          median_offset,
+          medians
+        ) do
+    size = Nx.size(pos)
+    {num_trees, num_nodes} = Nx.shape(medians)
+
+    left_mask = pos == left_sizes - 1
+
+    left_indices =
+      Nx.argsort(left_mask, direction: :desc, stable: true, type: :u32)
+      |> Nx.new_axis(0)
+      |> Nx.broadcast({num_trees, size})
+
+    left_first = Nx.take_along_axis(level_proj, left_indices, axis: 1)
+
+    right_mask = pos == right_sizes
+
+    right_indices =
+      Nx.argsort(right_mask, direction: :desc, stable: true, type: :u32)
+      |> Nx.new_axis(0)
+      |> Nx.broadcast({num_trees, size})
+
+    right_first = Nx.take_along_axis(level_proj, right_indices, axis: 1)
+
+    medians_first = (left_first + right_first) / 2
+
+    median_mask = width <= nodes and nodes < width + median_offset
+    median_pos = Nx.argsort(median_mask, direction: :desc, stable: true, type: :u32)
+    level_medians = Nx.take(medians_first, median_pos, axis: 1)
+
+    level_mask =
+      (median_offset <= nodes and nodes < median_offset + width)
+      |> Nx.new_axis(0)
+      |> Nx.broadcast({num_trees, num_nodes})
+
+    Nx.select(
+      level_mask,
+      level_medians,
+      medians
+    )
+  end
+
+  @doc """
+  Computes the leaf indices for every point in the input tensor.
+  If the input tensor contains n points, then the result has shape {n, num_trees, leaf_size}.
+
+  ## Examples
+
+      iex> key = Nx.Random.key(12)
+      iex> tensor = Nx.iota({5, 2})
+      iex> forest = Scholar.Neighbors.RandomProjectionForest.fit(tensor, num_trees: 3, min_leaf_size: 2, key: key)
+      iex> x = Nx.tensor([[3, 4]])
+      iex> Scholar.Neighbors.RandomProjectionForest.predict(forest, x)
+      #Nx.Tensor<
+        u32[1][3][3]
+        [
+          [
+            [0, 1, 2],
+            [0, 1, 2],
+            [4, 3, 2]
+          ]
+        ]
+      >
+  """
+  deftransform predict(%__MODULE__{} = forest, x) do
+    if Nx.rank(x) != 2 do
+      raise ArgumentError,
+            """
+            expected input tensor to have shape {num_samples, num_features}, \
+            got tensor with shape: #{inspect(Nx.shape(x))}\
+            """
+    end
+
+    if Nx.axis_size(forest.hyperplanes, 2) != Nx.axis_size(x, 1) do
+      raise ArgumentError,
+            """
+            expected hyperplanes and input tensor to have the same dimension, \
+            got #{inspect(Nx.axis_size(forest.hyperplanes, 2))} \
+            and #{inspect(Nx.axis_size(x, 1))}
+            """
+    end
+
+    predict_n(forest, x)
+  end
+
+  defn predict_n(forest, x) do
+    num_trees = forest.num_trees
+    leaf_size = forest.leaf_size
+    indices = forest.indices |> Nx.vectorize(:trees)
+    start_indices = compute_start_indices(forest, x, leaf_size: leaf_size) |> Nx.new_axis(1)
+    size = Nx.axis_size(x, 0)
+
+    pos =
+      Nx.iota({1, 1, leaf_size})
+      |> Nx.broadcast({num_trees, size, leaf_size})
+      |> Nx.vectorize(:trees)
+      |> Nx.add(start_indices)
+
+    Nx.take(indices, pos)
+    |> Nx.devectorize()
+    |> Nx.rename(nil)
+    |> Nx.transpose(axes: [1, 0, 2])
+  end
+
+  defn compute_start_indices(forest, x, opts) do
+    leaf_size = opts[:leaf_size]
+    size = Nx.axis_size(x, 0)
+    depth = forest.depth
+    num_trees = forest.num_trees
+    hyperplanes = forest.hyperplanes |> Nx.vectorize(:trees)
+    medians = forest.medians |> Nx.vectorize(:trees)
+
+    {start_indices, left?, cell_sizes, _} =
+      while {
+              start_indices = Nx.broadcast(Nx.u32(0), {num_trees, size}) |> Nx.vectorize(:trees),
+              _left? = Nx.broadcast(Nx.u8(0), {num_trees, size}) |> Nx.vectorize(:trees),
+              cell_sizes = Nx.broadcast(Nx.u32(size), {num_trees, size}) |> Nx.vectorize(:trees),
+              {
+                x,
+                hyperplanes,
+                medians,
+                level = 0,
+                nodes = Nx.broadcast(Nx.u32(0), {num_trees, size}) |> Nx.vectorize(:trees)
+              }
+            },
+            level < depth do
+        h = hyperplanes[level]
+        median = Nx.take(medians, nodes)
+        proj = Nx.dot(x, h)
+        left? = proj <= median
+
+        nodes =
+          Nx.select(
+            left?,
+            left_child(nodes),
+            right_child(nodes)
+          )
+
+        right_sizes = Nx.quotient(cell_sizes, 2)
+        left_sizes = right_sizes + Nx.remainder(cell_sizes, 2)
+        start_indices = Nx.select(left?, start_indices, start_indices + left_sizes)
+        cell_sizes = Nx.select(left?, left_sizes, right_sizes)
+
+        {
+          start_indices,
+          left?,
+          cell_sizes,
+          {x, hyperplanes, medians, level + 1, nodes}
+        }
+      end
+
+    Nx.select(not left? and cell_sizes < leaf_size, start_indices - 1, start_indices)
+  end
+
+  defn left_child(nodes) do
+    2 * nodes + 1
+  end
+
+  defn right_child(nodes) do
+    2 * nodes + 2
+  end
+end