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lib/scholar/manifold/mds.ex

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+defmodule Scholar.Manifold.MDS do
+  @moduledoc """
+  TSNE (t-Distributed Stochastic Neighbor Embedding) is a nonlinear dimensionality reduction technique.
+
+  ## References
+
+  * [t-SNE: t-Distributed Stochastic Neighbor Embedding](http://www.jmlr.org/papers/volume9/vandermaaten08a/vandermaaten08a.pdf)
+  """
+  import Nx.Defn
+  import Scholar.Shared
+  alias Scholar.Metrics.Distance
+
+  # initialize x randomly or pass the init x earlier
+  defnp smacof(dissimilarities, x, max_iter, opts) do
+    num_samples = Nx.axis_size(dissimilarities, 0)
+    similarities_flat = Nx.flatten((1 - Nx.tri(num_samples)) * dissimilarities)
+    similarities_flat_indices = remove_main_diag_indices(similarities_flat)
+
+    n = Nx.axis_size(dissimilarities, 0)
+
+    similarities_flat_w =
+      Nx.take(similarities_flat, similarities_flat_indices) |> Nx.reshape({n, n - 1})
+
+    res =
+      while {{x, stress = Nx.Constants.infinity(), i = 0}, dissimilarities, max_iter,
+             similarities_flat_indices, similarities_flat, old_stress = Nx.Constants.infinity(),
+             stop_value = 0},
+            i < max_iter and not stop_value do
+        dis = Distance.pairwise_euclidean(x)
+
+        disparities =
+          if opts[:metric] do
+            dissimilarities
+          else
+            dis_flat = Nx.flatten(dis)
+
+            dis_flat_indices = remove_main_diag_indices(dis_flat)
+
+            n = Nx.axis_size(dis, 0)
+
+            dis_flat_w = Nx.take(dis_flat, dis_flat_indices) |> Nx.reshape({n, n - 1})
+            # dis_flat_w = Nx.flatten(remove_main_diag(dis))
+
+            disparities_flat =
+              Scholar.Linear.IsotonicRegression.fit(similarities_flat_w, dis_flat_w)
+
+            disparities_flat =
+              Scholar.Linear.IsotonicRegression.predict(disparities_flat, similarities_flat_w)
+
+            # disparities = Nx.select(similarities_flat != 0, disparities_flat, disparities)
+
+            disparities = Nx.indexed_put(dis_flat, similarities_flat_indices, disparities_flat)
+            disparities = Nx.reshape(disparities, {n, n})
+
+            disparities * Nx.sum(Nx.sqrt(n * (n - 1) / 2 / disparities ** 2))
+          end
+
+        stress = Nx.sum((Nx.flatten(dis) - Nx.flatten(disparities)) ** 2) / 2
+
+        stress =
+          if opts[:normalized_stress] do
+            Nx.sqrt(stress / (Nx.sum(Nx.flatten(disparities) ** 2) / 2))
+          else
+            stress
+          end
+
+        dis = Nx.select(dis == 0, 1.0e-5, dis)
+        ratio = disparities / dis
+        b = -ratio
+        b = Nx.put_diagonal(b, Nx.take_diagonal(b) + Nx.sum(ratio, axes: [1]))
+        x = 1.0 / n * Nx.dot(b, x)
+
+        dis = Nx.sum(Nx.sqrt(Nx.sum(x ** 2, axes: [1])))
+
+        stop_value = if old_stress - stress / dis < opts[:eps], do: 1, else: 0
+
+        old_stress = stress / dis
+
+        {{x, stress, i + 1}, dissimilarities, max_iter, similarities_flat_indices,
+         similarities_flat, old_stress, stop_value}
+      end
+  end
+
+  defn remove_main_diag_indices(tensor) do
+    n = Nx.axis_size(tensor, 0)
+
+    temp =
+      Nx.broadcast(Nx.s64(0), {n})
+      |> Nx.indexed_put(Nx.new_axis(0, -1), Nx.s64(1))
+      |> Nx.tile([n - 1])
+
+    Nx.iota({n * (n - 1)}) + Nx.cumulative_sum(temp)
+    # indices = Nx.iota({n * (n - 1)}) + Nx.cumulative_sum(temp)
+    # Nx.take(Nx.flatten(tensor), indices) |> Nx.reshape({n, n - 1})
+  end
+end