feat: add LocalTangentSpaceAlignment

rumale-manifold/lib/rumale/manifold.rb

@@ -5,6 +5,7 @@
 require_relative 'manifold/laplacian_eigenmaps'
 require_relative 'manifold/locally_linear_embedding'
 require_relative 'manifold/hessian_eigenmaps'
+require_relative 'manifold/local_tangent_space_alignment'
 require_relative 'manifold/mds'
 require_relative 'manifold/tsne'
 require_relative 'manifold/version'

rumale-manifold/lib/rumale/manifold/local_tangent_space_alignment.rb

@@ -0,0 +1,142 @@
+# frozen_string_literal: true
+
+require 'rumale/base/estimator'
+require 'rumale/base/transformer'
+require 'rumale/pairwise_metric'
+require 'rumale/validation'
+
+module Rumale
+  module Manifold
+    # LocalTangentSpaceAlignment is a class that implements Local Tangent Space Alignment.
+    #
+    # @example
+    #   require 'numo/linalg/autoloader'
+    #   require 'rumale/manifold/local_tangent_space_alignment'
+    #
+    #   lem = Rumale::Manifold::LocalTangentSpaceAlignment.new(n_components: 2, n_neighbors: 15)
+    #   z = lem.fit_transform(x)
+    #
+    # *Reference*
+    # - Zhang, A., and Zha, H., "Principal Manifolds and Nonlinear Diemnsion Reduction via Local Tangent Space Alignment," SIAM Journal on Scientific Computing, vol. 26, iss. 1, pp. 313-338, 2004.
+    class LocalTangentSpaceAlignment < Rumale::Base::Estimator
+      include Rumale::Base::Transformer
+
+      # Return the data in representation space.
+      # @return [Numo::DFloat] (shape: [n_samples, n_components])
+      attr_reader :embedding
+
+      # Create a new transformer with Local Tangent Space Alignment.
+      #
+      # @param n_components [Integer] The number of dimensions on representation space.
+      # @param n_neighbors [Integer] The number of nearest neighbors for finding k-nearest neighbors
+      # @param reg_param [Float] The reguralization parameter for local gram matrix in transform method.
+      def initialize(n_components: 2, n_neighbors: 10, reg_param: 1e-3)
+        super()
+        @params = {
+          n_components: n_components,
+          n_neighbors: [1, n_neighbors].max,
+          reg_param: reg_param
+        }
+      end
+
+      # Fit the model with given training data.
+      #
+      # @overload fit(x) -> LocalTangentSpaceAlignment
+      #   @param x [Numo::DFloat] (shape: [n_samples, n_features]) The training data to be used for fitting the model.
+      #   @return [LocalTangentSpaceAlignment] The learned transformer itself.
+      def fit(x, _y = nil)
+        unless enable_linalg?(warning: false)
+          raise 'LocalTangentSpaceAlignment#fit requires Numo::Linalg but that is not loaded'
+        end
+
+        x = Rumale::Validation.check_convert_sample_array(x)
+
+        n_samples = x.shape[0]
+        distance_mat = Rumale::PairwiseMetric.squared_error(x)
+        neighbor_ids = neighbor_ids(distance_mat, @params[:n_neighbors], true)
+
+        affinity_mat = Numo::DFloat.zeros(n_samples, n_samples)
+        x_tangent = Numo::DFloat.zeros(@params[:n_neighbors], @params[:n_components] + 1)
+        x_tangent[true, 0] = 1.fdiv(Math.sqrt(@params[:n_neighbors]))
+
+        n_samples.times do |n|
+          x_local = x[neighbor_ids[n, true], true]
+          x_tangent[true, 1...] = right_singular_vectors(x_local, @params[:n_components])
+          weight_mat = x_tangent.dot(x_tangent.transpose)
+          neighbor_ids[n, true].each_with_index do |m, i|
+            affinity_mat[m, neighbor_ids[n, true]] -= weight_mat[i, true]
+            affinity_mat[m, m] += 1
+          end
+        end
+
+        kernel_mat = 0.5 * (affinity_mat.transpose + affinity_mat)
+        _, eig_vecs = Numo::Linalg.eigh(kernel_mat, vals_range: 1...(1 + @params[:n_components]))
+
+        @embedding = @params[:n_components] == 1 ? eig_vecs[true, 0].dup : eig_vecs.dup
+        @x_train = x.dup
+
+        self
+      end
+
+      # Fit the model with training data, and then transform them with the learned model.
+      #
+      # @overload fit_transform(x) -> Numo::DFloat
+      #   @param x [Numo::DFloat] (shape: [n_samples, n_features]) The training data to be used for fitting the model.
+      #   @return [Numo::DFloat] (shape: [n_samples, n_components]) The transformed data
+      def fit_transform(x, _y = nil)
+        unless enable_linalg?(warning: false)
+          raise 'LocalTangentSpaceAlignment#fit_transform requires Numo::Linalg but that is not loaded'
+        end
+
+        fit(x).transform(x)
+      end
+
+      # Transform the given data with the learned model.
+      # For out-of-sample data embedding, the same method as Locally Linear Embedding is used.
+      #
+      # @param x [Numo::DFloat] (shape: [n_samples, n_features]) The data to be transformed with the learned model.
+      # @return [Numo::DFloat] (shape: [n_samples, n_components]) The transformed data.
+      def transform(x)
+        x = Rumale::Validation.check_convert_sample_array(x)
+
+        n_samples = x.shape[0]
+        tol = @params[:reg_param].fdiv(@params[:n_neighbors])
+        distance_mat = Rumale::PairwiseMetric.squared_error(x, @x_train)
+        neighbor_ids = neighbor_ids(distance_mat, @params[:n_neighbors], false)
+        weight_mat = Numo::DFloat.zeros(n_samples, @x_train.shape[0])
+
+        n_samples.times do |n|
+          x_local = @x_train[neighbor_ids[n, true], true] - x[n, true]
+          gram_mat = x_local.dot(x_local.transpose)
+          gram_mat += tol * weight_mat.trace * Numo::DFloat.eye(@params[:n_neighbors])
+          weights = Numo::Linalg.solve(gram_mat, Numo::DFloat.ones(@params[:n_neighbors]))
+          weights /= weights.sum + 1e-8
+          weight_mat[n, neighbor_ids[n, true]] = weights
+        end
+
+        weight_mat.dot(@embedding)
+      end
+
+      private
+
+      def neighbor_ids(distance_mat, n_neighbors, contain_self)
+        n_samples = distance_mat.shape[0]
+        neighbor_ids = Numo::Int32.zeros(n_samples, n_neighbors)
+        if contain_self
+          n_samples.times { |n| neighbor_ids[n, true] = (distance_mat[n, true].sort_index.to_a - [n])[0...n_neighbors] }
+        else
+          n_samples.times { |n| neighbor_ids[n, true] = distance_mat[n, true].sort_index.to_a[0...n_neighbors] }
+        end
+        neighbor_ids
+      end
+
+      def right_singular_vectors(x_local, n_singulars)
+        n_samples = x_local.shape[0]
+        x_local -= x_local.mean(0)
+        gram_mat = x_local.dot(x_local.transpose)
+        _, evecs = Numo::Linalg.eigh(gram_mat, vals_range: (n_samples - n_singulars)...n_samples)
+        evecs.reverse(1).dup
+      end
+    end
+  end
+end

rumale-manifold/spec/rumale/manifold/local_tangent_space_alignment_spec.rb

@@ -0,0 +1,56 @@
+# frozen_string_literal: true
+
+require 'spec_helper'
+
+RSpec.describe Rumale::Manifold::LocalTangentSpaceAlignment do
+  let!(:samples) { swiss_roll }
+  let(:x) { samples[0] }
+  let(:x_test) { samples[1] }
+  let(:n_samples) { x.shape[0] }
+  let(:n_features) { x.shape[1] }
+  let(:n_test_samples) { x_test.shape[0] }
+  let(:ltsa) { described_class.new(n_components: n_components, n_neighbors: 20) }
+  let(:z) { ltsa.fit_transform(x) }
+  let(:z_test) { ltsa.transform(x_test) }
+
+  context 'when mapping to multi-dimensional subspace' do
+    let(:n_components) { 2 }
+
+    it 'maps high-dimensional data into low-dimensional data', :aggregate_failures do
+      expect(z).to be_a(Numo::DFloat)
+      expect(z).to be_contiguous
+      expect(z.ndim).to eq(2)
+      expect(z.shape[0]).to eq(n_samples)
+      expect(z.shape[1]).to eq(n_components)
+      expect(z_test).to be_a(Numo::DFloat)
+      expect(z_test).to be_contiguous
+      expect(z_test.ndim).to eq(2)
+      expect(z_test.shape[0]).to eq(n_test_samples)
+      expect(z_test.shape[1]).to eq(n_components)
+      expect(ltsa.embedding).to be_a(Numo::DFloat)
+      expect(ltsa.embedding).to be_contiguous
+      expect(ltsa.embedding.ndim).to eq(2)
+      expect(ltsa.embedding.shape[0]).to eq(n_samples)
+      expect(ltsa.embedding.shape[1]).to eq(n_components)
+    end
+  end
+
+  context 'when mapping to one-dimensional subspace' do
+    let(:n_components) { 1 }
+
+    it 'maps high-dimensional data into one-dimensional data', :aggregate_failures do
+      expect(z).to be_a(Numo::DFloat)
+      expect(z).to be_contiguous
+      expect(z.ndim).to eq(1)
+      expect(z.shape[0]).to eq(n_samples)
+      expect(z_test).to be_a(Numo::DFloat)
+      expect(z_test).to be_contiguous
+      expect(z_test.ndim).to eq(1)
+      expect(z_test.shape[0]).to eq(n_test_samples)
+      expect(ltsa.embedding).to be_a(Numo::DFloat)
+      expect(ltsa.embedding).to be_contiguous
+      expect(ltsa.embedding.ndim).to eq(1)
+      expect(ltsa.embedding.shape[0]).to eq(n_samples)
+    end
+  end
+end