private void CheckCofiGradient(double lambda) { Matrix X_s = Matrix.Rand(4, 3); Matrix T_s = Matrix.Rand(5, 3); Matrix Y_s = (X_s * T_s.T); Matrix R_s = Matrix.Zeros(Y_s.Rows, Y_s.Cols); Y_s[Matrix.Rand(Y_s.Rows, Y_s.Cols) > 0.5] = 0.0; R_s[Y_s == 0] = 1.0; Matrix X_ts = Matrix.NormRand(X_s.Rows, X_s.Cols); Matrix T_ts = Matrix.NormRand(T_s.Rows, T_s.Cols); ICostFunction costFunction = new CofiCostFunction() { R = R_s, X = X_ts, Y = Y_s.Unshape(), Lambda = 0, Regularizer = null, CollaborativeFeatures = 3 }; costFunction.Initialize(); Vector grad = costFunction.ComputeGradient(Vector.Combine(X_ts.Unshape(), T_ts.Unshape())); Vector numericalGrad = this.ComputeNumericalGradient( f => costFunction.ComputeCost(f), Vector.Combine(X_ts.Unshape(), T_ts.Unshape())); Assert.True(this.CheckNumericalGradient(numericalGrad, grad) < 0.0000000001); }
public void Test_Cofi_CostFunction() { Matrix rMat = Y.ToBinary(i => i > 0d); ICostFunction costFunction = new CofiCostFunction() { R = rMat, X = X, Y = Y.Unshape(), Lambda = 0, Regularizer = null, CollaborativeFeatures = X.Cols }; costFunction.Initialize(); double cost = costFunction.ComputeCost(Vector.Combine(X.Unshape(), Theta.Unshape())); Vector grad = costFunction.ComputeGradient(Vector.Combine(X.Unshape(), Theta.Unshape())); Almost.Equal(39.796d, System.Math.Round(cost, 3), 0.001); this.CheckCofiGradient(0); }
/// <summary> /// Generates a new Collaborative Filtering model. /// </summary> /// <param name="X">Training matrix values.</param> /// <param name="y">Vector of entity identifiers.</param> /// <returns></returns> public override IModel Generate(Matrix X, Vector y) { this.Preprocess(X.Copy()); // inputs are ratings from each user (X = entities x ratings), y = entity id. // create rating range in case we don't have one already if (this.Ratings == null) { this.Ratings = new Range(X.Min(), X.Max()); } // indicator matrix of 1's where rating was provided otherwise 0's. Matrix R = X.ToBinary(f => this.Ratings.Test(f)); // The mean needs to be values within rating range only. Vector mean = X.GetRows().Select(s => s.Where(w => this.Ratings.Test(w)).Sum() / s.Where(w => this.Ratings.Test(w)).Count() ).ToVector(); // update feature averages before preprocessing features. this.FeatureProperties.Average = mean; this.Preprocess(X); // where references could be user ratings and entities are movies / books, etc. int references = X.Cols, entities = X.Rows; // initialize Theta parameters Matrix ThetaX = Matrix.Rand(entities, this.CollaborativeFeatures, -1d); Matrix ThetaY = Matrix.Rand(references, this.CollaborativeFeatures, -1d); ICostFunction costFunction = new CofiCostFunction() { CollaborativeFeatures = this.CollaborativeFeatures, Lambda = this.Lambda, R = R, Regularizer = null, X = ThetaX, Y = X.Unshape() }; // we're optimising two params so combine them Vector Theta = Vector.Combine(ThetaX.Unshape(), ThetaY.Unshape()); Optimizer optimizer = new Optimizer(Theta, this.MaxIterations, this.LearningRate) { CostFunction = costFunction }; optimizer.Run(); // extract the optimised parameter Theta ThetaX = optimizer.Properties.Theta.Slice(0, (ThetaX.Rows * ThetaX.Cols) - 1).Reshape(entities, VectorType.Row); ThetaY = optimizer.Properties.Theta.Slice(ThetaX.Rows * ThetaX.Cols, Theta.Length - 1).Reshape(references, VectorType.Row); // create reference mappings, each value is the original index. this.ReferenceFeatureMap = (this.ReferenceFeatureMap == null ? Vector.Create(references, i => i) : this.ReferenceFeatureMap); this.EntityFeatureMap = (this.EntityFeatureMap == null ? Vector.Create(entities, i => i) : this.EntityFeatureMap); return(new CofiRecommenderModel() { Descriptor = this.Descriptor, NormalizeFeatures = this.NormalizeFeatures, FeatureNormalizer = this.FeatureNormalizer, FeatureProperties = this.FeatureProperties, Ratings = this.Ratings, ReferenceFeatureMap = this.ReferenceFeatureMap, EntityFeatureMap = this.EntityFeatureMap, Mu = mean, Y = y, Reference = X, ThetaX = ThetaX, ThetaY = ThetaY }); }