source: branches/Weighted TSNE/3.4/TSNE/TSNEAlgorithm.cs @ 15525

#region License Information
/* HeuristicLab
 * Copyright (C) 2002-2016 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
 *
 * This file is part of HeuristicLab.
 *
 * HeuristicLab is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * HeuristicLab is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
 */
#endregion

using System;
using System.Collections.Generic;
using System.Drawing;
using System.Linq;
using System.Threading;
using HeuristicLab.Analysis;
using HeuristicLab.Common;
using HeuristicLab.Core;
using HeuristicLab.Data;
using HeuristicLab.Optimization;
using HeuristicLab.Parameters;
using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
using HeuristicLab.PluginInfrastructure;
using HeuristicLab.Problems.DataAnalysis;
using HeuristicLab.Random;

namespace HeuristicLab.Algorithms.DataAnalysis {
  /// <summary>
  /// t-distributed stochastic neighbourhood embedding (tSNE) projects the data in a low dimensional 
  /// space to allow visual cluster identification.
  /// </summary>
  [Item("tSNE", "t-distributed stochastic neighbourhood embedding projects the data in a low " +
                "dimensional space to allow visual cluster identification. Implemented similar to: https://lvdmaaten.github.io/tsne/#implementations (Barnes-Hut t-SNE). Described in : https://lvdmaaten.github.io/publications/papers/JMLR_2014.pdf")]
  [Creatable(CreatableAttribute.Categories.DataAnalysis, Priority = 100)]
  [StorableClass]
  public sealed class TSNEAlgorithm : BasicAlgorithm {
    public override bool SupportsPause {
      get { return true; }
    }
    public override Type ProblemType {
      get { return typeof(IDataAnalysisProblem); }
    }
    public new IDataAnalysisProblem Problem {
      get { return (IDataAnalysisProblem) base.Problem; }
      set { base.Problem = value; }
    }

    #region Parameter names
    private const string DistanceFunctionParameterName = "DistanceFunction";
    private const string PerplexityParameterName = "Perplexity";
    private const string ThetaParameterName = "Theta";
    private const string NewDimensionsParameterName = "Dimensions";
    private const string MaxIterationsParameterName = "MaxIterations";
    private const string StopLyingIterationParameterName = "StopLyingIteration";
    private const string MomentumSwitchIterationParameterName = "MomentumSwitchIteration";
    private const string InitialMomentumParameterName = "InitialMomentum";
    private const string FinalMomentumParameterName = "FinalMomentum";
    private const string EtaParameterName = "Eta";
    private const string SetSeedRandomlyParameterName = "SetSeedRandomly";
    private const string SeedParameterName = "Seed";
    private const string ClassesNameParameterName = "ClassesName";
    private const string NormalizationParameterName = "Normalization";
    private const string RandomInitializationParameterName = "RandomInitialization";
    private const string UpdateIntervalParameterName = "UpdateInterval";
    #endregion

    #region Result names
    private const string IterationResultName = "Iteration";
    private const string ErrorResultName = "Error";
    private const string ErrorPlotResultName = "Error plot";
    private const string ScatterPlotResultName = "Scatterplot";
    private const string DataResultName = "Projected data";
    #endregion

    #region Parameter properties
    public IFixedValueParameter<DoubleValue> PerplexityParameter {
      get { return (IFixedValueParameter<DoubleValue>) Parameters[PerplexityParameterName]; }
    }
    public IFixedValueParameter<PercentValue> ThetaParameter {
      get { return (IFixedValueParameter<PercentValue>) Parameters[ThetaParameterName]; }
    }
    public IFixedValueParameter<IntValue> NewDimensionsParameter {
      get { return (IFixedValueParameter<IntValue>) Parameters[NewDimensionsParameterName]; }
    }
    public IConstrainedValueParameter<IDistance<double[]>> DistanceFunctionParameter {
      get { return (IConstrainedValueParameter<IDistance<double[]>>) Parameters[DistanceFunctionParameterName]; }
    }
    public IFixedValueParameter<IntValue> MaxIterationsParameter {
      get { return (IFixedValueParameter<IntValue>) Parameters[MaxIterationsParameterName]; }
    }
    public IFixedValueParameter<IntValue> StopLyingIterationParameter {
      get { return (IFixedValueParameter<IntValue>) Parameters[StopLyingIterationParameterName]; }
    }
    public IFixedValueParameter<IntValue> MomentumSwitchIterationParameter {
      get { return (IFixedValueParameter<IntValue>) Parameters[MomentumSwitchIterationParameterName]; }
    }
    public IFixedValueParameter<DoubleValue> InitialMomentumParameter {
      get { return (IFixedValueParameter<DoubleValue>) Parameters[InitialMomentumParameterName]; }
    }
    public IFixedValueParameter<DoubleValue> FinalMomentumParameter {
      get { return (IFixedValueParameter<DoubleValue>) Parameters[FinalMomentumParameterName]; }
    }
    public IFixedValueParameter<DoubleValue> EtaParameter {
      get { return (IFixedValueParameter<DoubleValue>) Parameters[EtaParameterName]; }
    }
    public IFixedValueParameter<BoolValue> SetSeedRandomlyParameter {
      get { return (IFixedValueParameter<BoolValue>) Parameters[SetSeedRandomlyParameterName]; }
    }
    public IFixedValueParameter<IntValue> SeedParameter {
      get { return (IFixedValueParameter<IntValue>) Parameters[SeedParameterName]; }
    }
    public IConstrainedValueParameter<StringValue> ClassesNameParameter {
      get { return (IConstrainedValueParameter<StringValue>) Parameters[ClassesNameParameterName]; }
    }
    public IFixedValueParameter<BoolValue> NormalizationParameter {
      get { return (IFixedValueParameter<BoolValue>) Parameters[NormalizationParameterName]; }
    }
    public IFixedValueParameter<BoolValue> RandomInitializationParameter {
      get { return (IFixedValueParameter<BoolValue>) Parameters[RandomInitializationParameterName]; }
    }
    public IFixedValueParameter<IntValue> UpdateIntervalParameter {
      get { return (IFixedValueParameter<IntValue>) Parameters[UpdateIntervalParameterName]; }
    }
    #endregion

    #region  Properties
    public IDistance<double[]> DistanceFunction {
      get { return DistanceFunctionParameter.Value; }
    }
    public double Perplexity {
      get { return PerplexityParameter.Value.Value; }
      set { PerplexityParameter.Value.Value = value; }
    }
    public double Theta {
      get { return ThetaParameter.Value.Value; }
      set { ThetaParameter.Value.Value = value; }
    }
    public int NewDimensions {
      get { return NewDimensionsParameter.Value.Value; }
      set { NewDimensionsParameter.Value.Value = value; }
    }
    public int MaxIterations {
      get { return MaxIterationsParameter.Value.Value; }
      set { MaxIterationsParameter.Value.Value = value; }
    }
    public int StopLyingIteration {
      get { return StopLyingIterationParameter.Value.Value; }
      set { StopLyingIterationParameter.Value.Value = value; }
    }
    public int MomentumSwitchIteration {
      get { return MomentumSwitchIterationParameter.Value.Value; }
      set { MomentumSwitchIterationParameter.Value.Value = value; }
    }
    public double InitialMomentum {
      get { return InitialMomentumParameter.Value.Value; }
      set { InitialMomentumParameter.Value.Value = value; }
    }
    public double FinalMomentum {
      get { return FinalMomentumParameter.Value.Value; }
      set { FinalMomentumParameter.Value.Value = value; }
    }
    public double Eta {
      get { return EtaParameter.Value.Value; }
      set { EtaParameter.Value.Value = value; }
    }
    public bool SetSeedRandomly {
      get { return SetSeedRandomlyParameter.Value.Value; }
      set { SetSeedRandomlyParameter.Value.Value = value; }
    }
    public int Seed {
      get { return SeedParameter.Value.Value; }
      set { SeedParameter.Value.Value = value; }
    }
    public string ClassesName {
      get { return ClassesNameParameter.Value != null ? ClassesNameParameter.Value.Value : null; }
      set { ClassesNameParameter.Value.Value = value; }
    }
    public bool Normalization {
      get { return NormalizationParameter.Value.Value; }
      set { NormalizationParameter.Value.Value = value; }
    }
    public bool RandomInitialization {
      get { return RandomInitializationParameter.Value.Value; }
      set { RandomInitializationParameter.Value.Value = value; }
    }

    public int UpdateInterval {
      get { return UpdateIntervalParameter.Value.Value; }
      set { UpdateIntervalParameter.Value.Value = value; }
    }
    #endregion

    #region Storable poperties
    [Storable]
    private Dictionary<string, List<int>> dataRowNames;
    [Storable]
    private Dictionary<string, ScatterPlotDataRow> dataRows;
    [Storable]
    private TSNEStatic<double[]>.TSNEState state;
    [Storable]
    private int iter;
    #endregion

    #region Constructors & Cloning
    [StorableConstructor]
    private TSNEAlgorithm(bool deserializing) : base(deserializing) { }

    [StorableHook(HookType.AfterDeserialization)]
    private void AfterDeserialization() {
      RegisterParameterEvents();
    }
    private TSNEAlgorithm(TSNEAlgorithm original, Cloner cloner) : base(original, cloner) {
      if (original.dataRowNames != null)
        dataRowNames = new Dictionary<string, List<int>>(original.dataRowNames);
      if (original.dataRows != null)
        dataRows = original.dataRows.ToDictionary(kvp => kvp.Key, kvp => cloner.Clone(kvp.Value));
      if (original.state != null)
        state = cloner.Clone(original.state);
      iter = original.iter;
    }
    public override IDeepCloneable Clone(Cloner cloner) {
      return new TSNEAlgorithm(this, cloner);
    }
    public TSNEAlgorithm() {
      var distances = new ItemSet<IDistance<double[]>>(ApplicationManager.Manager.GetInstances<IDistance<double[]>>());
      Parameters.Add(new ConstrainedValueParameter<IDistance<double[]>>(DistanceFunctionParameterName, "The distance function used to differentiate similar from non-similar points", distances, distances.OfType<EuclideanDistance>().FirstOrDefault()));
      Parameters.Add(new FixedValueParameter<DoubleValue>(PerplexityParameterName, "Perplexity-parameter of tSNE. Comparable to k in a k-nearest neighbour algorithm. Recommended value is floor(number of points /3) or lower", new DoubleValue(25)));
      Parameters.Add(new FixedValueParameter<PercentValue>(ThetaParameterName, "Value describing how much appoximated " +
                                                                               "gradients my differ from exact gradients. Set to 0 for exact calculation and in [0,1] otherwise. " +
                                                                               "Appropriate values for theta are between 0.1 and 0.7 (default = 0.5). CAUTION: exact calculation of " +
                                                                               "forces requires building a non-sparse N*N matrix where N is the number of data points. This may " +
                                                                               "exceed memory limitations. The function is designed to run on large (N > 5000) data sets. It may give" +
                                                                               " poor performance on very small data sets(it is better to use a standard t - SNE implementation on such data).", new PercentValue(0)));
      Parameters.Add(new FixedValueParameter<IntValue>(NewDimensionsParameterName, "Dimensionality of projected space (usually 2 for easy visual analysis)", new IntValue(2)));
      Parameters.Add(new FixedValueParameter<IntValue>(MaxIterationsParameterName, "Maximum number of iterations for gradient descent.", new IntValue(1000)));
      Parameters.Add(new FixedValueParameter<IntValue>(StopLyingIterationParameterName, "Number of iterations after which p is no longer approximated.", new IntValue(0)));
      Parameters.Add(new FixedValueParameter<IntValue>(MomentumSwitchIterationParameterName, "Number of iterations after which the momentum in the gradient descent is switched.", new IntValue(0)));
      Parameters.Add(new FixedValueParameter<DoubleValue>(InitialMomentumParameterName, "The initial momentum in the gradient descent.", new DoubleValue(0.5)));
      Parameters.Add(new FixedValueParameter<DoubleValue>(FinalMomentumParameterName, "The final momentum.", new DoubleValue(0.8)));
      Parameters.Add(new FixedValueParameter<DoubleValue>(EtaParameterName, "Gradient descent learning rate.", new DoubleValue(10)));
      Parameters.Add(new FixedValueParameter<BoolValue>(SetSeedRandomlyParameterName, "If the seed should be random.", new BoolValue(true)));
      Parameters.Add(new FixedValueParameter<IntValue>(SeedParameterName, "The seed used if it should not be random.", new IntValue(0)));
      Parameters.Add(new OptionalConstrainedValueParameter<StringValue>(ClassesNameParameterName, "Name of the column specifying the class lables of each data point. If this is not set training/test is used as labels."));
      Parameters.Add(new FixedValueParameter<BoolValue>(NormalizationParameterName, "Whether the data should be zero centered and have variance of 1 for each variable, so different scalings are ignored.", new BoolValue(true)));
      Parameters.Add(new FixedValueParameter<IntValue>(UpdateIntervalParameterName, "The interval after which the results will be updated.", new IntValue(50)));
      Parameters.Add(new FixedValueParameter<BoolValue>(RandomInitializationParameterName, "Wether data points should be randomly initialized or according to the first 2 dimensions", new BoolValue(true)));

      Parameters[UpdateIntervalParameterName].Hidden = true;

      MomentumSwitchIterationParameter.Hidden = true;
      InitialMomentumParameter.Hidden = true;
      FinalMomentumParameter.Hidden = true;
      StopLyingIterationParameter.Hidden = true;
      EtaParameter.Hidden = false;
      Problem = new RegressionProblem();
      RegisterParameterEvents();
    }
    #endregion

    public override void Prepare() {
      base.Prepare();
      dataRowNames = null;
      dataRows = null;
      state = null;
    }

    protected override void Run(CancellationToken cancellationToken) {
      var problemData = Problem.ProblemData;
      // set up and initialize everything if necessary
      if (state == null) {
        if (SetSeedRandomly) Seed = new System.Random().Next();
        var random = new MersenneTwister((uint) Seed);
        var dataset = problemData.Dataset;
        var allowedInputVariables = problemData.AllowedInputVariables.ToArray();
        var allindices = Problem.ProblemData.AllIndices.ToArray();

        // jagged array is required to meet the static method declarations of TSNEStatic<T> 
        var data = Enumerable.Range(0, dataset.Rows).Select(x => new double[allowedInputVariables.Length]).ToArray();
        var col = 0;
        foreach (var s in allowedInputVariables) {
          var row = 0;
          foreach (var d in dataset.GetDoubleValues(s)) {
            data[row][col] = d;
            row++;
          }
          col++;
        }

        if (Normalization) data = NormalizeInputData(data);
        var randomInit = Parameters.ContainsKey(RandomInitializationParameterName) ? RandomInitialization : true;
        state = TSNEStatic<double[]>.CreateState(data, DistanceFunction, random, NewDimensions, Perplexity, Theta, StopLyingIteration, MomentumSwitchIteration, InitialMomentum, FinalMomentum, Eta, randomInit);
        SetUpResults(allindices);
        iter = 0;
      }
      for (; iter < MaxIterations && !cancellationToken.IsCancellationRequested; iter++) {
        if (iter % UpdateInterval == 0) Analyze(state);
        TSNEStatic<double[]>.Iterate(state);
      }
      Analyze(state);
    }

    #region Events
    protected override void OnProblemChanged() {
      base.OnProblemChanged();
      if (Problem == null) return;
      OnProblemDataChanged(this, null);
    }

    protected override void RegisterProblemEvents() {
      base.RegisterProblemEvents();
      Problem.ProblemDataChanged += OnProblemDataChanged;
    }

    protected override void DeregisterProblemEvents() {
      base.DeregisterProblemEvents();
      Problem.ProblemDataChanged -= OnProblemDataChanged;
    }

    protected override void OnStopped() {
      base.OnStopped();
      state = null;
      dataRowNames = null;
      dataRows = null;
    }

    private void OnProblemDataChanged(object sender, EventArgs args) {
      if (Problem == null || Problem.ProblemData == null) return;
      OnPerplexityChanged(this, null);
      Problem.ProblemData.Changed += OnPerplexityChanged;
      Problem.ProblemData.Changed += OnColumnsChanged;
      Problem.ProblemData.Dataset.RowsChanged += OnPerplexityChanged;
      Problem.ProblemData.Dataset.ColumnsChanged += OnColumnsChanged;
      if (!Parameters.ContainsKey(ClassesNameParameterName)) return;
      ClassesNameParameter.ValidValues.Clear();
      foreach (var input in Problem.ProblemData.InputVariables) ClassesNameParameter.ValidValues.Add(input);
    }

    private void OnColumnsChanged(object sender, EventArgs e) {
      if (Problem == null || Problem.ProblemData == null || Problem.ProblemData.Dataset == null || !Parameters.ContainsKey(DistanceFunctionParameterName)) return;
      DistanceFunctionParameter.ValidValues.OfType<WeightedEuclideanDistance>().Single().Weights = new DoubleArray(Problem.ProblemData.AllowedInputVariables.Select(x => 1.0).ToArray());
    }

    private void RegisterParameterEvents() {
      PerplexityParameter.Value.ValueChanged -= OnPerplexityChanged;
      PerplexityParameter.Value.ValueChanged += OnPerplexityChanged;
    }

    private void OnPerplexityChanged(object sender, EventArgs e) {
      if (Problem == null || Problem.ProblemData == null || Problem.ProblemData.Dataset == null || !Parameters.ContainsKey(PerplexityParameterName)) return;
      PerplexityParameter.Value.ValueChanged -= OnPerplexityChanged;
      PerplexityParameter.Value.Value = Math.Max(1, Math.Min((Problem.ProblemData.Dataset.Rows - 1) / 3.0, Perplexity));
      PerplexityParameter.Value.ValueChanged += OnPerplexityChanged;
    }
    #endregion

    #region Helpers
    private void SetUpResults(IReadOnlyList<int> allIndices) {
      if (Results == null) return;
      var results = Results;
      dataRowNames = new Dictionary<string, List<int>>();
      dataRows = new Dictionary<string, ScatterPlotDataRow>();
      var problemData = Problem.ProblemData;

      if (!results.ContainsKey(IterationResultName)) results.Add(new Result(IterationResultName, new IntValue(0)));
      if (!results.ContainsKey(ErrorResultName)) results.Add(new Result(ErrorResultName, new DoubleValue(0)));
      if (!results.ContainsKey(ScatterPlotResultName)) results.Add(new Result(ScatterPlotResultName, "Plot of the projected data", new ScatterPlot(DataResultName, "")));
      if (!results.ContainsKey(DataResultName)) results.Add(new Result(DataResultName, "Projected Data", new DoubleMatrix()));
      if (!results.ContainsKey(ErrorPlotResultName)) {
        var errortable = new DataTable(ErrorPlotResultName, "Development of errors during gradient descent") {
          VisualProperties = {
            XAxisTitle = "UpdateIntervall",
            YAxisTitle = "Error",
            YAxisLogScale = true
          }
        };
        errortable.Rows.Add(new DataRow("Errors"));
        errortable.Rows["Errors"].VisualProperties.StartIndexZero = true;
        results.Add(new Result(ErrorPlotResultName, errortable));
      }

      //color datapoints acording to classes variable (be it double or string)
      if (!problemData.Dataset.VariableNames.Contains(ClassesName)) {
        dataRowNames.Add("Training", problemData.TrainingIndices.ToList());
        dataRowNames.Add("Test", problemData.TestIndices.ToList());
        return;
      }
      var classificationData = problemData as ClassificationProblemData;
      if (classificationData != null && classificationData.TargetVariable.Equals(ClassesName)) {
        var classNames = classificationData.ClassValues.Zip(classificationData.ClassNames, (v, n) => new {v, n}).ToDictionary(x => x.v, x => x.n);
        var classes = classificationData.Dataset.GetDoubleValues(classificationData.TargetVariable, allIndices).Select(v => classNames[v]).ToArray();
        for (var i = 0; i < classes.Length; i++) {
          if (!dataRowNames.ContainsKey(classes[i])) dataRowNames.Add(classes[i], new List<int>());
          dataRowNames[classes[i]].Add(i);
        }
      }
      else if (((Dataset) problemData.Dataset).VariableHasType<string>(ClassesName)) {
        var classes = problemData.Dataset.GetStringValues(ClassesName, allIndices).ToArray();
        for (var i = 0; i < classes.Length; i++) {
          if (!dataRowNames.ContainsKey(classes[i])) dataRowNames.Add(classes[i], new List<int>());
          dataRowNames[classes[i]].Add(i);
        }
      }
      else if (((Dataset) problemData.Dataset).VariableHasType<double>(ClassesName)) {
        var clusterdata = new Dataset(problemData.Dataset.DoubleVariables, problemData.Dataset.DoubleVariables.Select(v => problemData.Dataset.GetDoubleValues(v, allIndices).ToList()));
        const int contours = 8;
        Dictionary<int, string> contourMap;
        IClusteringModel clusterModel;
        double[][] borders;
        CreateClusters(clusterdata, ClassesName, contours, out clusterModel, out contourMap, out borders);
        var contourorder = borders.Select((x, i) => new {x, i}).OrderBy(x => x.x[0]).Select(x => x.i).ToArray();
        for (var i = 0; i < contours; i++) {
          var c = contourorder[i];
          var contourname = contourMap[c];
          dataRowNames.Add(contourname, new List<int>());
          dataRows.Add(contourname, new ScatterPlotDataRow(contourname, "", new List<Point2D<double>>()));
          dataRows[contourname].VisualProperties.Color = GetHeatMapColor(i, contours);
        }
        var allClusters = clusterModel.GetClusterValues(clusterdata, Enumerable.Range(0, clusterdata.Rows)).ToArray();
        for (var i = 0; i < clusterdata.Rows; i++) dataRowNames[contourMap[allClusters[i] - 1]].Add(i);
      }
      else if (((Dataset) problemData.Dataset).VariableHasType<DateTime>(ClassesName)) {
        var clusterdata = new Dataset(problemData.Dataset.DateTimeVariables, problemData.Dataset.DateTimeVariables.Select(v => problemData.Dataset.GetDoubleValues(v, allIndices).ToList()));
        const int contours = 8;
        Dictionary<int, string> contourMap;
        IClusteringModel clusterModel;
        double[][] borders;
        CreateClusters(clusterdata, ClassesName, contours, out clusterModel, out contourMap, out borders);
        var contourorder = borders.Select((x, i) => new {x, i}).OrderBy(x => x.x[0]).Select(x => x.i).ToArray();
        for (var i = 0; i < contours; i++) {
          var c = contourorder[i];
          var contourname = contourMap[c];
          dataRowNames.Add(contourname, new List<int>());
          dataRows.Add(contourname, new ScatterPlotDataRow(contourname, "", new List<Point2D<double>>()));
          dataRows[contourname].VisualProperties.Color = GetHeatMapColor(i, contours);
        }
        var allClusters = clusterModel.GetClusterValues(clusterdata, Enumerable.Range(0, clusterdata.Rows)).ToArray();
        for (var i = 0; i < clusterdata.Rows; i++) dataRowNames[contourMap[allClusters[i] - 1]].Add(i);
      }
      else {
        dataRowNames.Add("Training", problemData.TrainingIndices.ToList());
        dataRowNames.Add("Test", problemData.TestIndices.ToList());
      }
    }

    private void Analyze(TSNEStatic<double[]>.TSNEState tsneState) {
      if (Results == null) return;
      var results = Results;
      var plot = results[ErrorPlotResultName].Value as DataTable;
      if (plot == null) throw new ArgumentException("Could not create/access error data table in results collection.");
      var errors = plot.Rows["Errors"].Values;
      var c = tsneState.EvaluateError();
      errors.Add(c);
      ((IntValue) results[IterationResultName].Value).Value = tsneState.iter;
      ((DoubleValue) results[ErrorResultName].Value).Value = errors.Last();

      var ndata = NormalizeProjectedData(tsneState.newData);
      results[DataResultName].Value = new DoubleMatrix(ndata);
      var splot = results[ScatterPlotResultName].Value as ScatterPlot;
      FillScatterPlot(ndata, splot);
    }

    private void FillScatterPlot(double[,] lowDimData, ScatterPlot plot) {
      foreach (var rowName in dataRowNames.Keys) {
        if (!plot.Rows.ContainsKey(rowName)) {
          plot.Rows.Add(dataRows.ContainsKey(rowName) ? dataRows[rowName] : new ScatterPlotDataRow(rowName, "", new List<Point2D<double>>()));
          plot.Rows[rowName].VisualProperties.PointSize = 8;
        }
        plot.Rows[rowName].Points.Replace(dataRowNames[rowName].Select(i => new Point2D<double>(lowDimData[i, 0], lowDimData[i, 1])));
      }
    }

    private static double[,] NormalizeProjectedData(double[,] data) {
      var max = new double[data.GetLength(1)];
      var min = new double[data.GetLength(1)];
      var res = new double[data.GetLength(0), data.GetLength(1)];
      for (var i = 0; i < max.Length; i++) max[i] = min[i] = data[0, i];
      for (var i = 0; i < data.GetLength(0); i++)
      for (var j = 0; j < data.GetLength(1); j++) {
        var v = data[i, j];
        max[j] = Math.Max(max[j], v);
        min[j] = Math.Min(min[j], v);
      }
      for (var i = 0; i < data.GetLength(0); i++) {
        for (var j = 0; j < data.GetLength(1); j++) {
          var d = max[j] - min[j];
          var s = data[i, j] - (max[j] + min[j]) / 2; //shift data
          if (d.IsAlmost(0)) res[i, j] = data[i, j]; //no scaling possible
          else res[i, j] = s / d; //scale data
        }
      }
      return res;
    }

    private static double[][] NormalizeInputData(IReadOnlyList<IReadOnlyList<double>> data) {
      // as in tSNE implementation by van der Maaten
      var n = data[0].Count;
      var mean = new double[n];
      var max = new double[n];
      var nData = new double[data.Count][];
      for (var i = 0; i < n; i++) {
        mean[i] = Enumerable.Range(0, data.Count).Select(x => data[x][i]).Average();
        max[i] = Enumerable.Range(0, data.Count).Max(x => Math.Abs(data[x][i]));
      }
      for (var i = 0; i < data.Count; i++) {
        nData[i] = new double[n];
        for (var j = 0; j < n; j++) nData[i][j] = max[j].IsAlmost(0) ? data[i][j] - mean[j] : (data[i][j] - mean[j]) / max[j];
      }
      return nData;
    }

    private static Color GetHeatMapColor(int contourNr, int noContours) {
      return ConvertTotalToRgb(0, noContours, contourNr);
    }

    private static void CreateClusters(IDataset data, string target, int contours, out IClusteringModel contourCluster, out Dictionary<int, string> contourNames, out double[][] borders) {
      var cpd = new ClusteringProblemData((Dataset) data, new[] {target});
      contourCluster = KMeansClustering.CreateKMeansSolution(cpd, contours, 3).Model;

      borders = Enumerable.Range(0, contours).Select(x => new[] {double.MaxValue, double.MinValue}).ToArray();
      var clusters = contourCluster.GetClusterValues(cpd.Dataset, cpd.AllIndices).ToArray();
      var targetvalues = cpd.Dataset.GetDoubleValues(target).ToArray();
      foreach (var i in cpd.AllIndices) {
        var cl = clusters[i] - 1;
        var clv = targetvalues[i];
        if (borders[cl][0] > clv) borders[cl][0] = clv;
        if (borders[cl][1] < clv) borders[cl][1] = clv;
      }

      contourNames = new Dictionary<int, string>();
      for (var i = 0; i < contours; i++)
        contourNames.Add(i, "[" + borders[i][0] + ";" + borders[i][1] + "]");
    }

    private static Color ConvertTotalToRgb(double low, double high, double cell) {
      var colorGradient = ColorGradient.Colors;
      var range = high - low;
      var h = cell / range * colorGradient.Count;
      return colorGradient[(int) h];
    }
    #endregion
  }
}