1 | package de.ugoe.cs.quest.usageprofiles;
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2 |
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3 | import java.util.ArrayList;
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4 | import java.util.Collection;
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5 | import java.util.LinkedList;
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6 | import java.util.List;
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7 | import java.util.Random;
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8 | import java.util.logging.Level;
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9 |
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10 | import de.ugoe.cs.quest.eventcore.Event;
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11 | import de.ugoe.cs.util.StringTools;
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12 | import de.ugoe.cs.util.console.Console;
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13 | import edu.uci.ics.jung.graph.Graph;
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14 | import edu.uci.ics.jung.graph.SparseMultigraph;
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15 | import edu.uci.ics.jung.graph.util.EdgeType;
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16 |
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17 | import Jama.Matrix;
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18 |
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19 | /**
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20 | * <p>
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21 | * Implements first-order Markov models. The implementation is based on {@link HighOrderMarkovModel}
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22 | * and restricts the Markov order to 1. In comparison to {@link HighOrderMarkovModel}, more
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23 | * calculations are possible with first-order models, e.g., the calculation of the entropy (
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24 | * {@link #calcEntropy()}).
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25 | * </p>
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26 | *
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27 | * @author Steffen Herbold
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28 | * @version 1.0
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29 | */
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30 | public class FirstOrderMarkovModel extends HighOrderMarkovModel implements IDotCompatible {
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31 |
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32 | /**
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33 | * <p>
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34 | * Id for object serialization.
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35 | * </p>
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36 | */
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37 | private static final long serialVersionUID = 1L;
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38 |
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39 | /**
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40 | * <p>
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41 | * Maximum number of iterations when calculating the stationary distribution as the limit of
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42 | * multiplying the transmission matrix with itself.
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43 | * </p>
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44 | */
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45 | final static int MAX_STATDIST_ITERATIONS = 1000;
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46 |
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47 | /**
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48 | * <p>
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49 | * Constructor. Creates a new FirstOrderMarkovModel.
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50 | * </p>
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51 | *
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52 | * @param r
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53 | * random number generator used by probabilistic methods of the class
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54 | */
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55 | public FirstOrderMarkovModel(Random r) {
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56 | super(1, r);
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57 | }
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58 |
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59 | /**
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60 | * <p>
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61 | * Generates the transmission matrix of the Markov model.
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62 | * </p>
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63 | *
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64 | * @return transmission matrix
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65 | */
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66 | private Matrix getTransmissionMatrix() {
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67 | List<Event> knownSymbols = new ArrayList<Event>(trie.getKnownSymbols());
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68 | int numStates = knownSymbols.size();
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69 | Matrix transmissionMatrix = new Matrix(numStates, numStates);
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70 |
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71 | for (int i = 0; i < numStates; i++) {
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72 | Event currentSymbol = knownSymbols.get(i);
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73 | List<Event> context = new ArrayList<Event>();
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74 | context.add(currentSymbol);
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75 | for (int j = 0; j < numStates; j++) {
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76 | Event follower = knownSymbols.get(j);
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77 | double prob = getProbability(context, follower);
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78 | transmissionMatrix.set(i, j, prob);
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79 | }
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80 | }
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81 | return transmissionMatrix;
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82 | }
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83 |
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84 | /**
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85 | * <p>
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86 | * Calculates the entropy of the model. To make it possible that the model is stationary, a
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87 | * transition from {@link Event#ENDEVENT} to {@link Event#STARTEVENT} is added.
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88 | * </p>
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89 | *
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90 | * @return entropy of the model or NaN if it could not be calculated
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91 | */
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92 | public double calcEntropy() {
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93 | Matrix transmissionMatrix = getTransmissionMatrix();
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94 | List<Event> knownSymbols = new ArrayList<Event>(trie.getKnownSymbols());
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95 | int numStates = knownSymbols.size();
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96 |
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97 | List<Integer> startIndexList = new LinkedList<Integer>();
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98 | List<Integer> endIndexList = new LinkedList<Integer>();
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99 | for (int i = 0; i < knownSymbols.size(); i++) {
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100 | String id = knownSymbols.get(i).getId();
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101 | if (id.equals(Event.STARTEVENT.getId()) ||
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102 | id.contains(Event.STARTEVENT.getId() + "-=-"))
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103 | {
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104 | startIndexList.add(i);
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105 | }
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106 | if (id.equals(Event.ENDEVENT.getId()) || id.contains("-=-" + Event.ENDEVENT.getId())) {
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107 | endIndexList.add(i);
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108 | }
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109 | }
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110 |
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111 | if (startIndexList.isEmpty()) {
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112 | Console
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113 | .printerrln("Error calculating entropy. Initial state of markov chain not found.");
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114 | return Double.NaN;
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115 | }
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116 | if (endIndexList.isEmpty()) {
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117 | Console.printerrln("Error calculating entropy. End state of markov chain not found.");
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118 | return Double.NaN;
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119 | }
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120 | for (Integer i : endIndexList) {
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121 | for (Integer j : startIndexList) {
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122 | transmissionMatrix.set(i, j, 1);
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123 | }
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124 | }
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125 |
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126 | // Calculate stationary distribution by raising the power of the
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127 | // transmission matrix.
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128 | // The rank of the matrix should fall to 1 and each two should be the
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129 | // vector of the stationory distribution.
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130 | int iter = 0;
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131 | int rank = transmissionMatrix.rank();
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132 | Matrix stationaryMatrix = (Matrix) transmissionMatrix.clone();
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133 | while (iter < MAX_STATDIST_ITERATIONS && rank > 1) {
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134 | stationaryMatrix = stationaryMatrix.times(stationaryMatrix);
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135 | rank = stationaryMatrix.rank();
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136 | iter++;
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137 | }
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138 |
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139 | if (rank != 1) {
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140 | Console.traceln(Level.FINE, "rank: " + rank);
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141 | Console.printerrln("Unable to calculate stationary distribution.");
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142 | return Double.NaN;
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143 | }
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144 |
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145 | double entropy = 0.0;
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146 | for (int i = 0; i < numStates; i++) {
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147 | for (int j = 0; j < numStates; j++) {
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148 | if (transmissionMatrix.get(i, j) != 0 && transmissionMatrix.get(i, j) != 1) {
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149 | double tmp = stationaryMatrix.get(0, i);
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150 | tmp *= transmissionMatrix.get(i, j);
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151 | tmp *= Math.log(transmissionMatrix.get(i, j)) / Math.log(2);
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152 | entropy -= tmp;
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153 | }
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154 | }
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155 | }
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156 | return entropy;
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157 | }
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158 |
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159 | /**
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160 | * <p>
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161 | * The dot represenation of {@link FirstOrderMarkovModel}s is its graph representation with the
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162 | * states as nodes and directed edges weighted with transition probabilities.
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163 | * </p>
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164 | *
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165 | * @see de.ugoe.cs.quest.usageprofiles.IDotCompatible#getDotRepresentation()
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166 | */
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167 | @Override
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168 | public String getDotRepresentation() {
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169 | StringBuilder stringBuilder = new StringBuilder();
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170 | stringBuilder.append("digraph model {" + StringTools.ENDLINE);
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171 |
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172 | List<Event> knownSymbols = new ArrayList<Event>(trie.getKnownSymbols());
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173 | for (Event symbol : knownSymbols) {
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174 | final String thisSaneId = symbol.getId().replace("\"", "\\\"").replaceAll("[\r\n]", "");
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175 | stringBuilder.append(" " + knownSymbols.indexOf(symbol) + " [label=\"" + thisSaneId +
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176 | "\"];" + StringTools.ENDLINE);
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177 | List<Event> context = new ArrayList<Event>();
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178 | context.add(symbol);
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179 | Collection<Event> followers = trie.getFollowingSymbols(context);
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180 | for (Event follower : followers) {
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181 | stringBuilder.append(" " + knownSymbols.indexOf(symbol) + " -> " +
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182 | knownSymbols.indexOf(follower) + " ");
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183 | stringBuilder.append("[label=\"" + getProbability(context, follower) + "\"];" +
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184 | StringTools.ENDLINE);
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185 | }
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186 | }
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187 | stringBuilder.append('}' + StringTools.ENDLINE);
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188 | return stringBuilder.toString();
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189 | }
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190 |
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191 | /**
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192 | * <p>
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193 | * Returns a {@link Graph} representation of the model with the states as nodes and directed
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194 | * edges weighted with transition probabilities.
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195 | * </p>
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196 | *
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197 | * @return {@link Graph} of the model
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198 | */
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199 | public Graph<String, MarkovEdge> getGraph() {
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200 | Graph<String, MarkovEdge> graph = new SparseMultigraph<String, MarkovEdge>();
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201 |
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202 | List<Event> knownSymbols = new ArrayList<Event>(trie.getKnownSymbols());
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203 |
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204 | for (Event symbol : knownSymbols) {
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205 | String from = symbol.getId();
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206 | List<Event> context = new ArrayList<Event>();
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207 | context.add(symbol);
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208 |
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209 | Collection<Event> followers = trie.getFollowingSymbols(context);
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210 |
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211 | for (Event follower : followers) {
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212 | String to = follower.getId();
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213 | MarkovEdge prob = new MarkovEdge(getProbability(context, follower));
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214 | graph.addEdge(prob, from, to, EdgeType.DIRECTED);
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215 | }
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216 | }
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217 | return graph;
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218 | }
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219 |
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220 | /**
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221 | * Inner class used for the {@link Graph} representation of the model.
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222 | *
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223 | * @author Steffen Herbold
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224 | * @version 1.0
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225 | */
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226 | static public class MarkovEdge {
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227 | /**
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228 | * <p>
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229 | * Weight of the edge, i.e., its transition probability.
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230 | * </p>
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231 | */
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232 | double weight;
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233 |
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234 | /**
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235 | * <p>
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236 | * Constructor. Creates a new MarkovEdge.
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237 | * </p>
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238 | *
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239 | * @param weight
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240 | * weight of the edge, i.e., its transition probability
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241 | */
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242 | MarkovEdge(double weight) {
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243 | this.weight = weight;
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244 | }
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245 |
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246 | /**
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247 | * <p>
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248 | * The weight of the edge as {@link String}.
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249 | * </p>
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250 | */
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251 | public String toString() {
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252 | return "" + weight;
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253 | }
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254 | }
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255 |
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256 | }
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