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