1 | /*
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2 | * This program is free software; you can redistribute it and/or modify
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3 | * it under the terms of the GNU General Public License as published by
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4 | * the Free Software Foundation; either version 2 of the License, or
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5 | * (at your option) any later version.
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6 | *
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7 | * This program is distributed in the hope that it will be useful,
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8 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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9 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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10 | * GNU General Public License for more details.
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11 | *
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12 | * You should have received a copy of the GNU General Public License
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13 | * along with this program; if not, write to the Free Software
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14 | * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
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15 | */
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16 |
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17 | /*
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18 | * ContingencyTables.java
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19 | * Copyright (C) 1999 Eibe Frank
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20 | *
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21 | */
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22 |
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23 | package weka.core;
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24 |
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25 | /**
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26 | * Class implementing some statistical routines for contingency tables.
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27 | *
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28 | * @author Eibe Frank ([email protected])
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29 | * @version $Revision: 8815 $
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30 | */
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31 | public class ContingencyTables {
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32 |
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33 | /** The natural logarithm of 2 */
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34 | private static double log2 = Math.log(2);
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35 |
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36 | /**
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37 | * Returns chi-squared probability for a given matrix.
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38 | *
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39 | * @param matrix the contigency table
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40 | * @param yates is Yates' correction to be used?
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41 | * @return the chi-squared probability
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42 | */
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43 |
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44 | public static double chiSquared(double [][] matrix, boolean yates) {
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45 |
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46 | int df = (matrix.length - 1) * (matrix[0].length - 1);
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47 |
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48 | return Statistics.chiSquaredProbability(chiVal(matrix, yates), df);
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49 | }
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50 |
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51 | /**
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52 | * Computes chi-squared statistic for a contingency table.
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53 | *
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54 | * @param matrix the contigency table
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55 | * @param yates is Yates' correction to be used?
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56 | * @return the value of the chi-squared statistic
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57 | */
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58 | public static double chiVal(double [][] matrix, boolean useYates) {
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59 |
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60 | int df, nrows, ncols, row, col;
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61 | double[] rtotal, ctotal;
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62 | double expect = 0, chival = 0, n = 0;
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63 | boolean yates = true;
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64 |
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65 | nrows = matrix.length;
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66 | ncols = matrix[0].length;
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67 | rtotal = new double [nrows];
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68 | ctotal = new double [ncols];
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69 | for (row = 0; row < nrows; row++) {
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70 | for (col = 0; col < ncols; col++) {
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71 | rtotal[row] += matrix[row][col];
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72 | ctotal[col] += matrix[row][col];
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73 | n += matrix[row][col];
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74 | }
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75 | }
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76 | df = (nrows - 1)*(ncols - 1);
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77 | if ((df > 1) || (!useYates)) {
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78 | yates = false;
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79 | } else if (df <= 0) {
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80 | return 0;
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81 | }
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82 | chival = 0.0;
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83 | for (row = 0; row < nrows; row++) {
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84 | if (Utils.gr(rtotal[row], 0)) {
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85 | for (col = 0; col < ncols; col++) {
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86 | if (Utils.gr(ctotal[col], 0)) {
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87 | expect = (ctotal[col] * rtotal[row]) / n;
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88 | chival += chiCell (matrix[row][col], expect, yates);
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89 | }
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90 | }
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91 | }
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92 | }
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93 | return chival;
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94 | }
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95 |
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96 | /**
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97 | * Tests if Cochran's criterion is fullfilled for the given
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98 | * contingency table. Rows and columns with all zeros are not considered
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99 | * relevant.
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100 | *
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101 | * @param matrix the contigency table to be tested
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102 | * @return true if contingency table is ok, false if not
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103 | */
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104 | public static boolean cochransCriterion(double[][] matrix) {
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105 |
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106 | double[] rtotal, ctotal;
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107 | double n = 0, expect, smallfreq = 5;
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108 | int smallcount = 0, nonZeroRows = 0, nonZeroColumns = 0, nrows, ncols,
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109 | row, col;
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110 |
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111 | nrows = matrix.length;
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112 | ncols = matrix[0].length;
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113 |
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114 | rtotal = new double [nrows];
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115 | ctotal = new double [ncols];
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116 | for (row = 0; row < nrows; row++) {
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117 | for (col = 0; col < ncols; col++) {
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118 | rtotal[row] += matrix[row][col];
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119 | ctotal[col] += matrix[row][col];
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120 | n += matrix[row][col];
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121 | }
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122 | }
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123 | for (row = 0; row < nrows; row++) {
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124 | if (Utils.gr(rtotal[row], 0)) {
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125 | nonZeroRows++;
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126 | }
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127 | }
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128 | for (col = 0; col < ncols; col++) {
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129 | if (Utils.gr(ctotal[col], 0)) {
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130 | nonZeroColumns++;
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131 | }
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132 | }
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133 | for (row = 0; row < nrows; row++) {
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134 | if (Utils.gr(rtotal[row], 0)) {
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135 | for (col = 0; col < ncols; col++) {
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136 | if (Utils.gr(ctotal[col], 0)) {
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137 | expect = (ctotal[col] * rtotal[row]) / n;
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138 | if (Utils.sm(expect, smallfreq)) {
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139 | if (Utils.sm(expect, 1)) {
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140 | return false;
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141 | } else {
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142 | smallcount++;
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143 | if (smallcount > (nonZeroRows * nonZeroColumns) / smallfreq) {
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144 | return false;
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145 | }
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146 | }
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147 | }
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148 | }
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149 | }
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150 | }
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151 | }
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152 | return true;
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153 | }
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154 |
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155 | /**
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156 | * Computes Cramer's V for a contingency table.
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157 | *
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158 | * @param matrix the contingency table
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159 | * @return Cramer's V
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160 | */
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161 | public static double CramersV(double [][] matrix) {
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162 |
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163 | int row, col, nrows,ncols, min;
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164 | double n = 0;
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165 |
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166 | nrows = matrix.length;
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167 | ncols = matrix[0].length;
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168 | for (row = 0; row < nrows; row++) {
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169 | for (col = 0; col < ncols; col++) {
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170 | n += matrix[row][col];
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171 | }
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172 | }
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173 | min = nrows < ncols ? nrows-1 : ncols-1;
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174 | if ((min == 0) || Utils.eq(n, 0))
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175 | return 0;
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176 | return Math.sqrt(chiVal(matrix, false) / (n * (double)min));
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177 | }
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178 |
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179 | /**
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180 | * Computes the entropy of the given array.
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181 | *
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182 | * @param array the array
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183 | * @return the entropy
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184 | */
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185 | public static double entropy(double[] array) {
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186 |
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187 | double returnValue = 0, sum = 0;
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188 |
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189 | for (int i = 0; i < array.length; i++) {
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190 | returnValue -= lnFunc(array[i]);
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191 | sum += array[i];
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192 | }
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193 | if (Utils.eq(sum, 0)) {
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194 | return 0;
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195 | } else {
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196 | return (returnValue + lnFunc(sum)) / (sum * log2);
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197 | }
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198 | }
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199 |
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200 | /**
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201 | * Computes conditional entropy of the rows given
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202 | * the columns.
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203 | *
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204 | * @param matrix the contingency table
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205 | * @return the conditional entropy of the rows given the columns
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206 | */
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207 | public static double entropyConditionedOnColumns(double[][] matrix) {
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208 |
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209 | double returnValue = 0, sumForColumn, total = 0;
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210 |
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211 | for (int j = 0; j < matrix[0].length; j++) {
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212 | sumForColumn = 0;
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213 | for (int i = 0; i < matrix.length; i++) {
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214 | returnValue = returnValue + lnFunc(matrix[i][j]);
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215 | sumForColumn += matrix[i][j];
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216 | }
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217 | returnValue = returnValue - lnFunc(sumForColumn);
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218 | total += sumForColumn;
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219 | }
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220 | if (Utils.eq(total, 0)) {
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221 | return 0;
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222 | }
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223 | return -returnValue / (total * log2);
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224 | }
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225 |
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226 | /**
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227 | * Computes conditional entropy of the columns given
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228 | * the rows.
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229 | *
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230 | * @param matrix the contingency table
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231 | * @return the conditional entropy of the columns given the rows
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232 | */
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233 | public static double entropyConditionedOnRows(double[][] matrix) {
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234 |
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235 | double returnValue = 0, sumForRow, total = 0;
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236 |
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237 | for (int i = 0; i < matrix.length; i++) {
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238 | sumForRow = 0;
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239 | for (int j = 0; j < matrix[0].length; j++) {
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240 | returnValue = returnValue + lnFunc(matrix[i][j]);
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241 | sumForRow += matrix[i][j];
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242 | }
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243 | returnValue = returnValue - lnFunc(sumForRow);
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244 | total += sumForRow;
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245 | }
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246 | if (Utils.eq(total, 0)) {
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247 | return 0;
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248 | }
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249 | return -returnValue / (total * log2);
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250 | }
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251 |
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252 | /**
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253 | * Computes conditional entropy of the columns given the rows
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254 | * of the test matrix with respect to the train matrix. Uses a
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255 | * Laplace prior. Does NOT normalize the entropy.
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256 | *
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257 | * @param train the train matrix
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258 | * @param test the test matrix
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259 | * @param the number of symbols for Laplace
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260 | * @return the entropy
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261 | */
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262 | public static double entropyConditionedOnRows(double[][] train,
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263 | double[][] test,
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264 | double numClasses) {
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265 |
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266 | double returnValue = 0, trainSumForRow, testSumForRow, testSum = 0;
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267 |
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268 | for (int i = 0; i < test.length; i++) {
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269 | trainSumForRow = 0;
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270 | testSumForRow = 0;
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271 | for (int j = 0; j < test[0].length; j++) {
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272 | returnValue -= test[i][j] * Math.log(train[i][j] + 1);
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273 | trainSumForRow += train[i][j];
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274 | testSumForRow += test[i][j];
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275 | }
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276 | testSum = testSumForRow;
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277 | returnValue += testSumForRow * Math.log(trainSumForRow +
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278 | numClasses);
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279 | }
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280 | return returnValue / (testSum * log2);
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281 | }
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282 |
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283 | /**
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284 | * Computes the rows' entropy for the given contingency table.
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285 | *
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286 | * @param matrix the contingency table
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287 | * @return the rows' entropy
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288 | */
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289 | public static double entropyOverRows(double[][] matrix) {
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290 |
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291 | double returnValue = 0, sumForRow, total = 0;
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292 |
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293 | for (int i = 0; i < matrix.length; i++) {
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294 | sumForRow = 0;
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295 | for (int j = 0; j < matrix[0].length; j++) {
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296 | sumForRow += matrix[i][j];
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297 | }
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298 | returnValue = returnValue - lnFunc(sumForRow);
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299 | total += sumForRow;
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300 | }
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301 | if (Utils.eq(total, 0)) {
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302 | return 0;
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303 | }
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304 | return (returnValue + lnFunc(total)) / (total * log2);
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305 | }
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306 |
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307 | /**
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308 | * Computes the columns' entropy for the given contingency table.
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309 | *
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310 | * @param matrix the contingency table
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311 | * @return the columns' entropy
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312 | */
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313 | public static double entropyOverColumns(double[][] matrix){
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314 |
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315 | double returnValue = 0, sumForColumn, total = 0;
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316 |
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317 | for (int j = 0; j < matrix[0].length; j++){
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318 | sumForColumn = 0;
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319 | for (int i = 0; i < matrix.length; i++) {
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320 | sumForColumn += matrix[i][j];
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321 | }
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322 | returnValue = returnValue - lnFunc(sumForColumn);
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323 | total += sumForColumn;
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324 | }
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325 | if (Utils.eq(total, 0)) {
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326 | return 0;
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327 | }
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328 | return (returnValue + lnFunc(total)) / (total * log2);
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329 | }
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330 |
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331 | /**
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332 | * Computes gain ratio for contingency table (split on rows).
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333 | * Returns Double.MAX_VALUE if the split entropy is 0.
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334 | *
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335 | * @param matrix the contingency table
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336 | * @return the gain ratio
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337 | */
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338 | public static double gainRatio(double[][] matrix){
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339 |
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340 | double preSplit = 0, postSplit = 0, splitEnt = 0,
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341 | sumForRow, sumForColumn, total = 0, infoGain;
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342 |
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343 | // Compute entropy before split
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344 | for (int i = 0; i < matrix[0].length; i++) {
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345 | sumForColumn = 0;
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346 | for (int j = 0; j < matrix.length; j++)
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347 | sumForColumn += matrix[j][i];
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348 | preSplit += lnFunc(sumForColumn);
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349 | total += sumForColumn;
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350 | }
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351 | preSplit -= lnFunc(total);
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352 |
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353 | // Compute entropy after split and split entropy
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354 | for (int i = 0; i < matrix.length; i++) {
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355 | sumForRow = 0;
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356 | for (int j = 0; j < matrix[0].length; j++) {
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357 | postSplit += lnFunc(matrix[i][j]);
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358 | sumForRow += matrix[i][j];
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359 | }
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360 | splitEnt += lnFunc(sumForRow);
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361 | }
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362 | postSplit -= splitEnt;
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363 | splitEnt -= lnFunc(total);
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364 |
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365 | infoGain = preSplit - postSplit;
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366 | if (Utils.eq(splitEnt, 0))
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367 | return 0;
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368 | return infoGain / splitEnt;
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369 | }
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370 |
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371 | /**
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372 | * Returns negative base 2 logarithm of multiple hypergeometric
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373 | * probability for a contingency table.
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374 | *
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375 | * @param matrix the contingency table
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376 | * @return the log of the hypergeometric probability of the contingency table
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377 | */
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378 | public static double log2MultipleHypergeometric(double[][] matrix) {
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379 |
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380 | double sum = 0, sumForRow, sumForColumn, total = 0;
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381 |
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382 | for (int i = 0; i < matrix.length; i++) {
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383 | sumForRow = 0;
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384 | for (int j = 0; j < matrix[i].length; j++) {
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385 | sumForRow += matrix[i][j];
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386 | }
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387 | sum += SpecialFunctions.lnFactorial(sumForRow);
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388 | total += sumForRow;
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389 | }
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390 | for (int j = 0; j < matrix[0].length; j++) {
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391 | sumForColumn = 0;
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392 | for (int i = 0; i < matrix.length; i++) {
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393 | sumForColumn += matrix [i][j];
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394 | }
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395 | sum += SpecialFunctions.lnFactorial(sumForColumn);
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396 | }
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397 | for (int i = 0; i < matrix.length; i++) {
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398 | for (int j = 0; j < matrix[i].length; j++) {
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399 | sum -= SpecialFunctions.lnFactorial(matrix[i][j]);
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400 | }
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401 | }
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402 | sum -= SpecialFunctions.lnFactorial(total);
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403 | return -sum / log2;
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404 | }
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405 |
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406 | /**
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407 | * Reduces a matrix by deleting all zero rows and columns.
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408 | *
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409 | * @param matrix the matrix to be reduced
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410 | * @param the matrix with all zero rows and columns deleted
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411 | */
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412 | public static double[][] reduceMatrix(double[][] matrix) {
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413 |
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414 | int row, col, currCol, currRow, nrows, ncols,
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415 | nonZeroRows = 0, nonZeroColumns = 0;
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416 | double[] rtotal, ctotal;
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417 | double[][] newMatrix;
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418 |
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419 | nrows = matrix.length;
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420 | ncols = matrix[0].length;
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421 | rtotal = new double [nrows];
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422 | ctotal = new double [ncols];
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423 | for (row = 0; row < nrows; row++) {
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424 | for (col = 0; col < ncols; col++) {
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425 | rtotal[row] += matrix[row][col];
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426 | ctotal[col] += matrix[row][col];
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427 | }
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428 | }
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429 | for (row = 0; row < nrows; row++) {
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430 | if (Utils.gr(rtotal[row],0)) {
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431 | nonZeroRows++;
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432 | }
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433 | }
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434 | for (col = 0; col < ncols; col++) {
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435 | if (Utils.gr(ctotal[col],0)) {
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436 | nonZeroColumns++;
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437 | }
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438 | }
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439 | newMatrix = new double[nonZeroRows][nonZeroColumns];
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440 | currRow = 0;
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441 | for (row = 0; row < nrows; row++) {
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442 | if (Utils.gr(rtotal[row],0)) {
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443 | currCol = 0;
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444 | for (col = 0; col < ncols; col++) {
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445 | if (Utils.gr(ctotal[col],0)) {
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446 | newMatrix[currRow][currCol] = matrix[row][col];
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447 | currCol++;
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448 | }
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449 | }
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450 | currRow++;
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451 | }
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452 | }
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453 | return newMatrix;
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454 | }
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455 |
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456 | /**
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457 | * Calculates the symmetrical uncertainty for base 2.
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458 | *
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459 | * @param matrix the contingency table
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460 | * @return the calculated symmetrical uncertainty
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461 | *
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462 | */
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463 | public static double symmetricalUncertainty(double matrix[][]) {
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464 |
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465 | double sumForColumn, sumForRow, total = 0, columnEntropy = 0,
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466 | rowEntropy = 0, entropyConditionedOnRows = 0, infoGain = 0;
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467 |
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468 | // Compute entropy for columns
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469 | for (int i = 0; i < matrix[0].length; i++) {
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470 | sumForColumn = 0;
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471 | for (int j = 0; j < matrix.length; j++) {
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472 | sumForColumn += matrix[j][i];
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473 | }
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474 | columnEntropy += lnFunc(sumForColumn);
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475 | total += sumForColumn;
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476 | }
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477 | columnEntropy -= lnFunc(total);
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478 |
|
---|
479 | // Compute entropy for rows and conditional entropy
|
---|
480 | for (int i = 0; i < matrix.length; i++) {
|
---|
481 | sumForRow = 0;
|
---|
482 | for (int j = 0; j < matrix[0].length; j++) {
|
---|
483 | sumForRow += matrix[i][j];
|
---|
484 | entropyConditionedOnRows += lnFunc(matrix[i][j]);
|
---|
485 | }
|
---|
486 | rowEntropy += lnFunc(sumForRow);
|
---|
487 | }
|
---|
488 | entropyConditionedOnRows -= rowEntropy;
|
---|
489 | rowEntropy -= lnFunc(total);
|
---|
490 | infoGain = columnEntropy - entropyConditionedOnRows;
|
---|
491 | if (Utils.eq(columnEntropy, 0) || Utils.eq(rowEntropy, 0))
|
---|
492 | return 0;
|
---|
493 | return 2.0 * (infoGain / (columnEntropy + rowEntropy));
|
---|
494 | }
|
---|
495 |
|
---|
496 | /**
|
---|
497 | * Computes Goodman and Kruskal's tau-value for a contingency table.
|
---|
498 | *
|
---|
499 | * @param matrix the contingency table
|
---|
500 | * @param Goodman and Kruskal's tau-value
|
---|
501 | */
|
---|
502 | public static double tauVal(double[][] matrix) {
|
---|
503 |
|
---|
504 | int nrows, ncols, row, col;
|
---|
505 | double [] ctotal;
|
---|
506 | double maxcol = 0, max, maxtotal = 0, n = 0;
|
---|
507 |
|
---|
508 | nrows = matrix.length;
|
---|
509 | ncols = matrix[0].length;
|
---|
510 | ctotal = new double [ncols];
|
---|
511 | for (row = 0; row < nrows; row++) {
|
---|
512 | max = 0;
|
---|
513 | for (col = 0; col < ncols; col++) {
|
---|
514 | if (Utils.gr(matrix[row][col], max))
|
---|
515 | max = matrix[row][col];
|
---|
516 | ctotal[col] += matrix[row][col];
|
---|
517 | n += matrix[row][col];
|
---|
518 | }
|
---|
519 | maxtotal += max;
|
---|
520 | }
|
---|
521 | if (Utils.eq(n, 0)) {
|
---|
522 | return 0;
|
---|
523 | }
|
---|
524 | maxcol = ctotal[Utils.maxIndex(ctotal)];
|
---|
525 | return (maxtotal - maxcol)/(n - maxcol);
|
---|
526 | }
|
---|
527 |
|
---|
528 | /**
|
---|
529 | * Help method for computing entropy.
|
---|
530 | */
|
---|
531 | private static double lnFunc(double num){
|
---|
532 |
|
---|
533 | // Constant hard coded for efficiency reasons
|
---|
534 | if (num < 1e-6) {
|
---|
535 | return 0;
|
---|
536 | } else {
|
---|
537 | return num * Math.log(num);
|
---|
538 | }
|
---|
539 | }
|
---|
540 |
|
---|
541 | /**
|
---|
542 | * Computes chi-value for one cell in matrix.
|
---|
543 | * From Gary Perlman's unixstat.
|
---|
544 | */
|
---|
545 | private static double chiCell(double freq, double expect, boolean yates){
|
---|
546 |
|
---|
547 | double diff = freq - expect;
|
---|
548 |
|
---|
549 | if (yates) {
|
---|
550 | diff = Math.abs (diff) - 0.5;
|
---|
551 | if (diff < 0.0) { // over-correction
|
---|
552 | diff = 0.0;
|
---|
553 | }
|
---|
554 | }
|
---|
555 | if (Math.abs(expect) < 10e-10) {
|
---|
556 | return (0.0);
|
---|
557 | } else {
|
---|
558 | return (diff * diff / expect);
|
---|
559 | }
|
---|
560 | }
|
---|
561 |
|
---|
562 | /**
|
---|
563 | * Main method for testing this class.
|
---|
564 | */
|
---|
565 | public static void main(String[] ops) {
|
---|
566 |
|
---|
567 | double[] firstRow = {10, 5, 20};
|
---|
568 | double[] secondRow = {2, 10, 6};
|
---|
569 | double[] thirdRow = {5, 10, 10};
|
---|
570 | double[][] matrix = new double[3][0];
|
---|
571 |
|
---|
572 | matrix[0] = firstRow; matrix[1] = secondRow; matrix[2] = thirdRow;
|
---|
573 | for (int i = 0; i < matrix.length; i++) {
|
---|
574 | for (int j = 0; j < matrix[i].length; j++) {
|
---|
575 | System.out.print(matrix[i][j] + " ");
|
---|
576 | }
|
---|
577 | System.out.println();
|
---|
578 | }
|
---|
579 | System.out.println("Chi-squared probability: " +
|
---|
580 | ContingencyTables.chiSquared(matrix, false));
|
---|
581 | System.out.println("Chi-squared value: " +
|
---|
582 | ContingencyTables.chiVal(matrix, false));
|
---|
583 | System.out.println("Cochran's criterion fullfilled: " +
|
---|
584 | ContingencyTables.cochransCriterion(matrix));
|
---|
585 | System.out.println("Cramer's V: " +
|
---|
586 | ContingencyTables.CramersV(matrix));
|
---|
587 | System.out.println("Entropy of first row: " +
|
---|
588 | ContingencyTables.entropy(firstRow));
|
---|
589 | System.out.println("Entropy conditioned on columns: " +
|
---|
590 | ContingencyTables.entropyConditionedOnColumns(matrix));
|
---|
591 | System.out.println("Entropy conditioned on rows: " +
|
---|
592 | ContingencyTables.entropyConditionedOnRows(matrix));
|
---|
593 | System.out.println("Entropy conditioned on rows (with Laplace): " +
|
---|
594 | ContingencyTables.entropyConditionedOnRows(matrix, matrix, 3));
|
---|
595 | System.out.println("Entropy of rows: " +
|
---|
596 | ContingencyTables.entropyOverRows(matrix));
|
---|
597 | System.out.println("Entropy of columns: " +
|
---|
598 | ContingencyTables.entropyOverColumns(matrix));
|
---|
599 | System.out.println("Gain ratio: " +
|
---|
600 | ContingencyTables.gainRatio(matrix));
|
---|
601 | System.out.println("Negative log2 of multiple hypergeometric probability: " +
|
---|
602 | ContingencyTables.log2MultipleHypergeometric(matrix));
|
---|
603 | System.out.println("Symmetrical uncertainty: " +
|
---|
604 | ContingencyTables.symmetricalUncertainty(matrix));
|
---|
605 | System.out.println("Tau value: " +
|
---|
606 | ContingencyTables.tauVal(matrix));
|
---|
607 | double[][] newMatrix = new double[3][3];
|
---|
608 | newMatrix[0][0] = 1; newMatrix[0][1] = 0; newMatrix[0][2] = 1;
|
---|
609 | newMatrix[1][0] = 0; newMatrix[1][1] = 0; newMatrix[1][2] = 0;
|
---|
610 | newMatrix[2][0] = 1; newMatrix[2][1] = 0; newMatrix[2][2] = 1;
|
---|
611 | System.out.println("Matrix with empty row and column: ");
|
---|
612 | for (int i = 0; i < newMatrix.length; i++) {
|
---|
613 | for (int j = 0; j < newMatrix[i].length; j++) {
|
---|
614 | System.out.print(newMatrix[i][j] + " ");
|
---|
615 | }
|
---|
616 | System.out.println();
|
---|
617 | }
|
---|
618 | System.out.println("Reduced matrix: ");
|
---|
619 | newMatrix = ContingencyTables.reduceMatrix(newMatrix);
|
---|
620 | for (int i = 0; i < newMatrix.length; i++) {
|
---|
621 | for (int j = 0; j < newMatrix[i].length; j++) {
|
---|
622 | System.out.print(newMatrix[i][j] + " ");
|
---|
623 | }
|
---|
624 | System.out.println();
|
---|
625 | }
|
---|
626 | }
|
---|
627 | }
|
---|
628 |
|
---|
629 |
|
---|
630 |
|
---|
631 |
|
---|
632 |
|
---|
633 |
|
---|
634 |
|
---|
635 |
|
---|