Case Based Reasoning Lecture 4: CBR Tutorial on Decision Trees

Exercise 1 – Predicting the Risk for Loan Applications IncomeCredit RatingDebtCollateralRisk 1$0 to $15kbadhighnonehigh 2$15 to $35kunknownhighnonehigh 3$15 to $35kunknownlownonemoderate 4$0 to $15kunknownlownonehigh 5over $35kunknownlownonelow 6over $35kunknownlowadequatelow 7$0 to $15kbadlownonehigh 8over $35kbadlowadequatemoderate 9over $35kgoodlownonelow 10over $35kgoodhighadequatelow 11$0 to $15kgoodhighnonehigh 12$15 to $35kgoodhighnonemoderate 13over $35kgoodhighnonelow 14$15 to $35kbadhighnonehigh Create the decision tree index

Exercise 1 – Solution first part 6/14 cases are high risk, 3/14 cases are moderate risk, and 5/14 cases are low risk Entropy(S)= -6/14*log 2 6/14 - 3/14*log 2 3/14 - 5/14*log 2 5/14 = If income is the root of the decision tree, then: Entropy(0-15k) = - 4/4 * log 2 4/4 = 0 Entropy(15-35k)= - 2/4 * log 2 2/4 - 2/4 * log 2 2/4 = 1 Entropy(over 35k) = - 5/6 * log 2 5/6 - 1/6 * log 2 1/6 = 0.65 Expectation(income)= 4/14*Entropy(0-15) + 4/14*Entropy(15-35) + 6/14*Entropy(over 35k) = 0.56 Gain(income)=Entropy(S)–Expectation(income)= – 0.56 = 0.971

Exercise 2 – Predicting the Desirability of a Property PriceLocationStateDesirability 1AverageCentralOKYes 2HighCountrysideOKNo 3LowCentralGoodYes 4HighCentralGoodYes 5AverageCountrysideOKYes 6AverageCentralBadNo 7LowCountrysideBadYes Create the decision tree index

Exercise 3 – Predicting whether to Play Tennis or Not Create the decision tree index OutlookTemperatureHumidityWindyPlay SunnyHotHighFalseNo SunnyHotHighTrueNo CloudyHotHighFalseYes RainyMildHighFalseYes RainyCoolNormalFalseYes RainyCoolNormalTrueNo CloudyCoolNormalTrueYes SunnyMildHighFalseNo SunnyCoolNormalFalseYes RainyMildNormalFalseYes SunnyMildNormalTrueYes CloudyMildHighTrueYes CloudyHotNormalFalseYes RainyMildHighTrueNo