Data Mining: Practical Machine Learning Tools and Techniques, Second Edition
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- Bu səhifədəki naviqasiya:
- Table 4.8 Part of the contact lens data for which astigmatism
- Table 4.9 Part of the contact lens data for which astigmatism
4 . 4 C OV E R I N G A LG O R I T H M S : C O N S T RU C T I N G RU L E S 1 0 9 Considering the possibilities for the unknown term ? yields the seven choices: age = young
2/4 age
= pre-presbyopic 1/4
age = presbyopic 1/4 spectacle prescription = myope 3/6
spectacle prescription = hypermetrope 1/6 tear production rate = reduced 0/6
tear production rate = normal
4/6 (Again, count the entries in Table 4.8.) The last is a clear winner, getting four instances correct out of the six that it covers, and corresponds to the rule If astigmatism = yes and tear production rate = normal then recommendation = hard Should we stop here? Perhaps. But let’s say we are going for exact rules, no matter how complex they become. Table 4.9 shows the cases that are covered by the rule so far. The possibilities for the next term are now age = young
2/2 age
= pre-presbyopic 1/2
age = presbyopic 1/2 spectacle prescription = myope 3/3
spectacle prescription = hypermetrope 1/3 We need to choose between the first and fourth. So far we have treated the frac- tions numerically, but although these two are equal (both evaluate to 1), they have different coverage: one selects just two correct instances and the other Table 4.8 Part of the contact lens data for which astigmatism = yes. Age Spectacle Astigmatism Tear production Recommended prescription rate lenses
young myope
yes reduced
none young
myope yes
normal hard
young hypermetrope yes reduced
none young
hypermetrope yes
normal hard
pre-presbyopic myope
yes reduced
none pre-presbyopic myope yes
normal hard
pre-presbyopic hypermetrope yes reduced
none pre-presbyopic hypermetrope yes
normal none
presbyopic myope
yes reduced
none presbyopic myope yes
normal hard
presbyopic hypermetrope yes reduced
none presbyopic hypermetrope yes
normal none
P088407-Ch004.qxd 4/30/05 11:13 AM Page 109 selects three. In the event of a tie, we choose the rule with the greater coverage, giving the final rule: If astigmatism = yes and tear production rate = normal and spectacle prescription = myope then recommendation = hard This is indeed one of the rules given for the contact lens problem. But it only covers three of the four hard recommendations. So we delete these three from the set of instances and start again, looking for another rule of the form: If ? then recommendation = hard Following the same process, we will eventually find that age = young is the best choice for the first term. Its coverage is seven; the reason for the seven is that 3 instances have been removed from the original set, leaving 21 instances alto- gether. The best choice for the second term is astigmatism = yes, selecting 1/3 (actually, this is a tie); tear production rate = normal is the best for the third, selecting 1/1. If age = young and astigmatism = yes and tear production rate = normal then recommendation = hard This rule actually covers three of the original set of instances, two of which are covered by the previous rule—but that’s all right because the recommendation is the same for each rule. Now that all the hard-lens cases are covered, the next step is to proceed with the soft-lens ones in just the same way. Finally, rules are generated for the none case—unless we are seeking a rule set with a default rule, in which case explicit rules for the final outcome are unnecessary. What we have just described is the PRISM method for constructing rules. It generates only correct or “perfect” rules. It measures the success of a rule by the accuracy formula p/t. Any rule with accuracy less than 100% is “incorrect” in 1 1 0 C H A P T E R 4 | A LG O R I T H M S : T H E BA S I C M E T H O D S Table 4.9 Part of the contact lens data for which astigmatism = yes and tear production rate = normal. Age Spectacle Astigmatism Tear production Recommended prescription rate lenses
young myope
yes normal
hard young
hypermetrope yes
normal hard
pre-presbyopic myope
yes normal
hard pre-presbyopic hypermetrope yes
normal none
presbyopic myope
yes normal
hard presbyopic hypermetrope yes
normal none
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