Data Mining: Practical Machine Learning Tools and ... - LIDeCC

74 CHAPTER 3 | OUTPUT: KNOWLEDGE REPRESENTATIONTable 3.2Training data for the shapes problem.Width Height Sides Class2 4 4 standing3 6 4 standing4 3 4 lying7 8 3 standing7 6 3 lying2 9 4 standing9 1 4 lying10 2 3 lyingmation the learning algorithm will be given is the width, height, and number ofsides of each block. The training data is shown in Table 3.2.A propositional rule set that might be produced for this data is:if width ≥ 3.5 and height < 7.0 then lyingif height ≥ 3.5 then standingIn case you’re wondering, 3.5 is chosen as the breakpoint for width because it ishalfway between the width of the thinnest lying block, namely 4, and the widthof the fattest standing block whose height is less than 7, namely 3. Also, 7.0 ischosen as the breakpoint for height because it is halfway between the height ofthe tallest lying block, namely 6, and the shortest standing block whose widthis greater than 3.5, namely 8. It is common to place numeric thresholds halfwaybetween the values that delimit the boundaries of a concept.Although these two rules work well on the examples given, they are not verygood. Many new blocks would not be classified by either rule (e.g., one withwidth 1 and height 2), and it is easy to devise many legitimate blocks that therules would not fit.A person classifying the eight blocks would probably notice that“standing blocks are those that are taller than they are wide.” This rule doesnot compare attribute values with constants, it compares attributes with eachother:if width > height then lyingif height > width then standingThe actual values of the height and width attributes are not important; just theresult of comparing the two. Rules of this form are called relational, becausethey express relationships between attributes, rather than propositional, whichdenotes a fact about just one attribute.