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Classification and regression

Classification and regression
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Dr.JakeFinlay,Germany,Teacher
Published Date:22-07-2017
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Classification WWW.ThesisScientist.comClassification and regression  What is classification? What is regression?  Classification by decision tree induction  Bayesian Classification  Other Classification Methods  Rule based  K-NN  SVM  Bagging/Boosting WWW.ThesisScientist.comRule-Based Classifier Classify records by using a collection of “if…then…” rules Rule: (Condition)  y  where  Condition is a conjunctions of attributes  y is the class label  LHS: rule antecedent or condition  RHS: rule consequent  Examples of classification rules:  (Blood Type=Warm)  (Lay Eggs=Yes)  Birds  (Taxable Income 50K)  (Refund=Yes)  Evade=No WWW.ThesisScientist.comRule-based Classifier (Example) Name Blood Type Give Birth Can Fly Live in Water Class human warm yes no no mammals python cold no no no reptiles salmon cold no no yes fishes whale warm yes no yes mammals frog cold no no sometimes amphibians komodo cold no no no reptiles bat warm yes yes no mammals pigeon warm no yes no birds cat warm yes no no mammals leopard shark cold yes no yes fishes turtle cold no no sometimes reptiles penguin warm no no sometimes birds porcupine warm yes no no mammals eel cold no no yes fishes salamander cold no no sometimes amphibians gila monster cold no no no reptiles platypus warm no no no mammals owl warm no yes no birds dolphin warm yes no yes mammals eagle warm no yes no birds R1: (Give Birth = no)  (Can Fly = yes)  Birds R2: (Give Birth = no)  (Live in Water = yes)  Fishes R3: (Give Birth = yes)  (Blood Type = warm)  Mammals R4: (Give Birth = no)  (Can Fly = no)  Reptiles R5: (Live in Water = sometimes)  Amphibians WWW.ThesisScientist.comApplication of Rule-Based Classifier  A rule r covers an instance x if the attributes of the instance satisfy the condition of the rule R1: (Give Birth = no)  (Can Fly = yes)  Birds R2: (Give Birth = no)  (Live in Water = yes)  Fishes R3: (Give Birth = yes)  (Blood Type = warm)  Mammals R4: (Give Birth = no)  (Can Fly = no)  Reptiles R5: (Live in Water = sometimes)  Amphibians Name Blood Type Give Birth Can Fly Live in Water Class hawk warm no yes no ? grizzly bear warm yes no no ? The rule R1 covers a hawk = Bird The rule R3 covers the grizzly bear = Mammal WWW.ThesisScientist.comRule Coverage and Accuracy Tid Refund Marital Taxable Class Status Income Coverage of a rule: 1 Yes Single 125K No  Fraction of records 2 No Married 100K No that satisfy the 3 No Single 70K No antecedent of a rule 4 Yes Married 120K No 5 No Divorced 95K Yes Accuracy of a rule: 6 No Married 60K No  Fraction of records 7 Yes Divorced 220K No that satisfy both the 8 No Single 85K Yes antecedent and 9 No Married 75K No consequent of a 10 No Single 90K Yes 10 rule (Status=Single)  No WWW.ThesisScientist.com Coverage = 40%, Accuracy = 50%How does Rule-based Classifier Work? R1: (Give Birth = no)  (Can Fly = yes)  Birds R2: (Give Birth = no)  (Live in Water = yes)  Fishes R3: (Give Birth = yes)  (Blood Type = warm)  Mammals R4: (Give Birth = no)  (Can Fly = no)  Reptiles R5: (Live in Water = sometimes)  Amphibians Name Blood Type Give Birth Can Fly Live in Water Class lemur warm yes no no ? turtle cold no no sometimes ? dogfish shark cold yes no yes ? A lemur triggers rule R3, so it is classified as a mammal A turtle triggers both R4 and R5 A dogfish shark triggers none of the rules WWW.ThesisScientist.comCharacteristics of Rule-Based Classifier Mutually exclusive rules  Classifier contains mutually exclusive rules if the rules are independent of each other  Every record is covered by at most one rule Exhaustive rules  Classifier has exhaustive coverage if it accounts for every possible combination of attribute values  Each record is covered by at least one rule WWW.ThesisScientist.comFrom Decision Trees To Rules Classification Rules Refund (Refund=Yes) == No Yes No (Refund=No, Marital Status=Single,Divorced, NO NO Marital Taxable Income80K) == No Status Single, (Refund=No, Marital Status=Single,Divorced, Married Divorced Taxable Income80K) == Yes NO NO Taxable (Refund=No, Marital Status=Married) == No Income 80K 80K NO NO Y YE ES S Rules are mutually exclusive and exhaustive Rule set contains as much information as the tree WWW.ThesisScientist.comRules Can Be Simplified Tid Refund Marital Taxable Refund Cheat Status Income Yes No 1 Yes Single 125K No NO NO Marital 2 No 100K Married No Status Single, Married 3 No Single 70K No Divorced 4 Yes Married 120K No NO NO Taxable 5 No Divorced 95K Yes Income 6 No Married 60K No 80K 80K 7 Yes Divorced 220K No NO NO Y YE ES S 8 No Single 85K Yes 9 No Married 75K No 10 No Single 90K Yes 10 Initial Rule: (Refund=No)  (Status=Married)  No WWW.ThesisScientist.com Simplified Rule: (Status=Married)  NoEffect of Rule Simplification Rules are no longer mutually exclusive  A record may trigger more than one rule  Solution?  Ordered rule set  Unordered rule set – use voting schemes Rules are no longer exhaustive  A record may not trigger any rules  Solution?  Use a default class WWW.ThesisScientist.comOrdered Rule Set  Rules are rank ordered according to their priority  An ordered rule set is known as a decision list  When a test record is presented to the classifier  It is assigned to the class label of the highest ranked rule it has triggered  If none of the rules fired, it is assigned to the default class R1: (Give Birth = no)  (Can Fly = yes)  Birds R2: (Give Birth = no)  (Live in Water = yes)  Fishes R3: (Give Birth = yes)  (Blood Type = warm)  Mammals R4: (Give Birth = no)  (Can Fly = no)  Reptiles R5: (Live in Water = sometimes)  Amphibians Name Blood Type Give Birth Can Fly Live in Water Class WWW.ThesisScientist.com turtle cold no no sometimes ?Rule Ordering Schemes Rule-based ordering  Individual rules are ranked based on their quality Class-based ordering  Rules that belong to the same class appear together Rule-based Ordering Class-based Ordering (Refund=Yes) == No (Refund=Yes) == No (Refund=No, Marital Status=Single,Divorced, (Refund=No, Marital Status=Single,Divorced, Taxable Income80K) == No Taxable Income80K) == No (Refund=No, Marital Status=Single,Divorced, (Refund=No, Marital Status=Married) == No Taxable Income80K) == Yes (Refund=No, Marital Status=Single,Divorced, (Refund=No, Marital Status=Married) == No Taxable Income80K) == Yes WWW.ThesisScientist.comBuilding Classification Rules Direct Method:  Extract rules directly from data  e.g.: RIPPER, CN2, Holte’s 1R Indirect Method:  Extract rules from other classification models (e.g. decision trees, etc).  e.g: C4.5 rules WWW.ThesisScientist.comDirect Method: Sequential Covering 1. Start from an empty rule 2. Grow a rule using the Learn-One-Rule function 3. Remove training records covered by the rule 4. Repeat Step (2) and (3) until stopping criterion is met WWW.ThesisScientist.comExample of Sequential Covering (i) Original Data (ii) Step 1 WWW.ThesisScientist.comExample of Sequential Covering… R1 R1 R2 (iii) Step 2 (iv) Step 3 WWW.ThesisScientist.comAspects of Sequential Covering Rule Growing Instance Elimination Rule Evaluation Stopping Criterion Rule Pruning WWW.ThesisScientist.comRule Growing  Two common strategies Yes: 3 Refund=No, Refund=No, No: 4 Status=Single, Status=Single, Income=85K Income=90K (Class=Yes) (Class=Yes) Income Refund= Refund=No, Status = Status = Status = ... 80K No Single Divorced Status = Single Married (Class = Yes) Yes: 3 Yes: 2 Yes: 1 Yes: 0 Yes: 3 No: 4 No: 1 No: 0 No: 3 No: 1 (b) Specific-to-general (a) General-to-specific WWW.ThesisScientist.comRule Growing (Examples)  CN2 Algorithm:  Start from an empty conjunct:  Add conjuncts that minimizes the entropy measure: A, A,B, …  Determine the rule consequent by taking majority class of instances covered by the rule  RIPPER Algorithm:  Start from an empty rule: = class  Add conjuncts that maximizes FOIL’s information gain measure:  R0: = class (initial rule)  R1: A = class (rule after adding conjunct)  Gain(R0, R1) = t log (p1/(p1+n1)) – log (p0/(p0 + n0))  where t: number of positive instances covered by both R0 and R1 p0: number of positive instances covered by R0 n0: number of negative instances covered by R0 p1: number of positive instances covered by R1 n1: number of negative instances covered by R1 WWW.ThesisScientist.com