", { With rule-based ordering, the rules are organized into one long priority list, according to some measure of rule quality such as accuracy, coverage, or size or based on advice from domain experts. { "contentUrl": "https://slideplayer.com/slide/13513750/82/images/5/Rule-Based+Classification.jpg", A disjunction (logical OR) is implied between each of the extracted rules. "@type": "ImageObject", }, 5 This sequential learning of rules is in contrast to decision tree induction. "description": "Which is easily solved by the method of least squares using software for regression analysis. With class-based ordering, the classes are sorted in order of decreasing importance, such as by decreasing order of prevalence. The classifying attribute is loan decision, which indicates whether a loan is accepted (considered safe) or rejected (considered risky). "description": "Rule-Based Classification", An example of a multiple linear regression model based on two predictor attributes or variables, A1 and A2, is y = w0+w1x1+w2x2 where x1 and x2 are the values of attributes A1 and A2, respectively, in X. "@type": "ImageObject", X satisfies R1, which triggers the rule. "name": "Rule-Based Classification", Although it is easy to extract rules from a decision tree, we may need to do some more work by pruning the resulting rule set. "width": "1024" Vipin Kumar CSci 8980 Fall CSci 8980: Data Mining (Fall 2002) Vipin Kumar Army High Performance Computing Research Center Department of Computer. The classifying attribute is loan decision, which indicates whether a loan is accepted (considered safe) or rejected (considered risky). }, Data Mining Classification: Alternative Techniques. "contentUrl": "https://slideplayer.com/slide/13513750/82/images/27/Multiple+Linear+Regression.jpg", "width": "1024" Consider rule R1, which covers 2 of the 14 tuples. Each splitting criterion along a given path is logically ANDed to form the rule antecedent (IF part). "@context": "http://schema.org",

To learn a rule for the class accept, we start off with the most general rule possible, that is, the condition of the rule antecedent is empty. Chapter 4 Linear Regression 1. Straight-line regression analysis involves a response variable, y, and a single predictor variable, x. Consider a cubic polynomial relationship given by. "@context": "http://schema.org", The IF-part of a rule is known as the rule antecedent or precondition. We append by adding the attribute test as a logical conjunct to the existing condition of the rule antecedent. ", "contentUrl": "https://slideplayer.com/slide/13513750/82/images/17/Rule-Based+Classification.jpg", "name": "Rule-Based Classification", The class rule set with the least number of false positives is examined first. Each time it is faced with adding a new attribute test (conjunct) to the current rule, it picks the one that most improves the rule quality, based on the training samples. Because the path to each leaf in a decision tree corresponds to a rule, we can consider decision tree induction as learning a set of rules simultaneously. Because the rules are extracted directly from the tree, they are mutually exclusive and exhaustive. If more than one rule is triggered, then What if they each specify a different class We need a conflict resolution strategy to figure out which rule gets to fire and assign its class prediction to X. "@context": "http://schema.org", Rules are learned for one class at a time.

The method of least squares shown above can be extended to solve for w0, w1, and w2. "description": "Rule-based classifiers, where the learned model is represented as a set of IF-THEN rules. "contentUrl": "https://slideplayer.com/slide/13513750/82/images/24/Linear+Regression+Straight-line+regression+analysis+involves+a+response+variable%2C+y%2C+and+a+single+predictor+variable%2C+x..jpg", Each time a rule is learned, the tuples covered by the rule are removed, and the process repeats on the remaining tuples. }, 8 Most rule-based classification systems use a class-based rule-ordering strategy. "width": "1024" For example, what if a given response variable and predictor variable have a relationship that may be modelled by a polynomial function? In the rule antecedent, the condition consists of one or more attribute tests (such as age = youth, and student = yes) that are logically ANDed. }, 9 For example, suppose we have. Triggering does not always mean firing since there may be more than one rule that is satisfied! "description": "Rule Extraction from a Decision Tree. ", "name": "Rule-Based Classification", That is, y = b + wx. "@context": "http://schema.org", Rule Generation from Decision Tree Decision tree classifiers are popular method of classification due to it is easy understanding However, decision tree. Typically, rules are grown in a general-to-specific manner. "@type": "ImageObject", How, then, can we determine the class label of X? "@context": "http://schema.org", Lets see how we can use rule-based classification to predict the class label of a given tuple, X. An IF-THEN rule is an expression of the form. 6-1 Introduction To Empirical Models 6-1 Introduction To Empirical Models. Although it is easy to extract rules from a decision tree, we may need to do some more work by pruning the resulting rule set. "@type": "ImageObject", "width": "1024" "@type": "ImageObject", 2022 SlidePlayer.com Inc. All rights reserved. }, 18 { "@context": "http://schema.org", }, 17 ", "width": "1024" "@type": "ImageObject", If R1 is the only rule satisfied, then the rule fires by returning the class prediction for X. R1 can also be written as: If the condition in a rule antecedent holds true for a given tuple, we say that the rule antecedent is satisfied and that the rule covers the tuple. Rule-Based ClassificationRule Extraction from a Decision Tree Other problems arise during rule pruning, however, as the rules will no longer be mutually exclusive and exhaustive. { "contentUrl": "https://slideplayer.com/slide/13513750/82/images/22/Prediction+What+if+we+would+like+to+predict+a+continuous+value%2C+rather+than+a+categorical+label.jpg", "width": "1024" "contentUrl": "https://slideplayer.com/slide/13513750/82/images/12/Rule-Based+Classification.jpg", "contentUrl": "https://slideplayer.com/slide/13513750/82/images/21/Rule+Induction+Using+a+Sequential+Covering+Algorithm.jpg", y = w0 + w1x. Decision trees can become large and difficult to interpret. "width": "1024" The default rule is evaluated at the end, if and only if no other rule covers X. The size ordering scheme assigns the highest priority to the triggering rule that has the toughest requirements. ",

"width": "1024" Each splitting criterion along a given path is logically ANDed to form the rule antecedent (IF part). "contentUrl": "https://slideplayer.com/slide/13513750/82/images/8/Rule-Based+Classification.jpg", "@context": "http://schema.org", Multiple Linear RegressionMultiple linear regression is an extension of straight-line regression so as to involve more than one predictor variable. Prediction Regression analysis can be used to model the relationship between one or more independent or predictor variables and a dependent or response variable. Therefore, the order of the rules does not matter\u2014they are unordered. Numeric prediction is the task of predicting continuous (or ordered) values for given input. Within a rule set, the rules are not ordered. Rule-Based ClassificationThe rules consequent contains a class prediction. If more than one rule is triggered, then What if they each specify a different class? }, 12 "@type": "ImageObject", "@type": "ImageObject", }, 13 Polynomial regression is a special case of multiple regression. It groups all rules for a single class together, and then determines a ranking of these class rule sets. }, 6 To extract rules from a decision tree, one rule is created for each path from the root to a leaf node. IF condition THEN conclusion. We would like to classify X according to buys computer. We need a conflict resolution strategy to figure out which rule gets to fire and assign its class prediction to X. ", The leaf node holds the class prediction, forming the rule consequent ( THEN part). When rule ordering is used, the rule set is known as a decision list. In this way, the rules learned should be of high accuracy. Given a tuple, X, from a class labelled data set, D. let ncovers be the number of tuples covered by R, ncorrect be the number of tuples correctly classified by R and |D| be the number of tuples in D. We can define the coverage and accuracy of R as. coverage(R1) = 2\/ % accuracy (R1) = 2\/2 = 100%. How can we prune the rule set? For a given rule antecedent, any condition that does not improve the estimated accuracy of the rule can be pruned, thereby generalizing the rule. IF income = high THEN loan_decision =acceptRule Induction Using a Sequential Covering Algorithm Learn_One_Rule adopts a greedy depth-first strategy. The rules need not necessarily be of high coverage. "name": "Rule-Based Classification", In this way, the rule fires when no other rule is satisfied. What if there is no rule satisfied by X? "@context": "http://schema.org", "description": "It is the simplest form of regression, and models y as a linear function of x. Rule Induction Using a Sequential Covering AlgorithmEach time we add an attribute test to a rule, the resulting rule should cover more of the accept tuples. The THEN -part is the rule consequent. That is, the triggering rule with the most attribute tests is fired. ", A rule R can be assessed by its coverage and accuracy Given a tuple, X, from a class labelled data set, D. let ncovers be the number of tuples covered by R, ncorrect be the number of tuples correctly classified by R and |D| be the number of tuples in D. We can define the coverage and accuracy of R as Slides for Data Mining by I. H. Witten and E. Frank. Using IF-THEN Rules for Classification An IF-THEN rule is an expression of the form IF condition THEN conclusion. Polynomial regression is often of interest when there is just one predictor variable. "@type": "ImageObject", It is the simplest form of regression, and models y as a linear function of x. To convert this equation to linear form, we define new variables: Which is easily solved by the method of least squares using software for regression analysis. Covering Algorithms. { Rule-Based ClassificationConsider rule R1, which covers 2 of the 14 tuples. The classifying attribute is loan decision, which indicates whether a loan is accepted (considered safe) or rejected (considered risky). "width": "1024" Each time a rule is learned, the tuples covered by the rule are removed, and the process repeats on the remaining tuples. "name": "Non Linear Regression Consider a cubic polynomial relationship given by. where x1 and x2 are the values of attributes A1 and A2, respectively, in X. A rule R can be assessed by its coverage and accuracy. The IF -part of a rule is known as the rule antecedent or precondition. ", { "description": "The rule\u2019s consequent contains a class prediction. Therefore, the order of the rules does not matterthey are unordered. Any other rule that satisfies X is ignored. By applying transformations to the variables, we can convert the nonlinear model into a linear one that can then be solved by the method of least squares. The response variable is what we want to predict. Any other rule that satisfies X is ignored. Rule-Based ClassificationRule Extraction from a Decision Tree A disjunction (logical OR) is implied between each of the extracted rules. We start off with an empty rule and then gradually keep appending attribute tests to it. (That is, X = (x1, x2, : : : , xn).) Given a tuple described by predictor variables, we want to predict the associated value of the response variable. Polynomial regression is a special case of multiple regression. By exhaustive, there is one rule for each possible attribute-value combination, so that this set of rules does not require a default rule. The ordering may be class based or rule-based. "contentUrl": "https://slideplayer.com/slide/13513750/82/images/3/Rule-Based+Classification.jpg", ", "width": "1024" The rule is: We then consider each possible attribute test that may be added to the rule. In the context of data mining, the predictor variables are the attributes of interest describing the tuple. ", For example, we may wish to predict the salary of college graduates with 10 years of work experience. "description": "Consider rule R1, which covers 2 of the 14 tuples. The IF-part of a rule is known as the rule antecedent or precondition. "@type": "ImageObject", Rule-Based Classifiers. "description": "Let\u2019s see how we can use rule-based classification to predict the class label of a given tuple, X. A disjunction (logical OR) is implied between each of the extracted rules. "name": "Rule-Based Classification", }, 28 "contentUrl": "https://slideplayer.com/slide/13513750/82/images/15/Rule-Based+Classification.jpg", "contentUrl": "https://slideplayer.com/slide/13513750/82/images/14/Rule-Based+Classification.jpg", "contentUrl": "https://slideplayer.com/slide/13513750/82/images/1/Rule-Based+Classification.jpg", "name": "Rule-Based Classification", { "@context": "http://schema.org", Thank you!

{ An IF-THEN rule is an expression of the form. C4.5 orders the class rule sets so as to minimize the number of false-positive errors. Each time it is faced with adding a new attribute test (conjunct) to the current rule, it picks the one that most improves the rule quality, based on the training samples. "width": "1024" We append it to the condition, so that the current rule becomes: IF income = high THEN loan_decision =accept "@context": "http://schema.org", }, 16 The leaf node holds the class prediction, forming the rule consequent (THEN part). { Share buttons are a little bit lower. The size ordering scheme assigns the highest priority to the triggering rule that has the toughest requirements. Because the rules are extracted directly from the tree, they are mutually exclusive and exhaustive. { R1 can also be written as: If the condition in a rule antecedent holds true for a given tuple, we say that the rule antecedent is satisfied and that the rule covers the tuple. This may be the class in majority or the majority class of the tuples that were not covered by any rule. The rule is: We then consider each possible attribute test that may be added to the rule. If R1 is the only rule satisfied, then the rule fires by returning the class prediction for X. The default rule is evaluated at the end, if and only if no other rule covers X. "name": "Rule-Based Classification", "@context": "http://schema.org", With rule ordering, the triggering rule that appears earliest in the list has highest priority, and so it gets to fire its class prediction. Rule-Based ClassificationTriggering does not always mean firing since there may be more than one rule that is satisfied! It is a statistical methodology that was developed by Sir Frances Galton (1822 \u2013 1911), a mathematician who was also a cousin of Charles Darwin. Toughness is measured by the rule antecedent size. Other problems arise during rule pruning, however, as the rules will no longer be mutually exclusive and exhaustive. The Learn_One_Rule procedure finds the best rule for the current class, given the current set of training tuples. The process continues until the terminating condition is met, such as when there are no more training tuples or the quality of a rule returned is below a user-specified threshold. ", Linear Regression Our current rule grows to become: The process repeats, where at each step, we continue to greedily grow rules until the resulting rule meets an acceptable quality level. { { {

In this case, a fallback or default rule can be set up to specify a default class, based on a training set. "width": "1024" "description": "Let D be a training set consisting of values of predictor variable, x, for some population and their associated values for response variable, y. The rules extracted from decision trees that suffer from subtree repetition and replication can be large and difficult to follow. Given a tuple described by predictor variables, we want to predict the associated value of the response variable. "width": "1024" "name": "Rule-Based Classification", ", Ideally, when learning a rule for a class, Ci, we would like the rule to cover all (or many) of the training tuples of class Ci and none (or few) of the tuples from other classes. "@type": "ImageObject", Let D be a training set consisting of values of predictor variable, x, for some population and their associated values for response variable, y. "name": "Rule Induction Using a Sequential Covering Algorithm", If you wish to download it, please recommend it to your friends in any social system. Discriminant Analysis Discriminant analysis is a technique for analyzing data when the criterion or dependent variable is categorical and the predictor. ", "name": "Rule-Based Classification", (That is, X = (x1, x2, : : : , xn).). The method of least squares shown above can be extended to solve for w0, w1, and w2. "width": "1024" We append by adding the attribute test as a logical conjunct to the existing condition of the rule antecedent. { It groups all rules for a single class together, and then determines a ranking of these class rule sets. "contentUrl": "https://slideplayer.com/slide/13513750/82/images/23/Prediction+Regression+analysis+can+be+used+to+model+the+relationship+between+one+or+more..jpg", When rule ordering is used, the rule set is known as a decision list. "name": "Linear Regression These coefficients can be solved by the method of least squares. coverage(R1) = 2/ % accuracy (R1) = 2/2 = 100%. Rule-based classifiers, where the learned model is represented as a set of IF-THEN rules. We append it to the condition, so that the current rule becomes: IF income = high THEN loan_decision =accept. R1 can also be written as: If the condition in a rule antecedent holds true for a given tuple, we say that the rule antecedent is satisfied and that the rule covers the tuple. Rule-Based ClassificationRule Induction Using a Sequential Covering Algorithm Rules are learned for one class at a time. Learn_One_Rule adopts a greedy depth-first strategy. X satisfies R1, which triggers the rule. For example, after. The process continues until the terminating condition is met, such as when there are no more training tuples or the quality of a rule returned is below a user-specified threshold. Using IF-THEN Rules for Classification. For example, we may wish to predict the salary of college graduates with 10 years of work experience. "@type": "ImageObject", "width": "1024" The regression coefficients, w and b, can also be thought of as weights, so that we can equivalently write y = w0 + w1x

"@context": "http://schema.org", With rule ordering, the triggering rule that appears earliest in the list has highest priority, and so it gets to fire its class prediction. To extract rules from a decision tree, one rule is created for each path from the root to a leaf node.