ID3 Algorithm Abbas Rizvi CS157 B Spring 2010. What is the ID3 algorithm? ID3 stands for Iterative Dichotomiser 3 Algorithm used to generate a decision.

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Presentation transcript:

ID3 Algorithm Abbas Rizvi CS157 B Spring 2010

What is the ID3 algorithm? ID3 stands for Iterative Dichotomiser 3 Algorithm used to generate a decision tree. ID3 is a precursor to the C4.5 Algorithm.

History The ID3 algorithm was invented by Ross Quinlan. Quinlan was a computer science researcher in data mining, and decision theory. Received doctorate in computer science at the University of Washington in 1968.

Decision Tree Classifies data using the attributes Tree consists of decision nodes and decision leafs. Nodes can have two or more branches which represents the value for the attribute tested. Leafs nodes produces a homogeneous result.

The algorithm The ID3 follows the Occam’s razor principle. Attempts to create the smallest possible decision tree.

The Process Take all unused attributes and calculates their entropies. Chooses attribute that has the lowest entropy is minimum or when information gain is maximum Makes a node containing that attribute

The Algorithm Create a root node for the tree If all examples are positive, Return the single-node tree Root, with label = +. If all examples are negative, Return the single-node tree Root, with label = -. If number of predicting attributes is empty, then Return the single node tree Root, with label = most common value of the target attribute in the examples.

The Algorithm (cont.) Else –A = The Attribute that best classifies examples. –Decision Tree attribute for Root = A. –For each possible value, vi, of A, Add a new tree branch below Root, corresponding to the test A = vi. Let Examples( vi ), be the subset of examples that have the value vi for A If Examples( vi ) is empty –Then below this new branch add a leaf node with label = most common target value in the examples Else below this new branch add the subtree ID3 (Examples( vi ), Target_Attribute, Attributes – {A}) End Return Root

Entropy Formula to calculate A complete homogeneous sample has an entropy of 0 An equally divided sample as an entropy of 1 Entropy = - p+log2 (p+) -p-log2 (p-) for a sample of negative and positive elements.

Exercise Calculate the entropy Given: Set S contains14 examples 9 Positive values 5 Negative values

Exercise Entropy(S) = - (9/14) Log 2 (9/14) - (5/14) Log 2 (5/14) = 0.940

Information Gain Information gain is based on the decrease in entropy after a dataset is split on an attribute. Looking for which attribute creates the most homogeneous branches

Information Gain Example 14 examples, 9 positive 5 negative The attribute is Wind. Values of wind are Weak and Strong

Exercise (cont.) 8 occurrences of weak winds 6 occurrences of strong winds For the weak winds, 6 are positive and 2 are negative For the strong winds, 3 are positive and 3 are negative

Exercise (cont.) Gain(S,Wind) = Entropy(S) - (8/14)*Entropy (Weak) -(6/14)*Entropy (Strong) Entropy(Weak) = - (6/8)*log2(6/8) - (2/8)*log2(2/8) = Entropy(Strong) = - (3/6)*log2(3/6) - (3/6)*log2(3/6) = 1.00

Exercise (cont.) So… (8/14)* (6/14)*1.00 = 0.048

Advantage of ID3 Understandable prediction rules are created from the training data. Builds the fastest tree. Builds a short tree. Only need to test enough attributes until all data is classified. Finding leaf nodes enables test data to be pruned, reducing number of tests.

Disadvantage of ID3 Data may be over-fitted or over- classified, if a small sample is tested. Only one attribute at a time is tested for making a decision. Classifying continuous data may be computationally expensive, as many trees must be generated to see where to break the continuum.

Questions