Berry M.J.A. – Data Mining Techniques For Marketing, Sales & Customer Relationship Management

A decision tree model consists of a set of rules for dividing a large heterogeneous population into smaller, more homogeneous groups with respect to a particular target variable. A decision tree may be painstakingly constructed by hand in the manner of Linnaeus and the generations of taxonomists that followed him, or it may be grown automatically by applying any one of several decision tree algorithms to a model set comprised of preclassified data. This chapter is mostly concerned with the algorithms for automatically generating decision trees. The target variable is usually categorical and the decision tree model is used either to calculate the probability that a given record belongs to each of the categories, or to classify the record by assigning it to the most likely class. Decision trees can also be used to estimate the value of a continuous variable, although there are other techniques more suitable to that task.

Classification

Anyone familiar with the game of Twenty Questions will have no difficulty understanding how a decision tree classifies records. In the game, one player

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thinks of a particular place, person, or thing that would be known or recognized by all the participants, but the player gives no clue to its identity. The other players try to discover what it is by asking a series of yes-or-no questions. A good player rarely needs the full allotment of 20 questions to move all the way from

“Is it bigger than a bread box?” to “the Golden Gate Bridge.”

A decision tree represents such a series of questions. As in the game, the answer to the first question determines the follow-up question. The initial questions create broad categories with many members; follow-on questions divide the broad categories into smaller and smaller sets. If the questions are well chosen, a surprisingly short series is enough to accurately classify an incoming record.

The game of Twenty Questions illustrates the process of using a tree for appending a score or class to a record. A record enters the tree at the root node.

The root node applies a test to determine which child node the record will encounter next. There are different algorithms for choosing the initial test, but the goal is always the same: To choose the test that best discriminates among the target classes. This process is repeated until the record arrives at a leaf node.

All the records that end up at a given leaf of the tree are classified the same way. There is a unique path from the root to each leaf. That path is an expression of the rule used to classify the records.

Different leaves may make the same classification, although each leaf makes that classification for a different reason. For example, in a tree that classifies fruits and vegetables by color, the leaves for apple, tomato, and cherry might all predict “red,” albeit with varying degrees of confidence since there are likely to be examples of green apples, yellow tomatoes, and black cherries as well.

The decision tree in Figure 6.1 classifies potential catalog recipients as likely (1) or unlikely (0) to place an order if sent a new catalog.

The tree in Figure 6.1 was created using the SAS Enterprise Miner Tree Viewer tool. The chart is drawn according to the usual convention in data mining circles—with the root at the top and the leaves at the bottom, perhaps indicating that data miners ought to get out more to see how real trees grow.

Each node is labeled with a node number in the upper-right corner and the predicted class in the center. The decision rules to split each node are printed on the lines connecting each node to its children. The split at the root node on

“lifetime orders”; the left branch is for customers who had six or fewer orders and the right branch is for customers who had seven or more.

Any record that reaches leaf nodes 19, 14, 16, 17, or 18 is classified as likely to respond, because the predicted class in this case is 1. The paths to these leaf nodes describe the rules in the tree. For example, the rule for leaf 19 is If the customer has made more than 6.5 orders and it has been fewer than 765 days since the last order, the customer is likely to respond.

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lifetime orders