Decision Tree Induction

Decision Tree Induction (DTI) is an important step of the segmentation methodology. It can be viewed as a tool for the analysis of large datasets characterized by high dimensionality and nonstandard structure. Segmentation follows a nonparametric approach, since no hypotheses are made on the variable distribution. The resulting model has the structure of a tree graph. It is considered a supervised method, since a response criterion variable is explained by a set of predictors. In particular, segmentation consists of partitioning the objects (also called cases, individuals, observations, etc.) into a number of subgroups (on the basis of suitable partitioning of the modalities of the explanatory variables, the so-called predictors) in a recursive way, so that a tree-structure is produced. Typically, partitioning is in two subgroups yielding to binary trees, although ternary trees as well as r-way trees also can be built up. Two main targets can be achieved with tree-structures—classification and regression trees—on the basis of the type of response variable, which can be categorical or numerical. Tree-based methods are characterized by two main tasks: exploratory and decision. The first is to describe with the tree structure the dependence between the response and the predictors. The decision task is properly of DTI, aiming to define a decision rule for unseen objects for estimating unknown response class/values as well as validating the accuracy of the final results. For example, trees often are considered in creditscoring problems in order to describe and classify good and bad clients of a bank on the basis of socioeconomic indicators (e.g., age, working conditions, family status, etc.) and financial conditions (e.g., income, savings, payment methods, etc.). Conditional interactions describing the client profile can be detected looking at the paths along the tree, when going from the top to the terminal nodes. Each internal node of the tree is assigned a partition (or a split for binary tree) of the predictor space, and each terminal node is assigned a label class/value of the response. As a result, each tree path, characterized by a sequence of predictor interactions, can be viewed as a production rule yielding to a specific label class/value. The set of production rules constitutes the predictive learning of the response class/ value of new objects, where only measurements of the predictors are known. As an example, a new client of a bank is classified as a good client or a bad one by dropping it down the tree according to the set of splits (binary questions) of a tree path, until a terminal node labeled by a specific response-class is reached.