smile.classification

Class DecisionTree

java.lang.Object

smile.classification.DecisionTree

All Implemented Interfaces:

java.io.Serializable, Classifier<double[]>, SoftClassifier<double[]>

public class DecisionTree
extends java.lang.Object
implements SoftClassifier<double[]>, java.io.Serializable

Decision tree for classification. A decision tree can be learned by splitting the training set into subsets based on an attribute value test. This process is repeated on each derived subset in a recursive manner called recursive partitioning. The recursion is completed when the subset at a node all has the same value of the target variable, or when splitting no longer adds value to the predictions.

The algorithms that are used for constructing decision trees usually work top-down by choosing a variable at each step that is the next best variable to use in splitting the set of items. "Best" is defined by how well the variable splits the set into homogeneous subsets that have the same value of the target variable. Different algorithms use different formulae for measuring "best". Used by the CART algorithm, Gini impurity is a measure of how often a randomly chosen element from the set would be incorrectly labeled if it were randomly labeled according to the distribution of labels in the subset. Gini impurity can be computed by summing the probability of each item being chosen times the probability of a mistake in categorizing that item. It reaches its minimum (zero) when all cases in the node fall into a single target category. Information gain is another popular measure, used by the ID3, C4.5 and C5.0 algorithms. Information gain is based on the concept of entropy used in information theory. For categorical variables with different number of levels, however, information gain are biased in favor of those attributes with more levels. Instead, one may employ the information gain ratio, which solves the drawback of information gain.

Classification and Regression Tree techniques have a number of advantages over many of those alternative techniques.

Simple to understand and interpret.

In most cases, the interpretation of results summarized in a tree is very simple. This simplicity is useful not only for purposes of rapid classification of new observations, but can also often yield a much simpler "model" for explaining why observations are classified or predicted in a particular manner.

Able to handle both numerical and categorical data.

Other techniques are usually specialized in analyzing datasets that have only one type of variable.

Tree methods are nonparametric and nonlinear.

The final results of using tree methods for classification or regression can be summarized in a series of (usually few) logical if-then conditions (tree nodes). Therefore, there is no implicit assumption that the underlying relationships between the predictor variables and the dependent variable are linear, follow some specific non-linear link function, or that they are even monotonic in nature. Thus, tree methods are particularly well suited for data mining tasks, where there is often little a priori knowledge nor any coherent set of theories or predictions regarding which variables are related and how. In those types of data analytics, tree methods can often reveal simple relationships between just a few variables that could have easily gone unnoticed using other analytic techniques.

One major problem with classification and regression trees is their high variance. Often a small change in the data can result in a very different series of splits, making interpretation somewhat precarious. Besides, decision-tree learners can create over-complex trees that cause over-fitting. Mechanisms such as pruning are necessary to avoid this problem. Another limitation of trees is the lack of smoothness of the prediction surface.

Some techniques such as bagging, boosting, and random forest use more than one decision tree for their analysis.

See Also:

AdaBoost, GradientTreeBoost, RandomForest, Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	DecisionTree.SplitRule The criterion to choose variable to split instances.
static class	DecisionTree.Trainer Trainer for decision tree classifiers.

Constructor Summary

Constructors

Constructor and Description
DecisionTree(smile.data.Attribute[] attributes, double[][] x, int[] y, int maxNodes) Constructor.
DecisionTree(smile.data.Attribute[] attributes, double[][] x, int[] y, int maxNodes, DecisionTree.SplitRule rule) Constructor.
DecisionTree(smile.data.Attribute[] attributes, double[][] x, int[] y, int maxNodes, int nodeSize, DecisionTree.SplitRule rule) Constructor.
DecisionTree(smile.data.Attribute[] attributes, double[][] x, int[] y, int maxNodes, int nodeSize, int mtry, DecisionTree.SplitRule rule, int[] samples, int[][] order) Constructor.
DecisionTree(double[][] x, int[] y, int maxNodes) Constructor.
DecisionTree(double[][] x, int[] y, int maxNodes, DecisionTree.SplitRule rule) Constructor.
DecisionTree(double[][] x, int[] y, int maxNodes, int nodeSize, DecisionTree.SplitRule rule) Constructor.

Method Summary

Modifier and Type	Method and Description
double[]	importance() Returns the variable importance.
int	maxDepth() Returns the maximum depth" of the tree -- the number of nodes along the longest path from the root node down to the farthest leaf node.
int	predict(double[] x) Predicts the class label of an instance.
int	predict(double[] x, double[] posteriori) Predicts the class label of an instance and also calculate a posteriori probabilities.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

DecisionTree

public DecisionTree(double[][] x,
                    int[] y,
                    int maxNodes)

Constructor. Learns a classification tree with (most) given number of leaves. All attributes are assumed to be numeric.

Parameters:

x - the training instances.

y - the response variable.

maxNodes - the maximum number of leaf nodes in the tree.

DecisionTree

public DecisionTree(double[][] x,
                    int[] y,
                    int maxNodes,
                    DecisionTree.SplitRule rule)

Constructor. Learns a classification tree with (most) given number of leaves. All attributes are assumed to be numeric.

Parameters:

x - the training instances.

y - the response variable.

maxNodes - the maximum number of leaf nodes in the tree.

rule - the splitting rule.

DecisionTree

public DecisionTree(double[][] x,
                    int[] y,
                    int maxNodes,
                    int nodeSize,
                    DecisionTree.SplitRule rule)

Constructor. Learns a classification tree with (most) given number of leaves. All attributes are assumed to be numeric.

Parameters:

x - the training instances.

y - the response variable.

maxNodes - the maximum number of leaf nodes in the tree.

nodeSize - the minimum size of leaf nodes.

rule - the splitting rule.

DecisionTree

public DecisionTree(smile.data.Attribute[] attributes,
                    double[][] x,
                    int[] y,
                    int maxNodes)

Constructor. Learns a classification tree with (most) given number of leaves.

Parameters:

attributes - the attribute properties.

x - the training instances.

y - the response variable.

maxNodes - the maximum number of leaf nodes in the tree.

DecisionTree

public DecisionTree(smile.data.Attribute[] attributes,
                    double[][] x,
                    int[] y,
                    int maxNodes,
                    DecisionTree.SplitRule rule)

Constructor. Learns a classification tree with (most) given number of leaves.

Parameters:

attributes - the attribute properties.

x - the training instances.

y - the response variable.

maxNodes - the maximum number of leaf nodes in the tree.

rule - the splitting rule.

DecisionTree

public DecisionTree(smile.data.Attribute[] attributes,
                    double[][] x,
                    int[] y,
                    int maxNodes,
                    int nodeSize,
                    DecisionTree.SplitRule rule)

Constructor. Learns a classification tree with (most) given number of leaves.

Parameters:

attributes - the attribute properties.

x - the training instances.

y - the response variable.

nodeSize - the minimum size of leaf nodes.

maxNodes - the maximum number of leaf nodes in the tree.

rule - the splitting rule.

DecisionTree

public DecisionTree(smile.data.Attribute[] attributes,
                    double[][] x,
                    int[] y,
                    int maxNodes,
                    int nodeSize,
                    int mtry,
                    DecisionTree.SplitRule rule,
                    int[] samples,
                    int[][] order)

Constructor. Learns a classification tree for AdaBoost and Random Forest.

Parameters:

attributes - the attribute properties.

x - the training instances.

y - the response variable.

nodeSize - the minimum size of leaf nodes.

maxNodes - the maximum number of leaf nodes in the tree.

mtry - the number of input variables to pick to split on at each node. It seems that sqrt(p) give generally good performance, where p is the number of variables.

rule - the splitting rule.

order - the index of training values in ascending order. Note that only numeric attributes need be sorted.

samples - the sample set of instances for stochastic learning. samples[i] is the number of sampling for instance i.

Method Detail

importance

public double[] importance()

Returns the variable importance. Every time a split of a node is made on variable the (GINI, information gain, etc.) impurity criterion for the two descendent nodes is less than the parent node. Adding up the decreases for each individual variable over the tree gives a simple measure of variable importance.

Returns:

the variable importance

predict

public int predict(double[] x)

Description copied from interface: Classifier

Predicts the class label of an instance.

Specified by:

predict in interface Classifier<double[]>

Parameters:

x - the instance to be classified.

Returns:

the predicted class label

predict

public int predict(double[] x,
                   double[] posteriori)

Predicts the class label of an instance and also calculate a posteriori probabilities. The posteriori estimation is based on sample distribution in the leaf node. It is not accurate at all when be used in a single tree. It is mainly used by RandomForest in an ensemble way.

Specified by:

predict in interface SoftClassifier<double[]>

Parameters:

x - the instance to be classified.

posteriori - the array to store a posteriori probabilities on output.

Returns:

the predicted class label

maxDepth

public int maxDepth()

Returns the maximum depth" of the tree -- the number of nodes along the longest path from the root node down to the farthest leaf node.