# CompactClassificationTree

Package: classreg.learning.classif

Compact classification tree

## Description

Compact version of a classification tree (of class ClassificationTree). The compact version does not include the data for training the classification tree. Therefore, you cannot perform some tasks with a compact classification tree, such as cross validation. Use a compact classification tree for making predictions (classifications) of new data.

## Construction

ctree = compact(tree) constructs a compact decision tree from a full decision tree.

### Input Arguments

 tree A decision tree constructed using fitctree.

## Properties

 CategoricalPredictors Categorical predictor indices, specified as a vector of positive integers. CategoricalPredictors contains index values corresponding to the columns of the predictor data that contain categorical predictors. If none of the predictors are categorical, then this property is empty ([]). CategoricalSplits An n-by-2 cell array, where n is the number of categorical splits in tree. Each row in CategoricalSplits gives left and right values for a categorical split. For each branch node with categorical split j based on a categorical predictor variable z, the left child is chosen if z is in CategoricalSplits(j,1) and the right child is chosen if z is in CategoricalSplits(j,2). The splits are in the same order as nodes of the tree. Find the nodes for these splits by selecting 'categorical' cuts from top to bottom in the CutType property. Children An n-by-2 array containing the numbers of the child nodes for each node in tree, where n is the number of nodes. Leaf nodes have child node 0. ClassCount An n-by-k array of class counts for the nodes in tree, where n is the number of nodes and k is the number of classes. For any node number i, the class counts ClassCount(i,:) are counts of observations (from the data used in fitting the tree) from each class satisfying the conditions for node i. ClassNames List of the elements in Y with duplicates removed. ClassNames can be a numeric vector, vector of categorical variables, logical vector, character array, or cell array of character vectors. ClassNames has the same data type as the data in the argument Y. (The software treats string arrays as cell arrays of character vectors.) If the value of a property has at least one dimension of length k, then ClassNames indicates the order of the elements along that dimension (e.g., Cost and Prior). ClassProbability An n-by-k array of class probabilities for the nodes in tree, where n is the number of nodes and k is the number of classes. For any node number i, the class probabilities ClassProbability(i,:) are the estimated probabilities for each class for a point satisfying the conditions for node i. Cost Square matrix, where Cost(i,j) is the cost of classifying a point into class j if its true class is i (the rows correspond to the true class and the columns correspond to the predicted class). The order of the rows and columns of Cost corresponds to the order of the classes in ClassNames. The number of rows and columns in Cost is the number of unique classes in the response. This property is read-only. CutCategories An n-by-2 cell array of the categories used at branches in tree, where n is the number of nodes. For each branch node i based on a categorical predictor variable x, the left child is chosen if x is among the categories listed in CutCategories{i,1}, and the right child is chosen if x is among those listed in CutCategories{i,2}. Both columns of CutCategories are empty for branch nodes based on continuous predictors and for leaf nodes. CutPoint contains the cut points for 'continuous' cuts, and CutCategories contains the set of categories. CutPoint An n-element vector of the values used as cut points in tree, where n is the number of nodes. For each branch node i based on a continuous predictor variable x, the left child is chosen if x=CutPoint(i). CutPoint is NaN for branch nodes based on categorical predictors and for leaf nodes. CutPoint contains the cut points for 'continuous' cuts, and CutCategories contains the set of categories. CutType An n-element cell array indicating the type of cut at each node in tree, where n is the number of nodes. For each node i, CutType{i} is: 'continuous' — If the cut is defined in the form x < v for a variable x and cut point v.'categorical' — If the cut is defined by whether a variable x takes a value in a set of categories.'' — If i is a leaf node. CutPoint contains the cut points for 'continuous' cuts, and CutCategories contains the set of categories. CutPredictor An n-element cell array of the names of the variables used for branching in each node in tree, where n is the number of nodes. These variables are sometimes known as cut variables. For leaf nodes, CutPredictor contains an empty character vector. CutPoint contains the cut points for 'continuous' cuts, and CutCategories contains the set of categories. CutPredictorIndex An n-element array of numeric indices for the variables used for branching in each node in tree, where n is the number of nodes. For more information, see CutPredictor. ExpandedPredictorNames Expanded predictor names, stored as a cell array of character vectors. If the model uses encoding for categorical variables, then ExpandedPredictorNames includes the names that describe the expanded variables. Otherwise, ExpandedPredictorNames is the same as PredictorNames. IsBranchNode An n-element logical vector that is true for each branch node and false for each leaf node of tree. NodeClass An n-element cell array with the names of the most probable classes in each node of tree, where n is the number of nodes in the tree. Every element of this array is a character vector equal to one of the class names in ClassNames. NodeError An n-element vector of the errors of the nodes in tree, where n is the number of nodes. NodeError(i) is the misclassification probability for node i. NodeProbability An n-element vector of the probabilities of the nodes in tree, where n is the number of nodes. The probability of a node is computed as the proportion of observations from the original data that satisfy the conditions for the node. This proportion is adjusted for any prior probabilities assigned to each class. NodeRisk An n-element vector of the risk of the nodes in the tree, where n is the number of nodes. The risk for each node is the measure of impurity (Gini index or deviance) for this node weighted by the node probability. If the tree is grown by twoing, the risk for each node is zero. NodeSize An n-element vector of the sizes of the nodes in tree, where n is the number of nodes. The size of a node is defined as the number of observations from the data used to create the tree that satisfy the conditions for the node. NumNodes The number of nodes in tree. Parent An n-element vector containing the number of the parent node for each node in tree, where n is the number of nodes. The parent of the root node is 0. PredictorNames A cell array of names for the predictor variables, in the order in which they appear in X. Prior Numeric vector of prior probabilities for each class. The order of the elements of Prior corresponds to the order of the classes in ClassNames. The number of elements of Prior is the number of unique classes in the response. This property is read-only. PruneAlpha Numeric vector with one element per pruning level. If the pruning level ranges from 0 to M, then PruneAlpha has M + 1 elements sorted in ascending order. PruneAlpha(1) is for pruning level 0 (no pruning), PruneAlpha(2) is for pruning level 1, and so on. PruneList An n-element numeric vector with the pruning levels in each node of tree, where n is the number of nodes. The pruning levels range from 0 (no pruning) to M, where M is the distance between the deepest leaf and the root node. ResponseName Character vector describing the response variable Y. ScoreTransform Function handle for transforming scores, or character vector representing a built-in transformation function. 'none' means no transformation; equivalently, 'none' means @(x)x. For a list of built-in transformation functions and the syntax of custom transformation functions, see fitctree. Add or change a ScoreTransform function using dot notation: ctree.ScoreTransform = 'function' or ctree.ScoreTransform = @function SurrogateCutCategories An n-element cell array of the categories used for surrogate splits in tree, where n is the number of nodes in tree. For each node k, SurrogateCutCategories{k} is a cell array. The length of SurrogateCutCategories{k} is equal to the number of surrogate predictors found at this node. Every element of SurrogateCutCategories{k} is either an empty character vector for a continuous surrogate predictor, or is a two-element cell array with categories for a categorical surrogate predictor. The first element of this two-element cell array lists categories assigned to the left child by this surrogate split and the second element of this two-element cell array lists categories assigned to the right child by this surrogate split. The order of the surrogate split variables at each node is matched to the order of variables in SurrogateCutVar. The optimal-split variable at this node does not appear. For nonbranch (leaf) nodes, SurrogateCutCategories contains an empty cell. SurrogateCutFlip An n-element cell array of the numeric cut assignments used for surrogate splits in tree, where n is the number of nodes in tree. For each node k, SurrSurrogateCutFlip{k} is a numeric vector. The length of SurrogateCutFlip{k} is equal to the number of surrogate predictors found at this node. Every element of SurrogateCutFlip{k} is either zero for a categorical surrogate predictor, or a numeric cut assignment for a continuous surrogate predictor. The numeric cut assignment can be either –1 or +1. For every surrogate split with a numeric cut C based on a continuous predictor variable Z, the left child is chosen if Z

## Object Functions

 edge Classification edge loss Classification error margin Classification margins partialDependence Compute partial dependence plotPartialDependence Create partial dependence plot (PDP) and individual conditional expectation (ICE) plots predict Predict labels using classification tree predictorImportance Estimates of predictor importance for classification tree surrogateAssociation Mean predictive measure of association for surrogate splits in classification tree update Update model parameters for code generation view View classification tree

## Copy Semantics

Value. To learn how value classes affect copy operations, see Copying Objects.

## Examples

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Construct a compact classification tree for the Fisher iris data.

tree = fitctree(meas,species);
ctree = compact(tree);

Compare the size of the resulting tree to that of the original tree.

t = whos('tree'); % t.bytes = size of tree in bytes
c = whos('ctree'); % c.bytes = size of ctree in bytes
[c.bytes t.bytes]
ans = 1×2

5097       11762

The compact tree is smaller than the original tree.

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