CompactClassificationTree

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.

Creation

Create a CompactClassificationTree object from a full ClassificationTree model object by using compact.

Properties

expand all

`CategoricalPredictors` — Indices of categorical predictors
vector of positive integers | `[]`

This property is read-only.

Categorical predictor indices, specified as a vector of positive integers. CategoricalPredictors contains index values indicating that the corresponding predictors are categorical. The index values are between 1 and p, where p is the number of predictors used to train the model. If none of the predictors are categorical, then this property is empty ([]).

Data Types: single | double

`CategoricalSplit` — Categorical splits
`n`-by-2 cell array

This property is read-only.

Categorical splits, returned as an n-by-2 cell array, where n is the number of categorical splits in tree. Each row in CategoricalSplit 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 CategoricalSplit(j,1) and the right child is chosen if z is in CategoricalSplit(j,2). The splits are in the same order as nodes of the tree. Nodes for these splits can be found by running cuttype and selecting 'categorical' cuts from top to bottom.

Data Types: cell

`Children` — Numbers of the child nodes for each node
`n`-by-2 array

This property is read-only.

Numbers of the child nodes for each node in the tree, returned as an n-by-2 array, where n is the number of nodes. Leaf nodes have child node 0.

Data Types: double

`ClassCount` — Class counts
n-by-k array

This property is read-only.

Class counts for the nodes in tree, returned as an n-by-k array, 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.

Data Types: double

`ClassNames` — List of elements in `Y` with duplicates removed
categorical array | cell array of character vectors | character array | logical vector | numeric vector

This property is read-only.

List of the elements in Y with duplicates removed, returned as a categorical array, cell array of character vectors, character array, logical vector, or a numeric vector. ClassNames has the same data type as the data in the argument Y. (The software treats string arrays as cell arrays of character vectors.)

Data Types: double | logical | char | cell | categorical

`ClassProbability` — Class probabilities
`n`-by-k array

This property is read-only.

Class probabilities for the nodes in tree, returned as an n-by-k array, 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.

Data Types: double

`Cost` — Cost of classifying a point into class `j` when its true class is `i`
square matrix

Cost of classifying a point into class j when its true class is i, returned as a square matrix. The rows of Cost 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.

Data Types: double

`CutCategories` — Categories used at branches
`n`-by-2 cell array

This property is read-only.

Categories used at branches in tree, returned as an n-by-2 cell array, 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.

Data Types: cell

`CutPoint` — Values used as cut points
`n`-element vector

This property is read-only.

Values used as cut points in tree, returned as an n-element vector, 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) and the right 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.

Data Types: double

`CutPredictor` — Names of the variables used for branching in each node
cell array

This property is read-only.

Names of the variables used for branching in each node in tree, returned as an n-element cell array, 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.

Data Types: cell

`CutPredictorIndex` — Indices of variables used for branching in each node
`n`-element array

This property is read-only.

Indices of variables used for branching in each node in tree, returned as an n-element array, where n is the number of nodes. For more information, see CutPredictor.

Data Types: double

`CutType` — Type of cut at each node
`n`-element cell array

This property is read-only.

Type of cut at each node in tree, returned as an n-element cell array, 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.

Data Types: cell

`ExpandedPredictorNames` — Expanded predictor names
cell array of character vectors

This property is read-only.

Expanded predictor names, returned 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.

Data Types: cell

`IsBranchNode` — Indicator of branch nodes
logical vector

This property is read-only.

Indicator of branch nodes, returned as an n-element logical vector that is true for each branch node and false for each leaf node of tree.

Data Types: logical

`NodeClass` — Name of most probably class in each node
cell array

This property is read-only.

Name of most probably class in each node of tree, returned as a cell array with n elements, where n is the number of nodes in the tree. Each element of this array is a character vector equal to one of the class names in ClassNames.

Data Types: cell

`NodeError` — Misclassification probability for each node
`n`-element vector

This property is read-only.

Misclassification probability for each node in tree, returned as an n-element vector, where n is the number of nodes in the tree.

Data Types: double

`NodeProbability` — Proportion of observations in original data that satisfy the conditions for the node
`n`-element vector

This property is read-only.

Proportion of observations in original data that satisfy the conditions for each node in tree, returned as an n-element vector, where n is the number of nodes in the tree. The NodeProbability values are adjusted for any prior probabilities assigned to each class.

Data Types: double

`NodeRisk` — Impurity of nodes
`n`-element vector

This property is read-only.

Impurity of each node in tree, weighted by the node probability, returned as an n-element vector, where n is the number of nodes in the tree. The measure of impurity is the Gini index or deviance for the node, weighted by the node probability. If the tree is grown by twoing, the risk for each node is zero.

Data Types: double

`NodeSize` — Size of nodes
`n`-element vector

This property is read-only.

Size of the nodes in tree, returned as an n-element vector, where n is the number of nodes in the tree. The size of a node is the number of observations from the data used to create the tree that satisfy the conditions for the node.

Data Types: double

`NumNodes` — Number of nodes
positive integer

This property is read-only.

The number of nodes in tree, returned as a positive integer.

Data Types: double

`Parent` — Number of parents of nodes
`n`-element vector

This property is read-only.

Number of parents of each node in tree, returned as an n-element integer vector, where n is the number of nodes in the tree. The parent of the root node is 0.

Data Types: double

`PredictorNames` — Predictor names
cell array of character vectors

This property is read-only.

Predictor names, specified as a cell array of character vectors. The order of the entries in PredictorNames is the same as in the training data.

Data Types: cell

`Prior` — Prior probabilities for each class
`m`-element vector

Prior probabilities for each class, returned as an m-element vector, where m is the number of unique classes in the response. The order of the elements of Prior corresponds to the order of the classes in ClassNames.

Data Types: double

`PruneAlpha` — Alpha values for pruning the tree
real vector

Alpha values for pruning the tree, returned as a real 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.

For the meaning of the ɑ values, see How Decision Trees Create a Pruning Sequence.

Data Types: double

`PruneList` — Pruning levels of each node in tree
integer vector

Pruning levels of each node in the tree, returned as an integer vector with NumNodes elements. The pruning levels range from 0 (no pruning) to M, where M is the distance between the deepest leaf and the root node.

For details, see Pruning.

Data Types: double

`ResponseName` — Name of the response variable
character vector

This property is read-only.

Name of the response variable, returned as a character vector.

Data Types: char

`ScoreTransform` — Function for transforming scores
function handle | name of a built-in transformation function | `'none'`

Function for transforming scores, specified as a function handle or the name of 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

Data Types: char | string | function_handle

`SurrogateCutCategories` — Categories used for surrogate splits
`n`-element cell array

This property is read-only.

Categories used for surrogate splits, returned as an n-element cell array, 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.

Data Types: cell

`SurrogateCutFlip` — Numeric cut assignments used for surrogate splits
`n`-element cell array

This property is read-only.

Numeric cut assignments used for surrogate splits in tree, returned as an n-element cell array, where n is the number of nodes in tree. For each node k, SurrogateCutFlip{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<C and the cut assignment for this surrogate split is +1, or if Z≥C and the cut assignment for this surrogate split is –1. Similarly, the right child is chosen if Z≥C and the cut assignment for this surrogate split is +1, or if Z<C and the cut assignment for this surrogate split is –1. The order of the surrogate split variables at each node is matched to the order of variables in SurrogateCutPredictor. The optimal-split variable at this node does not appear. For nonbranch (leaf) nodes, SurrogateCutFlip contains an empty array.

Data Types: cell

`SurrogateCutPoint` — Numeric values used for surrogate splits
`n`-element cell array

This property is read-only.

Numeric values used for surrogate splits in tree, returned as an n-element cell array, where n is the number of nodes in tree. For each node k, SurrogateCutPoint{k} is a numeric vector. The length of SurrogateCutPoint{k} is equal to the number of surrogate predictors found at this node. Every element of SurrogateCutPoint{k} is either NaN for a categorical surrogate predictor, or a numeric cut for a continuous surrogate predictor. For every surrogate split with a numeric cut C based on a continuous predictor variable Z, the left child is chosen if Z<C and SurrogateCutFlip for this surrogate split is +1, or if Z≥C and SurrogateCutFlip for this surrogate split is –1. Similarly, the right child is chosen if Z≥C and SurrogateCutFlip for this surrogate split is +1, or if Z<C and SurrogateCutFlip for this surrogate split is –1. The order of the surrogate split variables at each node is matched to the order of variables returned by SurrogateCutPredictor. The optimal-split variable at this node does not appear. For nonbranch (leaf) nodes, SurrogateCutPoint contains an empty cell.

Data Types: cell

`SurrogateCutPredictor` — Names of variables used for surrogate splits in each node
`n`-element cell array

This property is read-only.

Names of the variables used for surrogate splits in each node in tree, returned as an n-element cell array, where n is the number of nodes in tree. Every element of SurrogateCutPredictor is a cell array with the names of the surrogate split variables at this node. The variables are sorted by the predictive measure of association with the optimal predictor in the descending order, and only variables with the positive predictive measure are included. The optimal-split variable at this node does not appear. For nonbranch (leaf) nodes, SurrogateCutPredictor contains an empty cell.

Data Types: cell

`SurrogateCutType` — Types of surrogate splits at each node
`n`-element cell array

This property is read-only.

Types of surrogate splits at each node in tree, returned as an n-element cell array, where n is the number of nodes in tree. For each node k, SurrogateCutType{k} is a cell array with the types of the surrogate split variables at this node. The variables are sorted by the predictive measure of association with the optimal predictor in the descending order, and only variables with the positive predictive measure are included. The order of the surrogate split variables at each node is matched to the order of variables in SurrogateCutPredictor. The optimal-split variable at this node does not appear. For nonbranch (leaf) nodes, SurrogateCutType contains an empty cell. A surrogate split type can be either 'continuous' if the cut is defined in the form Z<V for a variable Z and cut point V or 'categorical' if the cut is defined by whether Z takes a value in a set of categories.

Data Types: cell

`SurrogatePredictorAssociation` — Predictive measures of association for surrogate splits
`n`-element cell array

This property is read-only.

Predictive measures of association for surrogate splits in tree, returned as an n-element cell array, where n is the number of nodes in tree. For each node k, SurrogatePredictorAssociation{k} is a numeric vector. The length of SurrogatePredictorAssociation{k} is equal to the number of surrogate predictors found at this node. Every element of SurrogatePredictorAssociation{k} gives the predictive measure of association between the optimal split and this surrogate split. The order of the surrogate split variables at each node is the order of variables in SurrogateCutPredictor. The optimal-split variable at this node does not appear. For nonbranch (leaf) nodes, SurrogatePredictorAssociation contains an empty cell.

Data Types: cell

Object Functions

`compareHoldout`	Compare accuracies of two classification models using new data
`edge`	Classification edge for classification tree model
`gather`	Gather properties of Statistics and Machine Learning Toolbox object from GPU
`lime`	Local interpretable model-agnostic explanations (LIME)
`loss`	Classification loss for classification tree model
`margin`	Classification margins for classification tree model
`nodeVariableRange`	Retrieve variable range of decision tree node
`partialDependence`	Compute partial dependence
`plotPartialDependence`	Create partial dependence plot (PDP) and individual conditional expectation (ICE) plots
`predict`	Predict labels using classification tree model
`predictorImportance`	Estimates of predictor importance for classification tree
`shapley`	Shapley values
`surrogateAssociation`	Mean predictive measure of association for surrogate splits in classification tree
`update`	Update model parameters for code generation
`view`	View classification tree

Examples

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Construct a Compact Classification Tree

Open Live Script

Construct a compact classification tree for the Fisher iris data.

load fisheriris
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

        5001       11714

The compact tree is smaller than the original tree.

More About

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Impurity and Node Error

A decision tree splits nodes based on either impurity or node error.

Impurity means one of several things, depending on your choice of the SplitCriterion name-value argument:

Gini's Diversity Index (gdi) — The Gini index of a node is
$1 - \sum_{i} p^{2} (i),$
where the sum is over the classes i at the node, and p(i) is the observed fraction of classes with class i that reach the node. A node with just one class (a pure node) has Gini index 0; otherwise, the Gini index is positive. So the Gini index is a measure of node impurity.
Deviance ("deviance") — With p(i) defined the same as for the Gini index, the deviance of a node is
$- \sum_{i} p (i) \log_{2} p (i) .$
A pure node has deviance 0; otherwise, the deviance is positive.
Twoing rule ("twoing") — Twoing is not a purity measure of a node, but is a different measure for deciding how to split a node. Let L(i) denote the fraction of members of class i in the left child node after a split, and R(i) denote the fraction of members of class i in the right child node after a split. Choose the split criterion to maximize
$P (L) P (R) {(\sum_{i} | L (i) - R (i) |)}^{2},$
where P(L) and P(R) are the fractions of observations that split to the left and right, respectively. If the expression is large, the split made each child node purer. Similarly, if the expression is small, the split made each child node similar to each other and, therefore, similar to the parent node. The split did not increase node purity.
Node error — The node error is the fraction of misclassified classes at a node. If j is the class with the largest number of training samples at a node, the node error is
1 – p(j).

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

The predict and update functions support code generation.
To integrate the prediction of a classification tree model into Simulink^®, you can use the ClassificationTree Predict block in the Statistics and Machine Learning Toolbox™ library or a MATLAB^® Function block with the predict function.
When you train a classification tree using fitctree, the following restrictions apply.
- The value of the 'ScoreTransform' name-value pair argument cannot be an anonymous function. For fixed-point code generation, the 'ScoreTransform' value cannot be 'invlogit'.
- You cannot use surrogate splits; that is, the value of the 'Surrogate' name-value pair argument must be 'off'.
- For fixed-point code generation and code generation with a coder configurer, the following additional restrictions apply.
  - Categorical predictors (logical, categorical, char, string, or cell) are not supported. You cannot use the CategoricalPredictors name-value argument. To include categorical predictors in a model, preprocess them by using dummyvar before fitting the model.
  - Class labels with the categorical data type are not supported. Both the class label value in the training data (Tbl or Y) and the value of the ClassNames name-value argument cannot be an array with the categorical data type.

For more information, see Introduction to Code Generation.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

The following object functions fully support GPU arrays:
The following object functions offer limited support for GPU arrays:
The object functions execute on a GPU if at least one of the following applies:
- The model was fitted with GPU arrays.
- The predictor data that you pass to the object function is a GPU array.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2011a

CompactClassificationTree

Description

Creation

Properties

CategoricalPredictors — Indices of categorical predictors vector of positive integers | []

CategoricalSplit — Categorical splits n-by-2 cell array

Children — Numbers of the child nodes for each node n-by-2 array

ClassCount — Class counts n-by-k array

ClassNames — List of elements in Y with duplicates removed categorical array | cell array of character vectors | character array | logical vector | numeric vector

ClassProbability — Class probabilities n-by-k array

Cost — Cost of classifying a point into class j when its true class is i square matrix

CutCategories — Categories used at branches n-by-2 cell array

CutPoint — Values used as cut points n-element vector

CutPredictor — Names of the variables used for branching in each node cell array

CutPredictorIndex — Indices of variables used for branching in each node n-element array

CutType — Type of cut at each node n-element cell array

ExpandedPredictorNames — Expanded predictor names cell array of character vectors

IsBranchNode — Indicator of branch nodes logical vector

NodeClass — Name of most probably class in each node cell array

NodeError — Misclassification probability for each node n-element vector

NodeProbability — Proportion of observations in original data that satisfy the conditions for the node n-element vector

NodeRisk — Impurity of nodes n-element vector

NodeSize — Size of nodes n-element vector

NumNodes — Number of nodes positive integer

Parent — Number of parents of nodes n-element vector

PredictorNames — Predictor names cell array of character vectors

Prior — Prior probabilities for each class m-element vector

PruneAlpha — Alpha values for pruning the tree real vector

PruneList — Pruning levels of each node in tree integer vector

ResponseName — Name of the response variable character vector

ScoreTransform — Function for transforming scores function handle | name of a built-in transformation function | 'none'

SurrogateCutCategories — Categories used for surrogate splits n-element cell array

SurrogateCutFlip — Numeric cut assignments used for surrogate splits n-element cell array

SurrogateCutPoint — Numeric values used for surrogate splits n-element cell array

SurrogateCutPredictor — Names of variables used for surrogate splits in each node n-element cell array

SurrogateCutType — Types of surrogate splits at each node n-element cell array

SurrogatePredictorAssociation — Predictive measures of association for surrogate splits n-element cell array

Object Functions

Examples

Construct a Compact Classification Tree

More About

Impurity and Node Error

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

GPU Arrays Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Version History

See Also

Topics

`CategoricalPredictors` — Indices of categorical predictors
vector of positive integers | `[]`

`CategoricalSplit` — Categorical splits
`n`-by-2 cell array

`Children` — Numbers of the child nodes for each node
`n`-by-2 array

`ClassCount` — Class counts
n-by-k array

`ClassNames` — List of elements in `Y` with duplicates removed
categorical array | cell array of character vectors | character array | logical vector | numeric vector

`ClassProbability` — Class probabilities
`n`-by-k array

`Cost` — Cost of classifying a point into class `j` when its true class is `i`
square matrix

`CutCategories` — Categories used at branches
`n`-by-2 cell array

`CutPoint` — Values used as cut points
`n`-element vector

`CutPredictor` — Names of the variables used for branching in each node
cell array

`CutPredictorIndex` — Indices of variables used for branching in each node
`n`-element array

`CutType` — Type of cut at each node
`n`-element cell array

`ExpandedPredictorNames` — Expanded predictor names
cell array of character vectors

`IsBranchNode` — Indicator of branch nodes
logical vector

`NodeClass` — Name of most probably class in each node
cell array

`NodeError` — Misclassification probability for each node
`n`-element vector

`NodeProbability` — Proportion of observations in original data that satisfy the conditions for the node
`n`-element vector

`NodeRisk` — Impurity of nodes
`n`-element vector

`NodeSize` — Size of nodes
`n`-element vector

`NumNodes` — Number of nodes
positive integer

`Parent` — Number of parents of nodes
`n`-element vector

`PredictorNames` — Predictor names
cell array of character vectors

`Prior` — Prior probabilities for each class
`m`-element vector

`PruneAlpha` — Alpha values for pruning the tree
real vector

`PruneList` — Pruning levels of each node in tree
integer vector

`ResponseName` — Name of the response variable
character vector

`ScoreTransform` — Function for transforming scores
function handle | name of a built-in transformation function | `'none'`

`SurrogateCutCategories` — Categories used for surrogate splits
`n`-element cell array

`SurrogateCutFlip` — Numeric cut assignments used for surrogate splits
`n`-element cell array

`SurrogateCutPoint` — Numeric values used for surrogate splits
`n`-element cell array

`SurrogateCutPredictor` — Names of variables used for surrogate splits in each node
`n`-element cell array

`SurrogateCutType` — Types of surrogate splits at each node
`n`-element cell array

`SurrogatePredictorAssociation` — Predictive measures of association for surrogate splits
`n`-element cell array

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.