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package: classreg.learning.classif

compact classification tree

description

compact version of a classification tree (of class ). 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 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 (`[]`).
`categoricalsplit`	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.
`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 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.`
`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<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.
`surrogatecutpoint`	an n-element cell array of the numeric values used for surrogate splits in `tree`, 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.
`surrogatecuttype`	an n-element cell array indicating types of surrogate splits at each node in `tree`, 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.
`surrogatecutpredictor`	an n-element cell array of the names of the variables used for surrogate splits in each node in `tree`, 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.
`surrogatepredictorassociation`	an n-element cell array of the predictive measures of association for surrogate splits in `tree`, 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.

object functions

	compare accuracies of two classification models using new data
	classification edge
	gather properties of statistics and machine learning toolbox object from gpu
`lime`	local interpretable model-agnostic explanations (lime)
	classification error
	classification margins
	retrieve variable range of decision tree node
`partialdependence`	compute partial dependence
`plotpartialdependence`	create partial dependence plot (pdp) and individual conditional expectation (ice) plots
	predict labels using classification tree
	estimates of predictor importance for classification tree
`shapley`	shapley values
	mean predictive measure of association for surrogate splits in classification tree
`update`	update model parameters for code generation
	view classification tree

copy semantics

value. to learn how value classes affect copy operations, see .

examples

construct a compact classification tree

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
        5097       11762

the compact tree is smaller than the original tree.

more about

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 pair 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 and update functions support code generation.
to integrate the prediction of a classification tree model into simulink^®, you can use the 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 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 either of the following apply:
- 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