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
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 formX < v
for a variableX
and cut pointv
.'categorical'
— If the cut is defined by whether a variableX
takes a value in a set of categories.''
— Ifi
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
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
5001 11714
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
argument:
Gini's Diversity Index (
gdi
) — The Gini index of a node iswhere 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 isA 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 maximizewhere 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:
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
, orcell
) are not supported. You cannot use theCategoricalPredictors
name-value argument. To include categorical predictors in a model, preprocess them by usingdummyvar
before fitting the model.Class labels with the
categorical
data type are not supported. Both the class label value in the training data (Tbl
orY
) and the value of theClassNames
name-value argument cannot be an array with thecategorical
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
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