margin

Classification margins

Syntax

m = margin(tree,TBL,ResponseVarName)

m = margin(tree,TBL,Y)

m = margin(tree,X,Y)

Description

m = margin(tree,TBL,ResponseVarName) returns the classification margins for the table of predictors TBL and class labels TBL.ResponseVarName. For the definition, see Margin.

m = margin(tree,TBL,Y) returns the classification margins for the table of predictors TBL and class labels Y.

m = margin(tree,X,Y) returns the classification margins for the matrix of predictors X and class labels Y.

Input Arguments

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`tree` — Trained classification tree
`ClassificationTree` model object | `CompactClassificationTree` model object

Trained classification tree, specified as a ClassificationTree or CompactClassificationTree model object. That is, tree is a trained classification model returned by fitctree or compact.

`TBL` — Sample data
table

Sample data, specified as a table. Each row of TBL corresponds to one observation, and each column corresponds to one predictor variable. Optionally, TBL can contain additional columns for the response variable and observation weights. TBL must contain all the predictors used to train tree. Multi-column variables and cell arrays other than cell arrays of character vectors are not allowed.

If TBL contains the response variable used to train tree, then you do not need to specify ResponseVarName or Y.

If you train tree using sample data contained in a table, then the input data for this method must also be in a table.

Data Types: table

`X` — Data to classify
numeric matrix

Data to classify, specified as a numeric matrix. Each row of X represents one observation, and each column represents one predictor. X must have the same number of columns as the data used to train tree. X must have the same number of rows as the number of elements in Y.

Data Types: single | double

`ResponseVarName` — Response variable name
name of a variable in `TBL`

Response variable name, specified as the name of a variable in TBL. If TBL contains the response variable used to train tree, then you do not need to specify ResponseVarName.

If you specify ResponseVarName, then you must do so as a character vector or string scalar. For example, if the response variable is stored as TBL.Response, then specify it as 'Response'. Otherwise, the software treats all columns of TBL, including TBL.ResponseVarName, as predictors.

The response variable must be a categorical, character, or string array, logical or numeric vector, or cell array of character vectors. If the response variable is a character array, then each element must correspond to one row of the array.

Data Types: char | string

`Y` — Class labels
categorical array | character array | string array | logical vector | numeric vector | cell array of character vectors

Class labels, specified as a categorical, character, or string array, a logical or numeric vector, or a cell array of character vectors. Y must be of the same type as the classification used to train tree, and its number of elements must equal the number of rows of X.

Output Arguments

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`m` — Margin
numeric column vector

Margin, returned as a numeric column vector of length size(X,1). Each entry in m represents the margin for the corresponding rows of X and (true class) Y, computed using tree.

Examples

Compute the classification margin for the Fisher iris data, trained on its first two columns of data, and view the last 10 entries.

load fisheriris
X = meas(:,1:2);
tree = fitctree(X,species);
M = margin(tree,X,species);
M(end-10:end)

The classification tree trained on all the data is better.

tree = fitctree(meas,species);
M = margin(tree,meas,species);
M(end-10:end)

More About

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Margin

The classification margin is the difference between the classification score for the true class and maximal classification score for the false classes. Margin is a column vector with the same number of rows as in the matrix X.

Score (tree)

For trees, the score of a classification of a leaf node is the posterior probability of the classification at that node. The posterior probability of the classification at a node is the number of training sequences that lead to that node with the classification, divided by the number of training sequences that lead to that node.

For example, consider classifying a predictor X as true when X < 0.15 or X > 0.95, and X is false otherwise.

Generate 100 random points and classify them:

rng(0,'twister') % for reproducibility
X = rand(100,1);
Y = (abs(X - .55) > .4);
tree = fitctree(X,Y);
view(tree,'Mode','Graph')

Prune the tree:

tree1 = prune(tree,'Level',1);
view(tree1,'Mode','Graph')

The pruned tree correctly classifies observations that are less than 0.15 as true. It also correctly classifies observations from .15 to .94 as false. However, it incorrectly classifies observations that are greater than .94 as false. Therefore, the score for observations that are greater than .15 should be about .05/.85=.06 for true, and about .8/.85=.94 for false.

Compute the prediction scores for the first 10 rows of X:

[~,score] = predict(tree1,X(1:10));
[score X(1:10,:)]

ans = 10×3

    0.9059    0.0941    0.8147
    0.9059    0.0941    0.9058
         0    1.0000    0.1270
    0.9059    0.0941    0.9134
    0.9059    0.0941    0.6324
         0    1.0000    0.0975
    0.9059    0.0941    0.2785
    0.9059    0.0941    0.5469
    0.9059    0.0941    0.9575
    0.9059    0.0941    0.9649

Indeed, every value of X (the right-most column) that is less than 0.15 has associated scores (the left and center columns) of 0 and 1, while the other values of X have associated scores of 0.91 and 0.09. The difference (score 0.09 instead of the expected .06) is due to a statistical fluctuation: there are 8 observations in X in the range (.95,1) instead of the expected 5 observations.

Extended Capabilities

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

This function fully supports tall arrays. For more information, see Tall Arrays (MATLAB).

Documentation

margin

Syntax

Description

Input Arguments

`tree` — Trained classification tree
`ClassificationTree` model object | `CompactClassificationTree` model object

`TBL` — Sample data
table

`X` — Data to classify
numeric matrix

`ResponseVarName` — Response variable name
name of a variable in `TBL`

`Y` — Class labels
categorical array | character array | string array | logical vector | numeric vector | cell array of character vectors

Output Arguments

`m` — Margin
numeric column vector

Examples

More About

Margin

Score (tree)

Extended Capabilities

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

See Also

Statistics and Machine Learning Toolbox Documentation

Support

Documentation

margin

Syntax

Description

Input Arguments

tree — Trained classification tree ClassificationTree model object | CompactClassificationTree model object

TBL — Sample data table

X — Data to classify numeric matrix

ResponseVarName — Response variable name name of a variable in TBL

Y — Class labels categorical array | character array | string array | logical vector | numeric vector | cell array of character vectors

Output Arguments

m — Margin numeric column vector

Examples

More About

Margin

Score (tree)

Extended Capabilities

Tall Arrays Calculate with arrays that have more rows than fit in memory.

See Also

Statistics and Machine Learning Toolbox Documentation

Support

`tree` — Trained classification tree
`ClassificationTree` model object | `CompactClassificationTree` model object

`TBL` — Sample data
table

`X` — Data to classify
numeric matrix

`ResponseVarName` — Response variable name
name of a variable in `TBL`

`Y` — Class labels
categorical array | character array | string array | logical vector | numeric vector | cell array of character vectors

`m` — Margin
numeric column vector

Tall Arrays
Calculate with arrays that have more rows than fit in memory.