# templateECOC

Error-correcting output codes learner template

## Description

returns
an error-correcting output codes (ECOC) classification learner template.`t`

= templateECOC()

If you specify a default template, then the software uses default values for all input arguments during training.

returns
a template with additional options specified by one or more name-value
pair arguments.`t`

= templateECOC(`Name,Value`

)

For example, you can specify a coding design, whether to fit posterior probabilities, or the types of binary learners.

If you display `t`

in the Command Window, then
all options appear empty (`[]`

), except those that
you specify using name-value pair arguments. During training, the
software uses default values for empty options.

## Examples

### Create a Default ECOC Classification Learner Template

Use `templateECOC`

to create a default ECOC template.

t = templateECOC()

t = Fit template for classification ECOC. BinaryLearners: '' Coding: '' FitPosterior: [] Options: [] VerbosityLevel: [] NumConcurrent: [] Version: 1 Method: 'ECOC' Type: 'classification'

All properties of the template object are empty except for `Method`

and `Type`

. When you pass `t`

to `testckfold`

, the software fills in the empty properties with their respective default values. For example, the software fills the `BinaryLearners`

property with `'SVM'`

. For details on other default values, see `fitcecoc`

.

`t`

is a plan for an ECOC learner. When you create it, no computation occurs. You can pass `t`

to `testckfold`

to specify a plan for an ECOC classification model to statistically compare with another model.

### Statistically Compare Performance of Two ECOC Classification Models

One way to select predictors or features is to train two models where one that uses a subset of the predictors that trained the other. Statistically compare the predictive performances of the models. If there is sufficient evidence that model trained on fewer predictors performs better than the model trained using more of the predictors, then you can proceed with a more efficient model.

Load Fisher's iris data set. Plot all 2-dimensional combinations of predictors.

load fisheriris d = size(meas,2); % Number of predictors pairs = nchoosek(1:d,2)

`pairs = `*6×2*
1 2
1 3
1 4
2 3
2 4
3 4

for j = 1:size(pairs,1) subplot(3,2,j) gscatter(meas(:,pairs(j,1)),meas(:,pairs(j,2)),species) xlabel(sprintf('meas(:,%d)',pairs(j,1))) ylabel(sprintf('meas(:,%d)',pairs(j,2))) legend off end

Based on the scatterplot, `meas(:,3)`

and `meas(:,4)`

seem like they separate the groups well.

Create an ECOC template. Specify to use a one-versus-all coding design.

t = templateECOC('Coding','onevsall');

By default, the ECOC model uses linear SVM binary learners. You can choose other, supported algorithms by specifying them using the `'Learners'`

name-value pair argument.

Test whether an ECOC model that is just trained using predictors 3 and 4 performs at most as well as an ECOC model that is trained using all predictors. Rejecting this null hypothesis means that the ECOC model trained using predictors 3 and 4 performs better than the ECOC model trained using all predictors. Suppose $${C}_{1}$$ represents the classification error of the ECOC model trained using predictors 3 and 4 and $${C}_{2}$$ represents the classification error of the ECOC model trained using all predictors, then the test is:

$$\begin{array}{l}{H}_{0}:{C}_{1}\ge {C}_{2}\\ {H}_{1}:{C}_{1}<{C}_{2}\end{array}$$

By default, `testckfold`

conducts a 5-by-2 *k*-fold *F* test, which is not appropriate as a one-tailed test. Specify to conduct a 5-by-2 *k*-fold *t* test.

rng(1); % For reproducibility [h,pValue] = testckfold(t,t,meas(:,pairs(6,:)),meas,species,... 'Alternative','greater','Test','5x2t')

`h = `*logical*
0

pValue = 0.8940

The `h = 0`

indicates that there is not enough evidence to suggest that the model trained using predictors 3 and 4 is more accurate than the model trained using all predictors.

## Input Arguments

### Name-Value Arguments

Specify optional pairs of arguments as
`Name1=Value1,...,NameN=ValueN`

, where `Name`

is
the argument name and `Value`

is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.

*
Before R2021a, use commas to separate each name and value, and enclose*
`Name`

*in quotes.*

**Example: **`'Coding','ternarycomplete','FitPosterior',true,'Learners','tree'`

specifies
a ternary complete coding design, to transform scores to posterior
probabilities, and to grow classification trees for all binary learners.

`Coding`

— Coding design

`'onevsone'`

(default) | `'allpairs'`

| `'binarycomplete'`

| `'denserandom'`

| `'onevsall'`

| `'ordinal'`

| `'sparserandom'`

| `'ternarycomplete'`

| numeric matrix

Coding design name, specified as the comma-separated pair consisting
of `'Coding'`

and a numeric matrix or a value in
this table.

Value | Number of Binary Learners | Description |
---|---|---|

`'allpairs'` and `'onevsone'` | K(K – 1)/2 | For each binary learner, one class is positive, another is negative, and the software ignores the rest. This design exhausts all combinations of class pair assignments. |

`'binarycomplete'` | $${2}^{(K-1)}-1$$ | This design partitions the classes into all binary combinations, and does not ignore any
classes. For each binary learner, all class assignments are
`–1` and `1` with at least one positive
class and one negative class in the assignment. |

`'denserandom'` | Random, but approximately 10 log_{2}K | For each binary learner, the software randomly assigns classes into positive or negative classes, with at least one of each type. For more details, see Random Coding Design Matrices. |

`'onevsall'` | K | For each binary learner, one class is positive and the rest are negative. This design exhausts all combinations of positive class assignments. |

`'ordinal'` | K – 1 | For the first binary learner, the first class is negative and the rest are positive. For the second binary learner, the first two classes are negative and the rest are positive, and so on. |

`'sparserandom'` | Random, but approximately 15 log_{2}K | For each binary learner, the software randomly assigns classes as positive or negative with probability 0.25 for each, and ignores classes with probability 0.5. For more details, see Random Coding Design Matrices. |

`'ternarycomplete'` | $$\left({3}^{K}-{2}^{(K+1)}+1\right)/2$$ | This design partitions the classes into all ternary combinations. All class assignments are
`0` , `–1` , and `1` with
at least one positive class and one negative class in each assignment. |

You can also specify a coding design using a custom coding matrix, which is a
*K*-by-*L* matrix. Each row corresponds to a class
and each column corresponds to a binary learner. The class order (rows) corresponds to
the order in `ClassNames`

. Create the
matrix by following these guidelines:

Every element of the custom coding matrix must be

`–1`

,`0`

, or`1`

, and the value must correspond to a dichotomous class assignment. Consider`Coding(i,j)`

, the class that learner`j`

assigns to observations in class`i`

.Value Dichotomous Class Assignment `–1`

Learner `j`

assigns observations in class`i`

to a negative class.`0`

Before training, learner `j`

removes observations in class`i`

from the data set.`1`

Learner `j`

assigns observations in class`i`

to a positive class.Every column must contain at least one

`–1`

and one`1`

.For all column indices

`i`

,`j`

where`i`

≠`j`

,`Coding(:,i)`

cannot equal`Coding(:,j)`

, and`Coding(:,i)`

cannot equal`–Coding(:,j)`

.All rows of the custom coding matrix must be different.

For more details on the form of custom coding design matrices, see Custom Coding Design Matrices.

**Example: **`'Coding','ternarycomplete'`

**Data Types: **`char`

| `string`

| `double`

| `single`

| `int16`

| `int32`

| `int64`

| `int8`

`FitPosterior`

— Flag indicating whether to transform scores to posterior probabilities

`false`

or `0`

(default) | `true`

or `1`

Flag indicating whether to transform scores to posterior probabilities,
specified as the comma-separated pair consisting of `'FitPosterior'`

and
a `true`

(`1`

) or `false`

(`0`

).

If `FitPosterior`

is `true`

,
then the software transforms binary-learner classification scores
to posterior probabilities. You can obtain posterior probabilities
by using `kfoldPredict`

, `predict`

,
or `resubPredict`

.

`fitcecoc`

does not support fitting posterior probabilities if:

The ensemble method is

`AdaBoostM2`

,`LPBoost`

,`RUSBoost`

,`RobustBoost`

, or`TotalBoost`

.The binary learners (

`Learners`

) are linear or kernel classification models that implement SVM. To obtain posterior probabilities for linear or kernel classification models, implement logistic regression instead.

**Example: **`'FitPosterior',true`

**Data Types: **`logical`

`Learners`

— Binary learner templates

`'svm'`

(default) | `'discriminant'`

| `'kernel'`

| `'knn'`

| `'linear'`

| `'naivebayes'`

| `'tree'`

| template object | cell vector of template objects

Binary learner templates, specified as the comma-separated pair consisting of
`'Learners'`

and a character vector, string scalar, template
object, or cell vector of template objects. Specifically, you can specify binary
classifiers such as SVM, and the ensembles that use `GentleBoost`

,
`LogitBoost`

, and `RobustBoost`

, to solve
multiclass problems. However, `fitcecoc`

also supports multiclass
models as binary classifiers.

If

`Learners`

is a character vector or string scalar, then the software trains each binary learner using the default values of the specified algorithm. This table summarizes the available algorithms.Value Description `'discriminant'`

Discriminant analysis. For default options, see `templateDiscriminant`

.`'kernel'`

Kernel classification model. For default options, see `templateKernel`

.`'knn'`

*k*-nearest neighbors. For default options, see`templateKNN`

.`'linear'`

Linear classification model. For default options, see `templateLinear`

.`'naivebayes'`

Naive Bayes. For default options, see `templateNaiveBayes`

.`'svm'`

SVM. For default options, see `templateSVM`

.`'tree'`

Classification trees. For default options, see `templateTree`

.If

`Learners`

is a template object, then each binary learner trains according to the stored options. You can create a template object using:`templateDiscriminant`

, for discriminant analysis.`templateEnsemble`

, for ensemble learning. You must at least specify the learning method (`Method`

), the number of learners (`NLearn`

), and the type of learner (`Learners`

). You cannot use the`AdaBoostM2`

ensemble method for binary learning.`templateKernel`

, for kernel classification.`templateKNN`

, for*k*-nearest neighbors.`templateLinear`

, for linear classification.`templateNaiveBayes`

, for naive Bayes.`templateSVM`

, for SVM.`templateTree`

, for classification trees.

If

`Learners`

is a cell vector of template objects, then:Cell

*j*corresponds to binary learner*j*(in other words, column*j*of the coding design matrix), and the cell vector must have length*L*.*L*is the number of columns in the coding design matrix. For details, see`Coding`

.To use one of the built-in loss functions for prediction, then all binary learners must return a score in the same range. For example, you cannot include default SVM binary learners with default naive Bayes binary learners. The former returns a score in the range (-∞,∞), and the latter returns a posterior probability as a score. Otherwise, you must provide a custom loss as a function handle to functions such as

`predict`

and`loss`

.You cannot specify linear classification model learner templates with any other template.

Similarly, you cannot specify kernel classification model learner templates with any other template.

By default, the software trains learners using default SVM templates.

**Example: **`'Learners','tree'`

## Output Arguments

`t`

— ECOC classification template

template object

ECOC classification template, returned as a template object.
Pass `t`

to `testckfold`

to
specify how to create an ECOC classifier whose predictive performance
you want to compare with another classifier.

If you display `t`

to the Command Window, then
all, unspecified options appear empty (`[]`

). However,
the software replaces empty options with their corresponding default
values during training.

## Algorithms

### Custom Coding Design Matrices

Custom coding matrices must have a certain form. The software validates a custom coding matrix by ensuring:

Every element is –1, 0, or 1.

Every column contains as least one –1 and one 1.

For all distinct column vectors

*u*and*v*,*u*≠*v*and*u*≠ –*v*.All row vectors are unique.

The matrix can separate any two classes. That is, you can move from any row to any other row following these rules:

Move vertically from 1 to –1 or –1 to 1.

Move horizontally from a nonzero element to another nonzero element.

Use a column of the matrix for a vertical move only once.

If it is not possible to move from row

*i*to row*j*using these rules, then classes*i*and*j*cannot be separated by the design. For example, in the coding design$$\left[\begin{array}{cc}1& 0\\ -1& 0\\ 0& 1\\ 0& -1\end{array}\right]$$

classes 1 and 2 cannot be separated from classes 3 and 4 (that is, you cannot move horizontally from –1 in row 2 to column 2 because that position contains a 0). Therefore, the software rejects this coding design.

### Random Coding Design Matrices

For a given number of classes *K*, the software generates random coding
design matrices as follows.

The software generates one of these matrices:

Dense random — The software assigns 1 or –1 with equal probability to each element of the

*K*-by-*L*coding design matrix, where $${L}_{d}\approx \lceil 10{\mathrm{log}}_{2}K\rceil $$._{d}Sparse random — The software assigns 1 to each element of the

*K*-by-*L*coding design matrix with probability 0.25, –1 with probability 0.25, and 0 with probability 0.5, where $${L}_{s}\approx \lceil 15{\mathrm{log}}_{2}K\rceil $$._{s}

If a column does not contain at least one 1 and one –1, then the software removes that column.

For distinct columns

*u*and*v*, if*u*=*v*or*u*= –*v*, then the software removes*v*from the coding design matrix.

The software randomly generates 10,000 matrices by default, and retains the matrix with the largest, minimal, pairwise row distance based on the Hamming measure ([2]) given by

$$\Delta ({k}_{1},{k}_{2})=0.5{\displaystyle \sum}_{l=1}^{L}\left|{m}_{{k}_{1}l}\right|\left|{m}_{{k}_{2}l}\right|\left|{m}_{{k}_{1}l}-{m}_{{k}_{2}l}\right|,$$

where
*m _{kjl}* is an element of
coding design matrix

*j*.

## References

[1] Fürnkranz, Johannes. “Round Robin
Classification.” *J. Mach. Learn. Res.*, Vol. 2, 2002, pp.
721–747.

[2] Escalera, S., O. Pujol, and P. Radeva. “Separability of ternary codes for sparse designs of error-correcting output codes.” *Pattern Recog. Lett.*, Vol. 30, Issue 3, 2009, pp. 285–297.

## Version History

**Introduced in R2015a**

## See Also

`ClassificationECOC`

| `fitcecoc`

| `designecoc`

| `templateDiscriminant`

| `templateEnsemble`

| `templateKNN`

| `templateSVM`

| `templateTree`

| `predict`

| `testckfold`

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