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Class Definition: ClassificationPartitionedLinear

statistics: ClassificationPartitionedLinear

Cross-validated linear binary classifier.

A ClassificationPartitionedLinear object holds one ClassificationLinear per fold of a partition, each fitted to the observations the fold trains on. Every kfold method predicts each observation with the fold that held it out, so the estimate it returns is an out-of-sample one.

A ClassificationLinear stores no copy of its training data and so has no resubstitution methods and no compact form. This class is what takes their place: cross-validation is the way a linear model is asked how it would do on data it has not seen.

When the fold models carry a whole regularization path, every method returns one column per strength, in the order of the 'Lambda' that was asked for.

Create one with fitclinear and a cross-validation option, or directly.

See also: fitclinear, ClassificationLinear, ClassificationPartitionedKernel

Source Code: ClassificationPartitionedLinear

The ClassificationPartitionedLinear class contains the following properties:

A column of the same type as the response, shared by every fold. This property is read-only.

Cross-validate a linear classifier on the two overlapping iris species and read the out-of-sample error rate.

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 0.050000

A square numeric matrix with one row and one column per class. It is handed to every fold rather than re-derived by each. This property is read-only.

Cross-validate a linear classifier on the two overlapping iris species and read the out-of-sample error rate.

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 0.040000

A numeric row vector summing to one, in the order of ClassNames. Like the cost it is the parent’s and is handed to every fold, so a fold of an unbalanced problem does not quietly adopt a prior of its own. This property is read-only.

Cross-validate a linear classifier on the two overlapping iris species and read the out-of-sample error rate.

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 0.060000

A character vector naming a transformation, or the text of the function handle that was supplied, which may be assigned after the model is built. It is applied once to the assembled scores and is not handed to the folds. A transform the learner implies, as 'logistic' implies 'logit', does stay with the folds, and this one is then applied on top of it.

Cross-validate a linear classifier on the two overlapping iris species and read the out-of-sample error rate.

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 0.030000

Always 'Linear', the short name MATLAB uses. This property is read-only.

Cross-validate a linear classifier on the two overlapping iris species and read the out-of-sample error rate.

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 0.030000

A positive integer scalar, counting the rows that survived the removal of missing values. This property is read-only.

Cross-validate a linear classifier on the two overlapping iris species and read the out-of-sample error rate.

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 0.030000

In the type it was supplied in. This property is read-only.

Cross-validate a linear classifier on the two overlapping iris species and read the out-of-sample error rate.

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 0.030000

An Nx1 numeric vector summing to one, normalized within each class to that class’s cost-adjusted prior. This property is read-only.

Cross-validate a linear classifier on the two overlapping iris species and read the out-of-sample error rate.

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 0.030000

A cell array of character vectors. This property is read-only.

Cross-validate a linear classifier on the two overlapping iris species and read the out-of-sample error rate.

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 0.020000

A row vector of column indices, empty when every predictor is numeric. This property is read-only.

Cross-validate a linear classifier on the two overlapping iris species and read the out-of-sample error rate.

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 0.040000

A character vector, defaulting to 'Y'. This property is read-only.

Cross-validate a linear classifier on the two overlapping iris species and read the out-of-sample error rate.

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 0.030000

A cell column with one ClassificationLinear per fold, each fitted to the observations its fold trains on. This property is read-only.

Cross-validate a linear classifier on the two overlapping iris species and read the out-of-sample error rate.

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 0.030000

A positive integer scalar. A holdout partition has one fold and a leave-one-out partition has as many as there are observations. This property is read-only.

Cross-validate a linear classifier on the two overlapping iris species and read the out-of-sample error rate.

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 0.040000

A cvpartition object over the retained observations. This property is read-only.

Cross-validate a linear classifier on the two overlapping iris species and read the out-of-sample error rate.

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 1.0000e-02

A structure holding the parameters the folds were fitted with, carried through from the learner that was cross validated, beside NLearn, the number of folds, and the Version, Method and Type tags of this class, with LearnerTemplates naming the backing. The learner’s own tags are replaced rather than kept, so a cross-validated SVM reports Method as 'PartitionedLinear' and not 'SVM'.

Deviation from MATLAB. MATLAB reports the parameter record of the cross-validation ensemble here rather than of the learner, so it says nothing at all about how the folds were fitted: of its eighteen fields only the fold count, its partitioner and a fit template carry anything, and the rest are boosting settings left inert. Nor can the parameters be reached through the folds, a compact model carrying none in MATLAB. This class reports the fit instead, which is strictly more than MATLAB offers, and everything MATLAB’s record does carry is published here as the KFold, Partition, X, Y, W and CrossValidatedModel properties.

This property is read-only.

Cross-validate a linear classifier on the two overlapping iris species and read the out-of-sample error rate.

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 0.060000

The ClassificationPartitionedLinear class offers the following public methods:

ClassificationPartitionedLinear: obj = ClassificationPartitionedLinear (X, Y)
ClassificationPartitionedLinear: obj = ClassificationPartitionedLinear (…, name, value)

obj = ClassificationPartitionedLinear (X, Y) partitions the data into ten stratified folds and fits a ClassificationLinear to each.

obj = ClassificationPartitionedLinear (…, name, value) takes one of 'KFold', 'Holdout', 'Leaveout' and 'CVPartition' to say how to partition, and any option ClassificationLinear takes to say how to fit. 'CrossVal' is accepted and has no effect here, this class being cross-validated by construction.

The classes, the prior and the cost are resolved once over the whole data and handed to every fold. Anything left as 'auto' is not: each fold resolves 'Lambda' against its own training rows, so ten folds of a hundred observations each get one ninetieth rather than one hundredth. Both are MATLAB’s behaviour, measured.

See also: fitclinear, ClassificationLinear

Cross-validate a linear classifier on the two overlapping iris species and read the out-of-sample error rate.

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 0.030000
ClassificationPartitionedLinear: labels = kfoldPredict (obj)
ClassificationPartitionedLinear: [labels, scores] = kfoldPredict (obj)

Each observation is classified by the fold that held it out, so the labels are out-of-sample. An observation that no fold held out, which under a holdout partition is most of them, comes back missing rather than classified, and its scores come back NaN.

With L regularization strengths labels has one column per strength and scores is Nx2xL.

Cross-validate a linear classifier on the two overlapping iris species and read the out-of-sample error rate.

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 0.050000
ClassificationPartitionedLinear: m = kfoldMargin (obj)

The score the out-of-fold model gives the true class, less the score it gives the other one. An observation no fold held out comes back NaN. With L regularization strengths m has one column per strength.

Cross-validate a linear classifier on the two overlapping iris species and read the out-of-sample error rate.

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 0.030000
ClassificationPartitionedLinear: e = kfoldEdge (obj)
ClassificationPartitionedLinear: e = kfoldEdge (…, name, value)

e = kfoldEdge (…, name, value) takes 'Folds', a subset of the folds to average over, and 'Mode', either 'average', the default, or 'individual', which returns one row per fold instead.

Cross-validate a linear classifier on the two overlapping iris species and read the out-of-sample error rate.

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 0.050000
ClassificationPartitionedLinear: l = kfoldLoss (obj)
ClassificationPartitionedLinear: l = kfoldLoss (…, name, value)

l = kfoldLoss (obj) returns the out-of-fold misclassification rate.

l = kfoldLoss (…, name, value) takes 'LossFun', one of 'binodeviance', 'classifcost', 'classiferror', 'exponential', 'hinge', 'logit', 'mincost' and 'quadratic'; 'Folds'; and 'Mode'.

Cross-validate a linear classifier on the two overlapping iris species and read the out-of-sample error rate.

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 0.030000

Examples 

 load fisheriris
 X = meas(51:end,:);
 Y = species(51:end);
 CVMdl = ClassificationPartitionedLinear (X, Y, 'KFold', 5)
CVMdl =

  ClassificationPartitionedLinear

      CrossValidatedModel: 'Linear'
               ClassNames: {'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 100
                    KFold: 5
 outOfSample = kfoldLoss (CVMdl)
outOfSample = 0.030000