# fit

## Description

The `fit`

function fits a configured multiclass
error-correcting output codes (ECOC) classification model for incremental learning (`incrementalClassificationECOC`

object) to streaming data. To additionally track
performance metrics using the data as it arrives, use `updateMetricsAndFit`

instead.

To fit or cross-validate an ECOC classification model to an entire batch of data at once,
see `fitcecoc`

.

returns an incremental learning model `Mdl`

= fit(`Mdl`

,`X`

,`Y`

)`Mdl`

, which represents the input incremental learning model `Mdl`

trained using the predictor and response data, `X`

and
`Y`

respectively. Specifically, `fit`

fits
the model to the incoming data and stores the updated binary learners and configurations in
the output model `Mdl`

.

## Examples

### Incrementally Train Model with Little Prior Information

Fit an incremental ECOC learner when you know only the expected maximum number of classes in the data.

Create an incremental ECOC model. Specify that the maximum number of expected classes is 5.

Mdl = incrementalClassificationECOC(MaxNumClasses=5)

Mdl = incrementalClassificationECOC IsWarm: 0 Metrics: [1x2 table] ClassNames: [1x0 double] ScoreTransform: 'none' BinaryLearners: {10x1 cell} CodingName: 'onevsone' Decoding: 'lossweighted'

`Mdl`

is an `incrementalClassificationECOC`

model. All its properties are read-only. `Mdl`

can process at most 5 unique classes. By default, the prior class distribution `Mdl.Prior`

is empirical, which means the software updates the prior distribution as it encounters labels.

`Mdl`

must be fit to data before you can use it to perform any other operations.

Load the human activity data set. Randomly shuffle the data.

load humanactivity n = numel(actid); rng(1) % For reproducibility idx = randsample(n,n); X = feat(idx,:); Y = actid(idx);

For details on the data set, enter `Description`

at the command line.

Fit the incremental model to the training data, in chunks of 50 observations at a time, by using the `fit`

function. At each iteration:

Simulate a data stream by processing 50 observations.

Overwrite the previous incremental model with a new one fitted to the incoming observations.

Store the first model coefficient of the first binary learner $${\beta}_{11}$$ and the prior probability that the subject is moving (

`Y`

> 2) to see how these parameters evolve during incremental learning.

% Preallocation numObsPerChunk = 50; nchunk = floor(n/numObsPerChunk); beta11 = zeros(nchunk,1); priormoved = zeros(nchunk,1); % Incremental fitting for j = 1:nchunk ibegin = min(n,numObsPerChunk*(j-1) + 1); iend = min(n,numObsPerChunk*j); idx = ibegin:iend; Mdl = fit(Mdl,X(idx,:),Y(idx)); beta11(j) = Mdl.BinaryLearners{1}.Beta(1); priormoved(j) = sum(Mdl.Prior(Mdl.ClassNames > 2)); end

`Mdl`

is an `incrementalClassificationECOC`

model object trained on all the data in the stream.

To see how the parameters evolve during incremental learning, plot them on separate tiles.

t = tiledlayout(2,1); nexttile plot(beta11) xlim([0 nchunk]) ylabel("\beta_{11}") nexttile plot(priormoved) xlim([0 nchunk]) ylabel("\pi(Subject Is Moving)") xlabel(t,"Iteration")

`fit`

updates the coefficient as it processes each chunk. Because the prior class distribution is empirical, $$\pi $$(subject is moving) changes as `fit`

processes each chunk.

### Specify All Class Names Before Fitting

Fit an incremental ECOC learner when you know all the class names in the data.

Consider training a device to predict whether a subject is sitting, standing, walking, running, or dancing based on biometric data measured on the subject. The class names map 1 through 5 to an activity. Also, suppose that the researchers plan to expose the device to each class uniformly.

Create an incremental ECOC model for multiclass learning. Specify the class names and the uniform prior class distribution.

```
classnames = 1:5;
Mdl = incrementalClassificationECOC(ClassNames=classnames,Prior="uniform")
```

Mdl = incrementalClassificationECOC IsWarm: 0 Metrics: [1x2 table] ClassNames: [1 2 3 4 5] ScoreTransform: 'none' BinaryLearners: {10x1 cell} CodingName: 'onevsone' Decoding: 'lossweighted'

`Mdl`

is an `incrementalClassificationECOC`

model object. All its properties are read-only. During training, observed labels must be in `Mdl.ClassNames`

.

`Mdl`

must be fit to data before you can use it to perform any other operations.

Load the human activity data set. Randomly shuffle the data.

load humanactivity n = numel(actid); rng(1) % For reproducibility idx = randsample(n,n); X = feat(idx,:); Y = actid(idx);

For details on the data set, enter `Description`

at the command line.

Fit the incremental model to the training data by using the `fit`

function. Simulate a data stream by processing chunks of 50 observations at a time. At each iteration:

Process 50 observations.

Overwrite the previous incremental model with a new one fitted to the incoming observations.

Store the first model coefficient of the first binary learner $${\beta}_{11}$$ and the prior probability that the subject is moving (

`Y`

> 2) to see how these parameters evolve during incremental learning.

% Preallocation numObsPerChunk = 50; nchunk = floor(n/numObsPerChunk); beta11 = zeros(nchunk,1); priormoved = zeros(nchunk,1); % Incremental fitting for j = 1:nchunk ibegin = min(n,numObsPerChunk*(j-1) + 1); iend = min(n,numObsPerChunk*j); idx = ibegin:iend; Mdl = fit(Mdl,X(idx,:),Y(idx)); beta11(j) = Mdl.BinaryLearners{1}.Beta(1); priormoved(j) = sum(Mdl.Prior(Mdl.ClassNames > 2)); end

`Mdl`

is an `incrementalClassificationECOC`

model object trained on all the data in the stream.

To see how the parameters evolve during incremental learning, plot them on separate tiles.

t = tiledlayout(2,1); nexttile plot(beta11) xlim([0 nchunk]) ylabel("\beta_{11}") nexttile plot(priormoved) xlim([0 nchunk]) ylabel("\pi(Subject Is Moving)") xlabel(t,"Iteration")

`fit`

updates the posterior mean of the predictor distribution as it processes each chunk. Because the prior class distribution is specified as uniform, $$\pi $$(subject is moving) = 0.6 and does not change as `fit`

processes each chunk.

### Specify Orientation of Observations and Observation Weights

Train an ECOC classification model by using `fitcecoc`

, convert it to an incremental learner, track its performance on streaming data, and then fit the model to the data. For incremental learning functions, orient the observations in columns, and specify observation weights.

**Load and Preprocess Data**

Load the human activity data set. Randomly shuffle the data.

load humanactivity rng(1); % For reproducibility n = numel(actid); idx = randsample(n,n); X = feat(idx,:); Y = actid(idx);

For details on the data set, enter `Description`

at the command line.

Suppose that the data from a stationary subject (`Y`

<= 2) has double the quality of the data from a moving subject. Create a weight variable that assigns a weight of 2 to observations from a stationary subject and 1 to a moving subject.

W = ones(n,1) + (Y <=2);

**Train ECOC Classification Model**

Fit an ECOC classification model to a random sample of half the data. Specify observation weights.

idxtt = randsample([true false],n,true); TTMdl = fitcecoc(X(idxtt,:),Y(idxtt),Weights=W(idxtt))

TTMdl = ClassificationECOC ResponseName: 'Y' CategoricalPredictors: [] ClassNames: [1 2 3 4 5] ScoreTransform: 'none' BinaryLearners: {10x1 cell} CodingName: 'onevsone'

`TTMdl`

is a `ClassificationECOC`

model object representing a traditionally trained ECOC classification model.

**Convert Trained Model**

Convert the traditionally trained model to a model for incremental learning.

IncrementalMdl = incrementalLearner(TTMdl)

IncrementalMdl = incrementalClassificationECOC IsWarm: 1 Metrics: [1x2 table] ClassNames: [1 2 3 4 5] ScoreTransform: 'none' BinaryLearners: {10x1 cell} CodingName: 'onevsone' Decoding: 'lossweighted'

`IncrementalMdl`

is an `incrementalClassificationECOC`

model. Because class names are specified in `IncrementalMdl.ClassNames`

, labels encountered during incremental learning must be in `IncrementalMdl.ClassNames`

.

**Separately Track Performance Metrics and Fit Model**

Perform incremental learning on the rest of the data by using the `updateMetrics`

and `fit`

functions. For incremental learning, orient the observations of the predictor data in columns. At each iteration:

Simulate a data stream by processing 50 observations at a time.

Call

`updateMetrics`

to update the cumulative and window classification error of the model given the incoming chunk of observations. Overwrite the previous incremental model to update the losses in the`Metrics`

property. Note that the function does not fit the model to the chunk of data—the chunk is "new" data for the model. Specify that the observations are oriented in columns, and specify the observation weights.Store the classification error.

Call

`fit`

to fit the model to the incoming chunk of observations. Overwrite the previous incremental model to update the model parameters. Specify that the observations are oriented in columns, and specify the observation weights.

% Preallocation idxil = ~idxtt; nil = sum(idxil); numObsPerChunk = 50; nchunk = floor(nil/numObsPerChunk); mc = array2table(zeros(nchunk,2),VariableNames=["Cumulative","Window"]); Xil = X(idxil,:)'; Yil = Y(idxil); Wil = W(idxil); % Incremental fitting for j = 1:nchunk ibegin = min(nil,numObsPerChunk*(j-1) + 1); iend = min(nil,numObsPerChunk*j); idx = ibegin:iend; IncrementalMdl = updateMetrics(IncrementalMdl,Xil(:,idx),Yil(idx), ... Weights=Wil(idx),ObservationsIn="columns"); mc{j,:} = IncrementalMdl.Metrics{"ClassificationError",:}; IncrementalMdl = fit(IncrementalMdl,Xil(:,idx),Yil(idx), ... Weights=Wil(idx),ObservationsIn="columns"); end

`IncrementalMdl`

is an `incrementalClassificationECOC`

model object trained on all the data in the stream.

Alternatively, you can use `updateMetricsAndFit`

to update performance metrics of the model given a new chunk of data, and then fit the model to the data.

Plot a trace plot of the performance metrics.

plot(mc.Variables) xlim([0 nchunk]) legend(mc.Properties.VariableNames) ylabel("Classification Error") xlabel("Iteration")

The cumulative loss gradually stabilizes, whereas the window loss jumps throughout the training.

### Perform Conditional Training

Incrementally train an ECOC classification model only when its performance degrades.

Load the human activity data set. Randomly shuffle the data.

load humanactivity n = numel(actid); rng(1) % For reproducibility idx = randsample(n,n); X = feat(idx,:); Y = actid(idx);

For details on the data set, enter `Description`

at the command line.

Configure an ECOC classification model for incremental learning so that the maximum number of expected classes is 5, and the metrics window size is 1000. Prepare the model for `updateMetrics`

by fitting the model to the first 1000 observations.

Mdl = incrementalClassificationECOC(MaxNumClasses=5,MetricsWindowSize=1000); initobs = 1000; Mdl = fit(Mdl,X(1:initobs,:),Y(1:initobs));

`Mdl`

is an `incrementalClassificationECOC`

model object.

Determine whether the model is warm by querying the model property.

isWarm = Mdl.IsWarm

`isWarm = `*logical*
1

`Mdl.IsWarm`

is 1; therefore, `Mdl`

is warm.

Perform incremental learning, with conditional fitting, by following this procedure for each iteration:

Simulate a data stream by processing a chunk of 100 observations at a time.

Update the model performance on the incoming chunk of data.

Fit the model to the chunk of data only when the misclassification error rate is greater than 0.05.

When tracking performance and fitting, overwrite the previous incremental model.

Store the misclassification error rate and the first model coefficient of the first binary learner $${\beta}_{11}$$ to see how they evolve during training.

Track when

`fit`

trains the model.

% Preallocation numObsPerChunk = 100; nchunk = floor((n - initobs)/numObsPerChunk); beta11 = zeros(nchunk,1); ce = array2table(nan(nchunk,2),VariableNames=["Cumulative","Window"]); trained = false(nchunk,1); % Incremental fitting for j = 1:nchunk ibegin = min(n,numObsPerChunk*(j-1) + 1 + initobs); iend = min(n,numObsPerChunk*j + initobs); idx = ibegin:iend; Mdl = updateMetrics(Mdl,X(idx,:),Y(idx)); ce{j,:} = Mdl.Metrics{"ClassificationError",:}; if ce{j,2} > 0.05 Mdl = fit(Mdl,X(idx,:),Y(idx)); trained(j) = true; end beta11(j) = Mdl.BinaryLearners{1}.Beta(1); end

`Mdl`

is an `incrementalClassificationECOC`

model object trained on all the data in the stream.

To see how the model performance and $${\beta}_{11}$$ evolve during training, plot them on separate tiles.

t = tiledlayout(2,1); nexttile plot(beta11) hold on plot(find(trained),beta11(trained),"r.") xlim([0 nchunk]) ylabel("\beta_{11}") legend("\beta_{11}","Training occurs",Location="best") hold off nexttile plot(ce.Variables) yline(0.05,"--") xlim([0 nchunk]) ylabel("Misclassification Error Rate") legend(ce.Properties.VariableNames,Location="best") xlabel(t,"Iteration")

The trace plot of $${\beta}_{11}$$ shows periods of constant values, during which the loss within the previous observation window is at most 0.05.

## Input Arguments

`Mdl`

— Incremental learning model

`incrementalClassificationECOC`

model object

Incremental learning model to fit to streaming data, specified as an `incrementalClassificationECOC`

model object. You can create
`Mdl`

by calling `incrementalClassificationECOC`

directly, or by converting a supported, traditionally trained machine learning model
using the `incrementalLearner`

function.

`X`

— Chunk of predictor data

floating-point matrix

Chunk of predictor data, specified as a floating-point matrix of *n*
observations and `Mdl.NumPredictors`

predictor
variables. The value of the `ObservationsIn`

name-value
argument determines the orientation of the variables and observations. The default
`ObservationsIn`

value is `"rows"`

, which indicates that
observations in the predictor data are oriented along the rows of
`X`

.

The length of the observation labels `Y`

and the number of observations in `X`

must be equal; `Y(`

is the label of observation * j*)

*j*(row or column) in

`X`

.**Note**

If

`Mdl.NumPredictors`

= 0,`fit`

infers the number of predictors from`X`

, and sets the corresponding property of the output model. Otherwise, if the number of predictor variables in the streaming data changes from`Mdl.NumPredictors`

,`fit`

issues an error.`fit`

supports only floating-point input predictor data. If your input data includes categorical data, you must prepare an encoded version of the categorical data. Use`dummyvar`

to convert each categorical variable to a numeric matrix of dummy variables. Then, concatenate all dummy variable matrices and any other numeric predictors. For more details, see Dummy Variables.

**Data Types: **`single`

| `double`

`Y`

— Chunk of labels

categorical array | character array | string array | logical vector | floating-point vector | cell array of character vectors

Chunk of labels, specified as a categorical, character, or string array, a logical or floating-point vector, or a cell array of character vectors.

The length of the observation labels `Y`

and the number of
observations in `X`

must be equal;
`Y(`

is the label of observation
* j*)

*j*(row or column) in

`X`

.
`fit`

issues an error when one or both of these conditions
are met:

`Y`

contains a new label and the maximum number of classes has already been reached (see the`MaxNumClasses`

and`ClassNames`

arguments of`incrementalClassificationECOC`

).The

`ClassNames`

property of the input model`Mdl`

is nonempty, and the data types of`Y`

and`Mdl.ClassNames`

are different.

**Data Types: **`char`

| `string`

| `cell`

| `categorical`

| `logical`

| `single`

| `double`

**Note**

If an observation (predictor or label) or weight contains at
least one missing (`NaN`

) value, `fit`

ignores the
observation. Consequently, `fit`

uses fewer than *n*
observations to create an updated model, where *n* is the number of
observations in `X`

.

### 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.

**Example: **`ObservationsIn="columns",Weights=W`

specifies that the columns
of the predictor matrix correspond to observations, and the vector `W`

contains observation weights to apply during incremental learning.

`ObservationsIn`

— Predictor data observation dimension

`"rows"`

(default) | `"columns"`

Predictor data observation dimension, specified as `"rows"`

or
`"columns"`

.

**Example: **`ObservationsIn="columns"`

**Data Types: **`char`

| `string`

`Weights`

— Chunk of observation weights

floating-point vector of positive values

Chunk of observation weights, specified as a floating-point vector of positive values.
`fit`

weighs the observations in `X`

with the corresponding values in `Weights`

. The size of
`Weights`

must equal *n*, which is the number of
observations in `X`

.

By default, `Weights`

is `ones(`

.* n*,1)

For more details, including normalization schemes, see Observation Weights.

**Example: **`Weights=W`

specifies the observation weights as the vector
`W`

.

**Data Types: **`double`

| `single`

## Output Arguments

`Mdl`

— Updated ECOC classification model for incremental learning

`incrementalClassificationECOC`

model object

Updated ECOC classification model for incremental learning, returned as an
incremental learning model object of the same data type as the input model `Mdl`

, an `incrementalClassificationECOC`

object.

If you do not specify all expected classes by using the
`ClassNames`

name-value argument when you create the input model
`Mdl`

using `incrementalClassificationECOC`

, and `Y`

contains expected, but
unprocessed, classes, then `fit`

performs the following actions:

Append any new labels in

`Y`

to the tail of`Mdl.ClassNames`

.Expand

`Mdl.Prior`

to a length*c*vector of an updated empirical class distribution, where*c*is the number of classes in`Mdl.ClassNames`

.

## Tips

Unlike traditional training, incremental learning might not have a separate test (holdout) set. Therefore, to treat each incoming chunk of data as a test set, pass the incremental model and each incoming chunk to

`updateMetrics`

before training the model on the same data.

## Algorithms

### Observation Weights

If the prior class probability distribution is known (in other words, the prior distribution is not empirical), `fit`

normalizes observation weights to sum to the prior class probabilities in the respective classes. This action implies that the default observation weights are the respective prior class probabilities.

If the prior class probability distribution is empirical, the software normalizes the specified observation weights to sum to 1 each time you call `fit`

.

## Version History

**Introduced in R2022a**

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