# updateMetricsAndFit

Update performance metrics in ECOC incremental learning classification model given new data and train model

## Description

Given streaming data, `updateMetricsAndFit`

first evaluates the
performance of a configured multiclass error-correcting output codes (ECOC) classification
model for incremental learning (`incrementalClassificationECOC`

object) by calling `updateMetrics`

on
incoming data. Then `updateMetricsAndFit`

fits the model to that data by calling
`fit`

. In other
words, `updateMetricsAndFit`

performs *prequential evaluation*
because it treats each incoming chunk of data as a test set, and tracks performance metrics
measured cumulatively and over a specified window [1].

`updateMetricsAndFit`

provides a simple way to update model performance metrics
and train the model on each chunk of data. Alternatively, you can perform the operations
separately by calling `updateMetrics`

and then `fit`

,
which allows for more flexibility (for example, you can decide whether you need to train the
model based on its performance on a chunk of data).

returns an incremental learning model `Mdl`

= updateMetricsAndFit(`Mdl`

,`X`

,`Y`

)`Mdl`

, which is the input incremental learning model `Mdl`

with the following modifications:

`updateMetricsAndFit`

measures the model performance on the incoming predictor and response data,`X`

and`Y`

respectively. When the input model is*warm*(`Mdl.IsWarm`

is`true`

),`updateMetricsAndFit`

overwrites previously computed metrics, stored in the`Metrics`

property, with the new values. Otherwise,`updateMetricsAndFit`

stores`NaN`

values in`Metrics`

instead.`updateMetricsAndFit`

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

.

## Examples

### Update Performance Metrics and Train Model on Data Stream

Prepare an incremental ECOC learner by specifying the maximum number of classes. Track the model performance on streaming data and fit the model to the data in one call by using the `updateMetricsAndFit`

function.

Create an ECOC classification model for incremental learning by calling `incrementalClassificationECOC`

and specifying a maximum of 5 expected classes in the data.

Mdl = incrementalClassificationECOC(MaxNumClasses=5)

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

`Mdl`

is an `incrementalClassificationECOC`

model object. All its properties are read-only.

`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.

Implement incremental learning by performing the following actions at each iteration:

Simulate a data stream by processing a chunk of 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 $${\beta}_{11}$$, cumulative metrics, and window metrics to see how they evolve during incremental learning.

% Preallocation numObsPerChunk = 50; nchunk = floor(n/numObsPerChunk); mc = array2table(zeros(nchunk,2),VariableNames=["Cumulative","Window"]); beta11 = 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 = updateMetricsAndFit(Mdl,X(idx,:),Y(idx)); mc{j,:} = Mdl.Metrics{"ClassificationError",:}; beta11(j) = Mdl.BinaryLearners{1}.Beta(1); end

`Mdl`

is an `incrementalClassificationECOC`

model object trained on all the data in the stream. During incremental learning and after the model is warmed up, `updateMetricsAndFit`

checks the performance of the model on the incoming observations, and then fits the model to those observations.

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

t = tiledlayout(2,1); nexttile plot(beta11) ylabel("\beta_{11}") xlim([0 nchunk]) nexttile plot(mc.Variables) xlim([0 nchunk]) ylabel("Classification Error") xline(Mdl.MetricsWarmupPeriod/numObsPerChunk,"--") legend(mc.Properties.VariableNames) xlabel(t,"Iteration")

The plot indicates that `updateMetricsAndFit`

performs the following actions:

Fit $${\beta}_{11}$$ during all incremental learning iterations.

Compute the performance metrics after the metrics warm-up period only.

Compute the cumulative metrics during each iteration.

Compute the window metrics after processing 200 observations (4 iterations).

### Specify Orientation of Observations and Observation Weights

Train an ECOC classification model by using `fitcecoc`

and convert it to an incremental learner by using `incrementalLearner`

. Track the model performance on streaming data and fit the model to streaming data in one call by using `updateMetricsAndFit`

. Specify the orientation of observations and the observation weights when you call `updateMetricsAndFit`

.

**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 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.

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' Properties, Methods

`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' Properties, Methods

`IncrementalMdl`

is an `incrementalClassificationECOC`

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

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

.

**Track Performance Metrics and Fit Model**

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

function. Transpose the predictor matrix, and specify the data orientation when you call `updateMetricsAndFit`

. At each iteration:

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

Call

`updateMetricsAndFit`

to update the cumulative and window performance metrics of the model given the incoming chunk of observations, and then fit the model to the data. Overwrite the previous incremental model with a new one. Specify that the observations are oriented in columns, and specify the observation weights.Store the misclassification error rate.

% 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 = updateMetricsAndFit(IncrementalMdl,Xil(:,idx),Yil(idx), ... Weights=Wil(idx),ObservationsIn="columns"); mc{j,:} = IncrementalMdl.Metrics{"ClassificationError",:}; end

`IncrementalMdl`

is an `incrementalClassificationECOC`

model object trained on all the data in the stream.

Create a trace plot of the misclassification error rate.

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

The cumulative loss initially jumps, but stabilizes around 0.03, whereas the window loss jumps throughout the training.

## Input Arguments

`Mdl`

— Incremental learning model

`incrementalClassificationECOC`

model object

Incremental learning model whose performance is measured and then the model is fit
to 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.

If `Mdl.IsWarm`

is `false`

,
`updateMetricsAndFit`

does not track the performance of the model. For more
details, see Performance Metrics.

`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,`updateMetricsAndFit`

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`

,`updateMetricsAndFit`

issues an error.`updateMetricsAndFit`

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`

.
`updateMetricsAndFit`

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, `updateMetricsAndFit`

ignores the
observation. Consequently, `updateMetricsAndFit`

uses fewer than *n*
observations to compute the model performance and 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.
`updateMetricsAndFit`

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`

, `incrementalClassificationECOC`

.

If the model is not warm, `updateMetricsAndFit`

does not compute
performance metrics. As a result, the `Metrics`

property of
`Mdl`

remains completely composed of `NaN`

values.
If the model is warm, `updateMetricsAndFit`

computes the cumulative and
window performance metrics on the new data `X`

and
`Y`

, and overwrites the corresponding elements of
`Mdl.Metrics`

. For more details, see Performance Metrics.

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 `updateMetricsAndFit`

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`

.

## Algorithms

### Performance Metrics

`updateMetrics`

and`updateMetricsAndFit`

track model performance metrics, specified by the row labels of the table in`Mdl.Metrics`

, from new data only when the incremental model is*warm*(`IsWarm`

property is`true`

).If you create an incremental model by using

`incrementalLearner`

and`MetricsWarmupPeriod`

is 0 (default for`incrementalLearner`

), the model is warm at creation.Otherwise, an incremental model becomes warm after the

`fit`

or`updateMetricsAndFit`

function performs both of these actions:Fit the incremental model to

`Mdl.MetricsWarmupPeriod`

observations, which is the*metrics warm-up period*.Fit the incremental model to all expected classes (see the

`MaxNumClasses`

and`ClassNames`

arguments of`incrementalClassificationECOC`

).

The

`Mdl.Metrics`

property stores two forms of each performance metric as variables (columns) of a table,`Cumulative`

and`Window`

, with individual metrics in rows. When the incremental model is warm,`updateMetrics`

and`updateMetricsAndFit`

update the metrics at the following frequencies:`Cumulative`

— The functions compute cumulative metrics since the start of model performance tracking. The functions update metrics every time you call the functions and base the calculation on the entire supplied data set.`Window`

— The functions compute metrics based on all observations within a window determined by the`Mdl.MetricsWindowSize`

property.`Mdl.MetricsWindowSize`

also determines the frequency at which the software updates`Window`

metrics. For example, if`Mdl.MetricsWindowSize`

is 20, the functions compute metrics based on the last 20 observations in the supplied data (`X((end – 20 + 1):end,:)`

and`Y((end – 20 + 1):end)`

).Incremental functions that track performance metrics within a window use the following process:

Store a buffer of length

`Mdl.MetricsWindowSize`

for each specified metric, and store a buffer of observation weights.Populate elements of the metrics buffer with the model performance based on batches of incoming observations, and store corresponding observation weights in the weights buffer.

When the buffer is filled, overwrite

`Mdl.Metrics.Window`

with the weighted average performance in the metrics window. If the buffer is overfilled when the function processes a batch of observations, the latest incoming`Mdl.MetricsWindowSize`

observations enter the buffer, and the earliest observations are removed from the buffer. For example, suppose`Mdl.MetricsWindowSize`

is 20, the metrics buffer has 10 values from a previously processed batch, and 15 values are incoming. To compose the length 20 window, the function uses the measurements from the 15 incoming observations and the latest 5 measurements from the previous batch.

The software omits an observation with a

`NaN`

score when computing the`Cumulative`

and`Window`

performance metric values.

### Observation Weights

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

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 `updateMetricsAndFit`

.

## References

[1] Bifet, Albert, Ricard Gavaldá, Geoffrey Holmes, and Bernhard Pfahringer. *Machine Learning for Data Streams with Practical Example in MOA*. Cambridge, MA: The MIT Press, 2007.

## Version History

**Introduced in R2022a**

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