# updateMetricsAndFit

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

## Syntax

Mdl = updateMetricsAndFit(Mdl,X,Y)
Mdl = updateMetricsAndFit(Mdl,X,Y,Name=Value)

## 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).

example

Mdl = updateMetricsAndFit(Mdl,X,Y) returns an incremental learning model 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. 

example

Mdl = updateMetricsAndFit(Mdl,X,Y,Name=Value) uses additional options specified by one or more name-value arguments. For example, you can specify that the columns of the predictor data matrix correspond to observations, and set observation weights.

## Examples

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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).

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 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:

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

2. 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.

3. 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

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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.

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(j) is the label of observation 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

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(j) is the label of observation 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.

Predictor data observation dimension, specified as "rows" or "columns".

Example: ObservationsIn="columns"

Data Types: char | string

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

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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:

1. Append any new labels in Y to the tail of Mdl.ClassNames.

2. 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

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### 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:

1. Store a buffer of length Mdl.MetricsWindowSize for each specified metric, and store a buffer of observation weights.

2. 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.

3. 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