# updateMetrics

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

Since R2022a

## Description

Given streaming data, updateMetrics measures the performance of a configured multiclass error-correcting output codes (ECOC) classification model for incremental learning (incrementalClassificationECOC object). updateMetrics stores the performance metrics in the output model.

updateMetrics allows for flexible incremental learning. After you call the function to update model performance metrics on an incoming chunk of data, you can perform other actions before you train the model to the data. For example, you can decide whether you need to train the model based on its performance on a chunk of data. Alternatively, you can both update model performance metrics and train the model on the data as it arrives, in one call, by using the updateMetricsAndFit function.

To measure the model performance on a specified batch of data, call loss instead.

example

Mdl = updateMetrics(Mdl,X,Y) returns an incremental learning model Mdl, which is the input incremental learning model Mdl modified to contain the model performance metrics on the incoming predictor and response data, X and Y respectively.

When the input model is warm (Mdl.IsWarm is true), updateMetrics overwrites previously computed metrics, stored in the Metrics property, with the new values. Otherwise, updateMetrics stores NaN values in Metrics instead.

example

Mdl = updateMetrics(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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Train an ECOC classification model by using fitcecoc, convert it to an incremental learner, and then track its performance to streaming data.

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

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.

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))
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 model.

Convert Trained Model

Convert the traditionally trained classification 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. The model display shows that the model is warm (IsWarm is 1). Therefore, updateMetrics can track model performance metrics given data.

Track Performance Metrics

Track the model performance on the rest of the data by using the updateMetrics function. Simulate a data stream by processing 50 observations at a time. At each iteration:

1. 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 Metrics property. Note that the function does not fit the model to the chunk of data—the chunk is "new" data for the model.

2. Store the classification error and first model coefficient of the first binary learner ${\beta }_{11}$.

% Preallocation
idxil = ~idxtt;
nil = sum(idxil);
numObsPerChunk = 50;
nchunk = floor(nil/numObsPerChunk);
mc = array2table(zeros(nchunk,2),VariableNames=["Cumulative","Window"]);
beta11 = [IncrementalMdl.BinaryLearners{1}.Beta(1); zeros(nchunk,1)];
Xil = X(idxil,:);
Yil = Y(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));
mc{j,:} = IncrementalMdl.Metrics{"ClassificationError",:};
beta11(j+1) = IncrementalMdl.BinaryLearners{1}.Beta(1);
end

IncrementalMdl is an incrementalClassificationECOC model object that has tracked the model performance to observations in the data stream.

Plot a trace plot of the performance metrics and estimated coefficient ${\beta }_{11}$ on separate tiles.

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

The cumulative loss is stable, whereas the window loss jumps throughout the training. ${\beta }_{11}$ does not change because updateMetrics does not fit the model to the data.

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 the human activity data set. Randomly shuffle the data.

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'

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. 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:

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

2. 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.

3. Store the classification error.

4. 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.

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

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

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.

Prepare an incremental ECOC learner by specifying the maximum number of classes. Configure the model to track its performance and the performance of each binary learner in the model.

Create an ECOC model for incremental learning by calling incrementalClassificationECOC. Specify a maximum of 5 expected classes in the data, and specify to update the performance metrics of binary learners in the model.

Mdl = incrementalClassificationECOC(MaxNumClasses=5,UpdateBinaryLearnerMetrics=true);

Mdl is an incrementalClassificationECOC model. All its properties are read-only.

Display the coding design matrix.

Mdl.CodingMatrix
ans = 5×10

1     1     1     1     0     0     0     0     0     0
-1     0     0     0     1     1     1     0     0     0
0    -1     0     0    -1     0     0     1     1     0
0     0    -1     0     0    -1     0    -1     0     1
0     0     0    -1     0     0    -1     0    -1    -1

Each row corresponds to a class, and each column corresponds to a binary learner. For example, the first binary learner is for classes 1 and 2, and the fourth binary learner is for classes 1 and 5, where both learners assume class 1 as a positive class.

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

isWarm = Mdl.IsWarm
isWarm = logical
0

Mdl.IsWarm is 0; therefore, Mdl is not warm.

Determine the number of observations that incremental fitting functions, such as fit, must process before measuring the performance of the model by displaying the size of the metrics warm-up period.

numObsBeforeMetrics = Mdl.MetricsWarmupPeriod
numObsBeforeMetrics = 1000

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

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

The response vector actid contains the activity IDs in integers: 1, 2, 3, 4, and 5 representing sitting, standing, walking, running, and dancing, respectively. 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.

• Measure model performance metrics on the incoming chunk using updateMetrics, and overwrite the input model.

• Fit the model to the incoming chunk, and overwrite the input model.

• Store the first model coefficient of the first binary learner ${\beta }_{11}$.

• Store the misclassification error rates for the model and its binary learners.

% Preallocation
numObsPerChunk = 50;
nchunk = floor(n/numObsPerChunk);
ce = array2table(zeros(nchunk,2),VariableNames=["Cumulative","Window"]);
beta11 = zeros(nchunk,1);

numBinaryLearners = length(Mdl.BinaryLearners);
BinaryLearnerIsWarm = zeros(numBinaryLearners,1);
numtrainobs = zeros(nchunk,numBinaryLearners);
blMetrics = cell(numBinaryLearners,1);
for k = 1:numBinaryLearners
blMetrics{k} = array2table(zeros(nchunk,2),VariableNames=["Cumulative","Window"]);
end

% Incremental learning
for j = 1:nchunk
ibegin = min(n,numObsPerChunk*(j-1) + 1);
iend   = min(n,numObsPerChunk*j);
idx = ibegin:iend;
Mdl = updateMetrics(Mdl,X(idx,:),Y(idx));
ce{j,:} = Mdl.Metrics{"ClassificationError",:};
for k = 1:numBinaryLearners
blMetrics{k}{j,:} = Mdl.BinaryLearners{k}.Metrics{"ClassificationError",:};
end

Mdl = fit(Mdl,X(idx,:),Y(idx));
beta11(j) = Mdl.BinaryLearners{1}.Beta(1);
for k = 1:numBinaryLearners
numtrainobs(j,k) = Mdl.BinaryLearners{k}.NumTrainingObservations;
if Mdl.BinaryLearners{k}.IsWarm == false
BinaryLearnerIsWarm(k) = j;
end
end
end

Mdl is an incrementalClassificationECOC model object trained on all the data in the stream.

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

figure
t = tiledlayout(2,1);
nexttile
plot(beta11)
ylabel("\beta_{11}")
xlim([0 nchunk])
nexttile
plot(ce.Variables)
ylabel("ClassificationError")
xline(numObsBeforeMetrics/numObsPerChunk,"--")
xlim([0 nchunk])
legend(ce.Properties.VariableNames)
xlabel(t,"Iteration")

mdlIsWarm = numObsBeforeMetrics/numObsPerChunk
mdlIsWarm = 20

The plot suggests that fit always fits the model to the data, and updateMetrics does not track the classification error until after the metrics warm-up period (20 chunks).

Plot the performance metrics of the binary learners for class 3.

bl = find(Mdl.CodingMatrix(3,:)); % Find binary learners for class 3

figure
t = tiledlayout(length(bl),1);
ax = zeros(length(bl),1);
for i = 1 : length(bl)
ax(i) = nexttile;
plot(blMetrics{bl(i)}.Variables)
xline(numObsBeforeMetrics/numObsPerChunk,"--")
xline(BinaryLearnerIsWarm(1),":")
xlim([0 nchunk])
positiveClass = find(Mdl.CodingMatrix(:,bl(i))==1);
negativeClass = find(Mdl.CodingMatrix(:,bl(i))==-1);
title(join(["Binary Learner for classes ",positiveClass," and ",negativeClass]))
end
legend(ax(1),blMetrics{bl(1)}.Properties.VariableNames,Location="best")
ylim([0,0.02])
ylabel(t,"ClassificationError")
xlabel(t,"Iteration")

BinaryLearnerIsWarm(bl)
ans = 4×1

42
41
51
60

A binary learner becomes warm after the software fits the learner to 1000 observations. Because each binary learner uses only the observations corresponding to its positive or negative classes, binary learners become warm at different learning iterations. Also, updateMetrics updates the Window metrics for the binary learners asynchronously.

The first plot shows that the classification error (or misclassification rate) is 0 for the binary learner that determines an activity between sitting (class 1) and walking (class 3). The next three plots show the misclassification rates for the three binary learners that distinguish walking (class 3) from standing (class 2), running (class 4), and dancing (class 5), respectively. These three binary learners have higher misclassification rates than the first binary learner.

## Input Arguments

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Incremental learning model whose performance is measured, 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, updateMetrics does not track the performance of the model. Before updateMetrics can track performance metrics, you must perform both of these actions:

• Fit the input model Mdl to all expected classes (see the MaxNumClasses and ClassNames arguments of incrementalClassificationECOC).

• Fit the input model Mdl to Mdl.MetricsWarmupPeriod observations by passing Mdl and the data to fit. 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, updateMetrics 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, updateMetrics issues an error.

• updateMetrics 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.

updateMetrics 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, updateMetrics ignores the observation. Consequently, updateMetrics uses fewer than n observations to compute the model performance, 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. updateMetrics 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, an incrementalClassificationECOC object.

If the model is not warm, updateMetrics does not compute performance metrics. As a result, the Metrics property of Mdl remains completely composed of NaN values. If the model is warm, updateMetrics computes the cumulative and window performance metrics on the new data X and Y, and overwrites the corresponding elements of Mdl.Metrics. All other properties of the input model Mdl carry over to the output model Mdl. For more details, see Performance Metrics.

## 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 using fit.

## 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), updateMetrics 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 updateMetrics.

## Version History

Introduced in R2022a