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# predict

Class: CompactClassificationSVM

Predict labels using support vector machine classification model

## Syntax

``label = predict(SVMModel,X)``
``````[label,score] = predict(SVMModel,X)``````

## Description

example

````label = predict(SVMModel,X)` returns a vector of predicted class labels for the predictor data in the table or matrix `X`, based on the full or compact, trained SVM classification model `SVMModel`.```

example

``````[label,score] = predict(SVMModel,X)``` also returns a matrix of scores (`score`), indicating the likelihood that a label comes from a particular class. For SVM, likelihood measures are either classification scores or class posterior probabilities. For each observation in `X`, the predicted class label corresponds to the maximum score among all classes.```

## Input Arguments

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SVM classification model, specified as a `ClassificationSVM` model object or `CompactClassificationSVM` model object returned by `fitcsvm` or `compact`, respectively.

Predictor data to be classified, specified as a numeric matrix or table.

Each row of `X` corresponds to one observation, and each column corresponds to one variable.

• For a numeric matrix:

• The variables making up the columns of `X` must have the same order as the predictor variables that trained `SVMModel`.

• If you trained `SVMModel` using a table (for example, `Tbl`) and `Tbl` contains all numeric predictor variables, then `X` can be a numeric matrix. To treat numeric predictors in `Tbl` as categorical during training, identify categorical predictors using the `CategoricalPredictors` name-value pair argument of `fitcsvm`. If `Tbl` contains heterogeneous predictor variables (for example, numeric and categorical data types) and `X` is a numeric matrix, then `predict` throws an error.

• For a table:

• `predict` does not support multicolumn variables and cell arrays other than cell arrays of character vectors.

• If you trained `SVMModel` using a table (for example, `Tbl`), then all predictor variables in `X` must have the same variable names and data types as those that trained `SVMModel` (stored in `SVMModel.PredictorNames`). However, the column order of `X` does not need to correspond to the column order of `Tbl`. `Tbl` and `X` can contain additional variables (response variables, observation weights, etc.), but `predict` ignores them.

• If you trained `SVMModel` using a numeric matrix, then the predictor names in `SVMModel.PredictorNames` and corresponding predictor variable names in `X` must be the same. To specify predictor names during training, see the `PredictorNames` name-value pair argument of `fitcsvm`. All predictor variables in `X` must be numeric vectors. `X` can contain additional variables (response variables, observation weights, etc.), but `predict` ignores them.

If you set `'Standardize',true` in `fitcsvm` to train `SVMModel`, then the software standardizes the columns of `X` using the corresponding means in `SVMModel.Mu` and standard deviations in `SVMModel.Sigma`.

Data Types: `table` | `double` | `single`

## Output Arguments

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Predicted class labels, returned as a categorical or character array, logical or numeric vector, or cell array of character vectors.

`label`:

For one-class learning, the elements of `label` are the one class represented in the observed class labels.

Predicted class scores or posterior probabilities, returned as a numeric column vector or numeric matrix.

• For one-class learning, `score` is a column vector with the same number of rows as the training observations (`X`). The elements are the positive class scores for the corresponding observations. You cannot obtain posterior probabilities for one-class learning.

• For two-class learning, `score` is a two-column matrix with the same number of rows as `X`.

• If you fit the optimal score-to-posterior probability transformation function using `fitPosterior` or `fitSVMPosterior`, then `score` contains class posterior probabilities. That is, if the value of `SVMModel.ScoreTransform` is not `none`, then the elements of the first and second columns of `score` are the negative class (`SVMModel.ClassNames{1}`) and positive class (`SVMModel.ClassNames{2}`) posterior probabilities for the corresponding observations, respectively.

• Otherwise, the elements of the first column are the negative class scores and the elements of the second column are the positive class scores for the corresponding observations.

If `SVMModel``.KernelParameters.Function` is `'linear'`, then the software estimates the classification score for the observation x using

`$f\left(x\right)=\left(x/s\right)\prime \beta +b.$`
`SVMModel` stores β, b, s in the properties `Beta`, `Bias`, and `KernelParameters``.Scale`, respectively.

## Examples

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Load the `ionosphere` data set.

```load ionosphere rng(1); % For reproducibility ```

Train an SVM classifier. Specify a 15% holdout sample for testing. It is good practice to specify the class order and standardize the data.

```CVSVMModel = fitcsvm(X,Y,'Holdout',0.15,'ClassNames',{'b','g'},... 'Standardize',true); CompactSVMModel = CVSVMModel.Trained{1}; % Extract trained, compact classifier testInds = test(CVSVMModel.Partition); % Extract the test indices XTest = X(testInds,:); YTest = Y(testInds,:); ```

`CVSVMModel` is a `ClassificationPartitionedModel` classifier. It contains the property `Trained`, which is a 1-by-1 cell array holding a `CompactClassificationSVM` classifier that the software trained using the training set.

Label the test sample observations. Display the results for the first 10 observations in the test sample.

```[label,score] = predict(CompactSVMModel,XTest); table(YTest(1:10),label(1:10),score(1:10,2),'VariableNames',... {'TrueLabel','PredictedLabel','Score'}) ```
```ans = 10x3 table TrueLabel PredictedLabel Score _________ ______________ ________ 'b' 'b' -1.7178 'g' 'g' 2.0003 'b' 'b' -9.6847 'g' 'g' 2.5619 'b' 'b' -1.5481 'g' 'g' 2.0984 'b' 'b' -2.7017 'b' 'b' -0.66307 'g' 'g' 1.6047 'g' 'g' 1.7731 ```

A goal of classification is to predict labels of new observations using a trained algorithm. Many applications train algorithms on large data sets, which can use resources that are better used elsewhere. This example shows how to efficiently label new observations using an SVM classifier.

Load the ionosphere data set. Suppose that the last 10 observations become available after training the SVM classifier.

```load ionosphere n = size(X,1); % Training sample size isInds = 1:(n-10); % In-sample indices oosInds = (n-9):n; % Out-of-sample indices ```

Train an SVM classifier. It is good practice to standardize the predictors and specify the order of the classes. Conserve memory by reducing the size of the trained SVM classifier.

```SVMModel = fitcsvm(X(isInds,:),Y(isInds),'Standardize',true,... 'ClassNames',{'b','g'}); CompactSVMModel = compact(SVMModel); whos('SVMModel','CompactSVMModel') ```
``` Name Size Bytes Class Attributes CompactSVMModel 1x1 29936 classreg.learning.classif.CompactClassificationSVM SVMModel 1x1 137268 ClassificationSVM ```

The positive class is `'g'`. The `CompactClassificationSVM` classifier (`CompactSVMModel`) uses less space than the `ClassificationSVM` classifier (`SVMModel`) because the latter stores the data.

Estimate the optimal score-to-posterior-probability-transformation function.

```CompactSVMModel = fitPosterior(CompactSVMModel,... X(isInds,:),Y(isInds)) ```
```CompactSVMModel = classreg.learning.classif.CompactClassificationSVM ResponseName: 'Y' CategoricalPredictors: [] ClassNames: {'b' 'g'} ScoreTransform: '@(S)sigmoid(S,-1.968351e+00,3.122242e-01)' Alpha: [88x1 double] Bias: -0.2142 KernelParameters: [1x1 struct] Mu: [1x34 double] Sigma: [1x34 double] SupportVectors: [88x34 double] SupportVectorLabels: [88x1 double] ```

The optimal score transformation function (`CompactSVMModel.ScoreTransform`) is the sigmoid function because the classes are inseparable.

Predict the out-of-sample labels and positive class posterior probabilities. Since true labels are available, compare them with the predicted labels.

```[labels,PostProbs] = predict(CompactSVMModel,X(oosInds,:)); table(Y(oosInds),labels,PostProbs(:,2),'VariableNames',... {'TrueLabels','PredictedLabels','PosClassPosterior'}) ```
```ans = 10x3 table TrueLabels PredictedLabels PosClassPosterior __________ _______________ _________________ 'g' 'g' 0.98419 'g' 'g' 0.95545 'g' 'g' 0.67792 'g' 'g' 0.94447 'g' 'g' 0.98744 'g' 'g' 0.9248 'g' 'g' 0.9711 'g' 'g' 0.96986 'g' 'g' 0.97803 'g' 'g' 0.94361 ```

`PostProbs` is a 10-by-2 matrix, where the first column is the negative class posterior probabilities, and the second column is the positive class posterior probabilities corresponding to the new observations.

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## Algorithms

• By default and irrespective of the model kernel function, MATLAB® uses the dual representation of the score function to classify observations based on trained SVM models, specifically

`$\stackrel{^}{f}\left(x\right)=\sum _{j=1}^{n}{\stackrel{^}{\alpha }}_{j}{y}_{j}G\left(x,{x}_{j}\right)+\stackrel{^}{b}.$`
This prediction method requires, among other things, the trained support vectors and α coefficients (see the `SupportVectors` and `Alpha` properties of the SVM model).

If you are using a linear SVM model for classification and there are many support vectors, then this prediction method can be slow. To efficiently classify observations based on a linear SVM model, remove the support vectors from the model object using `discardSupportVectors`. The resulting model uses the simple linear score function for prediction instead, specifically

`$\stackrel{^}{f}\left(x\right)={x}^{\prime }\stackrel{^}{\beta }+\stackrel{^}{b}.$`
For more details, see Support Vector Machines for Binary Classification.

• By default, the software computes optimal posterior probabilities using Platt’s method [1]:

1. Performing 10-fold cross validation

2. Fitting the sigmoid function parameters to the scores returned from the cross validation

3. Estimating the posterior probabilities by entering the cross-validation scores into the fitted sigmoid function

• The software incorporates prior probabilities in the SVM objective function during training.

• For SVM, `predict` classifies observations into the class yielding the largest score (i.e., the largest posterior probability). The software accounts for misclassification costs by applying the average-cost correction before training the classifier. That is, given the class prior vector P, misclassification cost matrix C, and observation weight vector w, the software defines a new vector of observation weights (W) such that

`${W}_{j}={w}_{j}{P}_{j}\sum _{k=1}^{K}{C}_{jk}.$`

## References

[1] Platt, J. “Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods.” Advances in Large Margin Classifiers. MIT Press, 1999, pages 61–74.