Load Data

Load thedigitimages.

loaddigitimages.mat

imagesis a 28-by-28-by-3000 array ofuint16integers. Each page is a raster image of a digit. Each element is a pixel intensity. Corresponding labels are in the 3000-by-1 numeric vectorY. For more details, enterDescriptionat the command line.

Store the number of observations and the number of predictor variables. Create a data partition that specifies to hold out 20% of the data. Extract training and test set indices from the data partition.

rng(1);% For reproducibilityn = size(images,3); p = numel(images(:,:,1)); cvp = cvpartition(n,'Holdout',0.20); idxTrn = training(cvp); idxTest = test(cvp);

Rescale Data

Rescale the pixel intensities so that they range in the interval [0,1] within each image. Specifically, suppose $$p_{ij}$$is pixel intensity $$j$$within image $$i$$. For image $$i$$, rescale all of its pixel intensities by using this formula:

X = double(images);fori = 1:n minX = min(min(X(:,:,i))); maxX = max(max(X(:,:,i))); X(:,:,i) = (X(:,:,i) - minX)/(maxX - minX);end

Reshape Data

For code generation, the predictor data for training must be in a table of numeric variables or a numeric matrix.

Reshape the data to a matrix such that predictor variables correspond to columns and images correspond to rows. Becausereshapetakes elements column-wise, transpose its result.

X = reshape(X,[p,n])';

Train and Optimize Classification Models

Cross-validate an ECOC model of SVM binary learners and a random forest based on the training observations. Use 5-fold cross-validation.

For the ECOC model, specify predictor standardization and optimize classification error over the ECOC coding design and the SVM box constraint. Explore all combinations of these values:

coding = {'onevsone''onevsall'}; boxconstraint = logspace(-1,2,3); cvLossECOC = nan(numel(coding),numel(boxconstraint));% For preallocationfori = 1:numel(coding)forj = 1:numel(boxconstraint) t = templateSVM('BoxConstraint',boxconstraint(j),'Standardize',true); CVMdl = fitcecoc(X(idxTrn,:),Y(idxTrn),'Learners',t,'KFold',5,...'Coding',coding{i}); cvLossECOC(i,j) = kfoldLoss(CVMdl); fprintf('cvLossECOC = %f for model using %s coding and box constraint=%f\n',...cvLossECOC(i,j),coding{i},boxconstraint(j))endend

cvLossECOC = 0.058333 for model using onevsone coding and box constraint=0.100000 cvLossECOC = 0.057083 for model using onevsone coding and box constraint=3.162278 cvLossECOC = 0.050000 for model using onevsone coding and box constraint=100.000000 cvLossECOC = 0.120417 for model using onevsall coding and box constraint=0.100000 cvLossECOC = 0.121667 for model using onevsall coding and box constraint=3.162278 cvLossECOC = 0.127917 for model using onevsall coding and box constraint=100.000000

For the random forest, vary the maximum number of splits by using the values in the sequence $$\{3^2,3^3,...,3^m\}$$. m is such that $$3^m$$is no greater thann- 1. To reproduce random predictor selections, specify'Reproducible',true.

n = size(X,1); m = floor(log(n - 1)/log(3)); maxNumSplits = 3.^(2:m); cvLossRF = nan(numel(maxNumSplits));fori = 1:numel(maxNumSplits) t = templateTree('MaxNumSplits',maxNumSplits(i),'Reproducible',true); CVMdl = fitcensemble(X(idxTrn,:),Y(idxTrn),'Method','bag','Learners',t,...'KFold',5); cvLossRF(i) = kfoldLoss(CVMdl); fprintf('cvLossRF = %f for model using %d as the maximum number of splits\n',...cvLossRF(i),maxNumSplits(i))end

cvLossRF = 0.323750 for model using 9 as the maximum number of splits cvLossRF = 0.198333 for model using 27 as the maximum number of splits cvLossRF = 0.075417 for model using 81 as the maximum number of splits cvLossRF = 0.017083 for model using 243 as the maximum number of splits cvLossRF = 0.012083 for model using 729 as the maximum number of splits cvLossRF = 0.012083 for model using 2187 as the maximum number of splits

For each algorithm, determine the hyperparameter indices that yield the minimal misclassification rates.

minCVLossECOC = min(cvLossECOC(:))

minCVLossECOC = 0.0500

linIdx = find(cvLossECOC == minCVLossECOC,1); [bestI,bestJ] = ind2sub(size(cvLossECOC),linIdx); bestCoding = coding{bestI}

bestCoding = 'onevsone'

bestBoxConstraint = boxconstraint(bestJ)

bestBoxConstraint = 100

minCVLossRF = min(cvLossRF(:))

minCVLossRF = 0.0121

linIdx = find(cvLossRF == minCVLossRF,1); [bestI,bestJ] = ind2sub(size(cvLossRF),linIdx); bestMNS = maxNumSplits(bestI)

bestMNS = 729

The random forest achieves a smaller cross-validated misclassification rate.

Train an ECOC model and a random forest using the training data. Supply the optimal hyperparameter combinations.

t = templateSVM('BoxConstraint',bestBoxConstraint,'Standardize',true); MdlECOC = fitcecoc(X(idxTrn,:),Y(idxTrn),'Learners',t,'Coding',bestCoding); t = templateTree('MaxNumSplits',bestMNS); MdlRF = fitcensemble(X(idxTrn,:),Y(idxTrn),'Method','bag','Learners',t);

Create a variable for the test sample images and use the trained models to predict test sample labels.

testImages = X(idxTest,:); testLabelsECOC = predict(MdlECOC,testImages); testLabelsRF = predict(MdlRF,testImages);

分类模型保存到磁盘

MdlECOCandMdlRFare predictive classification models, but you must prepare them for code generation. SaveMdlECOCandMdlRFto your present working folder usingsaveLearnerForCoder.

saveLearnerForCoder(MdlECOC,'DigitImagesECOC'); saveLearnerForCoder(MdlRF,'DigitImagesRF');

Create System Object for Prediction

Create two System objects, one for the ECOC model and the other for the random forest, that:

typeECOCClassifier.m% Display contents of ECOCClassifier.m file

classdef ECOCClassifier < matlab.System % ECOCCLASSIFIER Predict image labels from trained ECOC model % % ECOCCLASSIFIER loads the trained ECOC model from % |'DigitImagesECOC.mat'|, and predicts labels for new observations % based on the trained model. The ECOC model in % |'DigitImagesECOC.mat'| was cross-validated using the training data % in the sample data |digitimages.mat|. properties(Access = private) CompactMdl % The compacted, trained ECOC model end methods(Access = protected) function setupImpl(obj) % Load ECOC model from file obj.CompactMdl = loadLearnerForCoder('DigitImagesECOC'); end function y = stepImpl(obj,u) y = predict(obj.CompactMdl,u); end function flag = isInputSizeMutableImpl(obj,index) % Return false if input size is not allowed to change while % system is running flag = false; end function dataout = getOutputDataTypeImpl(~) dataout = 'double'; end function sizeout = getOutputSizeImpl(~) sizeout = [1 1]; end end end

typeRFClassifier.m% Display contents of RFClassifier.m file

classdef RFClassifier < matlab.System % RFCLASSIFIER Predict image labels from trained random forest % % RFCLASSIFIER loads the trained random forest from % |'DigitImagesRF.mat'|, and predicts labels for new observations based % on the trained model. The random forest in |'DigitImagesRF.mat'| % was cross-validated using the training data in the sample data % |digitimages.mat|. properties(Access = private) CompactMdl % The compacted, trained random forest end methods(Access = protected) function setupImpl(obj) % Load random forest from file obj.CompactMdl = loadLearnerForCoder('DigitImagesRF'); end function y = stepImpl(obj,u) y = predict(obj.CompactMdl,u); end function flag = isInputSizeMutableImpl(obj,index) % Return false if input size is not allowed to change while % system is running flag = false; end function dataout = getOutputDataTypeImpl(~) dataout = 'double'; end function sizeout = getOutputSizeImpl(~) sizeout = [1 1]; end end end

Note:If you click the button located in the upper-right section of this page and open this example in MATLAB®, then MATLAB® opens the example folder. This folder includes the files used in this example.

For System object basic requirements, seeDefine Basic System Objects.

Define Prediction Functions for Code Generation

Define two MATLAB functions calledpredictDigitECOCSO.mandpredictDigitRFSO.m. The functions:

typepredictDigitECOCSO.m% Display contents of predictDigitECOCSO.m file

函数标签= predictDigitECOCSO (X) % # codegen %PREDICTDIGITECOCSO Classify digit in image using ECOC Model System object % PREDICTDIGITECOCSO classifies the 28-by-28 images in the rows of X % using the compact ECOC model in the System object ECOCClassifier, and % then returns class labels in label. classifier = ECOCClassifier; label = step(classifier,X); end

typepredictDigitRFSO.m% Display contents of predictDigitRFSO.m file

function label = predictDigitRFSO(X) %#codegen %PREDICTDIGITRFSO Classify digit in image using RF Model System object % PREDICTDIGITRFSO classifies the 28-by-28 images in the rows of X % using the compact random forest in the System object RFClassifier, and % then returns class labels in label. classifier = RFClassifier; label = step(classifier,X); end

Compile MATLAB Function to MEX File

Compile the prediction function that achieves better test-sample accuracy to a MEX file by usingcodegen. Specify the test set images by using the-argsargument.

if(minCVLossECOC <= minCVLossRF) codegenpredictDigitECOCSO-argstestImageselsecodegenpredictDigitRFSO-argstestImagesend

Verify that the generated MEX file produces the same predictions as the MATLAB function.

if(minCVLossECOC <= minCVLossRF) mexLabels = predictDigitECOCSO_mex(testImages); verifyMEX = sum(mexLabels == testLabelsECOC) == numel(testLabelsECOC)elsemexLabels = predictDigitRFSO_mex(testImages); verifyMEX = sum(mexLabels == testLabelsRF) == numel(testLabelsRF)end

verifyMEX =logical1

verifyMEXis1, which indicates that the predictions made by the generated MEX file and the corresponding MATLAB function are the same.

Predict Labels by Using System Objects in Simulink

Create a video file that displays the test-set images frame-by-frame.

v= VideoWriter('testImages.avi','Uncompressed AVI'); v.FrameRate = 1; open(v); dim = sqrt(p)*[1 1];forj = 1:size(testImages,1) writeVideo(v,reshape(testImages(j,:),dim));endclose(v);

Define a function calledscalePixelIntensities.mthat converts RGB images to grayscale, and then scales the resulting pixel intensities so that their values are in the interval [0,1].

typescalePixelIntensities.m% Display contents of scalePixelIntensities.m file

function x = scalePixelIntensities(imdat) %SCALEPIXELINTENSITIES Scales image pixel intensities % SCALEPIXELINTENSITIES scales the pixel intensities of the image such % that the result x is a row vector of values in the interval [0,1]. imdat = rgb2gray(imdat); minimdat = min(min(imdat)); maximdat = max(max(imdat)); x = (imdat - minimdat)/(maximdat - minimdat); end

加载Simulink® modelslexClassifyAndDisplayDigitImages.slx.

SimMdlName ='slexClassifyAndDisplayDigitImages'; open_system(SimMdlName);

The figure displays the Simulink® model. At the beginning of simulation, the From Multimedia File block loads the video file of the test-set images. For each image in the video:

Simulate the model.

sim(SimMdlName)

The model displays all 600 test-set images and its prediction quickly. The last image remains in the video display. You can generate predictions and display them with corresponding images one-by-one by clicking theStep Forwardbutton instead.

If you also have a Simulink® Coder™ license, then you can generate C code fromslexClassifyAndDisplayDigitImages.slxin Simulink® or from the command line usingrtwbuild(Simulink Coder). For more details, seeGenerate C Code for a Model(Simulink Coder).