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This example shows how to classify the genre of a musical excerpt using wavelet time scattering and the audio datastore. In wavelet scattering, data is propagated through a series of wavelet transforms, nonlinearities, and averaging to produce low-variance representations of the data. These low-variance representations are then used as inputs to a classifier.

The data set used in this example is the GTZAN Genre Collection [7][8]. The data is provided as a zipped tar archive which is approximately 1.2 GB. The uncompressed data set requires about 3 GB of disk space. Extracting the compressed tar file from the link provided in the references creates a folder with ten subfolders. Each subfolder is named for the genre of music samples it contains. The genres are: blues, classical, country, disco, hiphop, jazz, metal, pop, reggae, and rock. There are 100 examples of each genre and each audio file consists of about 30 seconds of data sampled at 22050 Hz. In the original paper, the authors used a number of time-domain and frequency-domain features including mel-frequency cepstral (MFC) coefficients extracted from each music example and a Gaussian mixture model (GMM) classification to achieve an accuracy of 61 percent [7]. Subsequently, deep learning networks have been applied to this data. In most cases, these deep learning approaches consist of convolutional neural networks (CNN) with the MFC coefficients or spectrograms as the input to the deep CNN. These approaches have resulted in performance of around 84% [4]. An LSTM approach with spectrogram time slices resulted in 79% accuracy and time-domain and frequency-domain features coupled with an ensemble learning approach (AdaBoost) resulted in 82% accuracy on a test set [2][3]. Recently, a sparse representation machine learning approach achieved approximately 89% accuracy [6].

The only parameters to specify in a wavelet time scattering framework are the duration of the time invariance, the number of wavelet filter banks, and the number of wavelets per octave. For most applications, cascading the data through two wavelet filter banks is sufficient. In this example, we use the default scattering framework which uses two wavelet filter banks. The first filter bank has 8 wavelets per octave and the second filter bank has 1 wavelet per octave. For this example, set the invariant scale to be 0.5 seconds, which corresponds to slightly more than 11,000 samples for the given sampling rate. Create the wavelet time scattering decomposition framework.

sf = waveletScattering('SignalLength',2^19,'SamplingFrequency',22050,... 'InvarianceScale',0.5);

To understand the role of the invariance scale, obtain and plot the scaling filter in time along with the real and imaginary parts of the coarsest-scale wavelet from the first filter bank. Note that the time-support of the scaling filter is essentially 0.5 seconds as designed. Further, the time support of the coarsest-scale wavelet does not exceed the invariant scale of the wavelet scattering decomposition.

[fb,f,filterparams] = filterbank(sf); phi = ifftshift(ifft(fb{1}.phift)); psiL1 = ifftshift(ifft(fb{2}.psift(:,end))); dt = 1/22050; time = -2^18*dt:dt:2^18*dt-dt; scalplt = plot(time,phi,'linewidth',1.5); hold on grid on ylimits = [-3e-4 3e-4]; ylim(ylimits); plot([-0.25 -0.25],ylimits,'k--'); plot([0.25 0.25],ylimits,'k--'); xlim([-0.6 0.6]); xlabel('Seconds'); ylabel('Amplitude'); wavplt = plot(time,[real(psiL1) imag(psiL1)]); legend([scalplt wavplt(1) wavplt(2)],{'Scaling Function','Wavelet-Real Part','Wavelet-Imaginary Part'}); title({'Scaling Function';'Coarsest-Scale Wavelet First Filter Bank'}) hold off

The audio datastore enables you to manage collections of audio data files. For machine or deep learning, the audio datastore not only manages the flow of audio data from files and folders, the audio datastore also manages the association of labels with the data and provides the ability to randomly partition your data into different sets for training, validation, and testing. In this example, use the audio datastore to manage the GTZAN music genre collection. Recall each subfolder of the collection is named for the genre it represents. Set the `'IncludeSubFolders'`

property to `true`

to instruct the audio datastore to use subfolders and set the `'LabelSource'`

property to `'foldernames'`

to create data labels based on the subfolder names. This example assumes the top-level directory is inside your MATLAB `tempdir`

directory and is called 'genres'. Ensure that `location`

is the correct path to the top-level data folder on your machine. The top-level data folder on your machine should contain ten subfolders each named for the ten genres and must only contain audio files corresponding to those genres.

location = fullfile(tempdir,'genres'); ads = audioDatastore(location,'IncludeSubFolders',true,... 'LabelSource','foldernames');

Run the following to obtain a count of the musical genres in the data set.

countEachLabel(ads)

ans = 10×2 table Label Count _________ _____ blues 100 classical 100 country 100 disco 100 hiphop 100 jazz 100 metal 100 pop 100 reggae 100 rock 100

As previously stated, there are 10 genres with 100 files each.

Create training and test sets to develop and test our classifier. We use 80% of the data for training and hold out the remaining 20% for testing. The `shuffle`

function of the audio datastore randomly shuffles the data. Do this prior to splitting the data by label to randomize the data. In this example, we set the random number generator seed for reproducibility. Use the audio datastore `splitEachLabel`

function to perform the 80-20 split. `splitEachLabel`

ensures that all classes are equally represented.

rng(100); ads = shuffle(ads); [adsTrain,adsTest] = splitEachLabel(ads,0.8); countEachLabel(adsTrain) countEachLabel(adsTest)

ans = 10×2 table Label Count _________ _____ blues 80 classical 80 country 80 disco 80 hiphop 80 jazz 80 metal 80 pop 80 reggae 80 rock 80 ans = 10×2 table Label Count _________ _____ blues 20 classical 20 country 20 disco 20 hiphop 20 jazz 20 metal 20 pop 20 reggae 20 rock 20

You see that there are 800 records in the training data as expected and 200 records in the test data. Additionally, there are 80 examples of each genre in the training set and 20 examples of each genre in the test set.

`audioDatastore`

works with MATLAB tall arrays. Create tall arrays for both the training and test sets. Depending on your system, the number of workers in the parallel pool MATLAB creates may be different.

Ttrain = tall(adsTrain); Ttest = tall(adsTest);

Starting parallel pool (parpool) using the 'local' profile ... Connected to the parallel pool (number of workers: 6).

To obtain the scattering features, define a helper function, `helperscatfeatures`

, that obtains the natural logarithm of the scattering features for 2^19 samples of each audio file and subsamples the number of scattering windows by 8. The source code for `helperscatfeatures`

is listed in the appendix. We will compute the wavelet scattering features for both the training and test data.

scatteringTrain = cellfun(@(x)helperscatfeatures(x,sf),Ttrain,'UniformOutput',false); scatteringTest = cellfun(@(x)helperscatfeatures(x,sf),Ttest,'UniformOutput',false);

Compute the scattering features on the training data and bundle all the features together in a matrix. This process takes several minutes.

TrainFeatures = gather(scatteringTrain); TrainFeatures = cell2mat(TrainFeatures);

Evaluating tall expression using the Parallel Pool 'local': - Pass 1 of 1: Completed in 3 min 40 sec Evaluation completed in 3 min 40 sec

Repeat this process for the test data.

TestFeatures = gather(scatteringTest); TestFeatures = cell2mat(TestFeatures);

Evaluating tall expression using the Parallel Pool 'local': - Pass 1 of 1: Completed in 56 sec Evaluation completed in 56 sec

Each row of `TrainFeatures`

and `TestFeatures`

is one scattering time window across the 341 paths in the scattering transform of each audio signal. For each music sample, we have 32 such time windows. Accordingly, the feature matrix for the training data is 25600-by-341. The number of rows is equal to the number of training examples (800) multiplied by the number of scattering windows per example (32). Similarly, the scattering feature matrix for the test data is 6400-by-341. There are 200 test examples and 32 windows per example. Create a genre label for each of the 32 windows in the wavelet scattering feature matrix for the training data.

numTimeWindows = 32; trainLabels = adsTrain.Labels; numTrainSignals = numel(trainLabels); trainLabels = repmat(trainLabels,1,numTimeWindows); trainLabels = reshape(trainLabels',numTrainSignals*numTimeWindows,1);

Repeat the process for the test data.

testLabels = adsTest.Labels; numTestSignals = numel(testLabels); testLabels = repmat(testLabels,1,numTimeWindows); testLabels = reshape(testLabels',numTestSignals*numTimeWindows,1);

In this example, use a multi-class support vector machine (SVM) classifier with a cubic polynomial kernel. Fit the SVM to the training data.

template = templateSVM(... 'KernelFunction', 'polynomial', ... 'PolynomialOrder', 3, ... 'KernelScale', 'auto', ... 'BoxConstraint', 1, ... 'Standardize', true); Classes = {'blues','classical','country','disco','hiphop','jazz',... 'metal','pop','reggae','rock'}; classificationSVM = fitcecoc(... TrainFeatures, ... trainLabels, ... 'Learners', template, ... 'Coding', 'onevsone','ClassNames',categorical(Classes));

Use the SVM model fit to the scattering transforms of the training data to predict the music genres for the test data. Recall there are 32 time windows for each signal in the scattering transform. Use a simple majority vote to predict the genre. The helper function `helperMajorityVote`

obtains the mode of the genre labels over all 32 scattering windows. If there is no unique mode, `helperMajorityVote`

returns a classification error indicated by `'NoUniqueMode'`

. This results in an extra column in the confusion matrix. The source code for `helperMajorityVote`

is listed in the appendix.

predLabels = predict(classificationSVM,TestFeatures); [TestVotes,TestCounts] = helperMajorityVote(predLabels,adsTest.Labels,categorical(Classes)); testAccuracy = sum(eq(TestVotes,adsTest.Labels))/numTestSignals*100;

The test accuracy, `testAccuracy`

, is 88 percent. This accuracy is comparable with the state of the art of the GTZAN dataset.

Display the confusion matrix to inspect the genre-by-genre accuracy rates. Recall there are 20 examples in each class.

confusionchart(TestVotes,adsTest.Labels)

The diagonal of the confusion matrix plot shows that the classification accuracies for the individual genres is quite good in general. Extract these genre accuracies and plot separately.

cm = confusionmat(TestVotes,adsTest.Labels); cm(:,end) = []; genreAccuracy = diag(cm)./20*100; figure; bar(genreAccuracy) set(gca,'XTickLabels',Classes); xtickangle(gca,30); title('Percentage Correct by Genre - Test Set');

This example demonstrated the use of wavelet time scattering and the audio datastore in music genre classification. In this example, wavelet time scattering achieved an classification accuracy comparable to state of the art performance for the GTZAN dataset. As opposed to other approaches requiring the extraction of a number of time-domain and frequency-domain features, wavelet scattering only required the specification of a single parameter, the scale of the time invariant. The audio datastore enabled us to efficiently manage the transfer of a large dataset from disk into MATLAB and permitted us to randomize the data and accurately retain genre membership of the randomized data through the classification workflow.

Anden, J. and Mallat, S. 2014. Deep scattering spectrum. IEEE Transactions on Signal Processing, Vol. 62, 16, pp. 4114-4128.

Bergstra, J., Casagrande, N., Erhan, D., Eck, D., and Kegl, B. Aggregate features and AdaBoost for music classification. Machine Learning, Vol. 65, Issue 2-3, pp. 473-484.

Irvin, J., Chartock, E., and Hollander, N. 2016. Recurrent neural networks with attention for genre classification. https://www.semanticscholar.org/paper/Recurrent-Neural-Networks-with-Attention-for-Genre-Irvin/6da301817851f19107447e4c72e682e3f183ae8a

Li, T., Chan, A.B., and Chun, A. 2010. Automatic musical pattern feature extraction using convolutional neural network. International Conference Data Mining and Applications.

Mallat. S. 2012. Group invariant scattering. Communications on Pure and Applied Mathematics, Vol. 65, 10, pp. 1331-1398.

Panagakis, Y., Kotropoulos, C.L., and Arce, G.R. 2014. Music genre classification via joint sparse low-rank representation of audio features. IEEE Transactions on Audio, Speech, and Language Processing, 22, 12, pp. 1905-1917.

Tzanetakis, G. and Cook, P. 2002. Music genre classification of audio signals. IEEE Transactions on Speech and Audio Processing, Vol. 10, No. 5, pp. 293-302.

*GTZAN Genre Collection*.`http://marsyas.info/downloads/datasets.html`

**helperMajorityVote** -- This function returns the mode of the class labels predicted over a number of feature vectors. In wavelet time scattering, we obtain a class label for each time window. If no unique mode is found a label of 'NoUniqueMode' is returned to denote a classification error.

function [ClassVotes,ClassCounts] = helperMajorityVote(predLabels,origLabels,classes) % This function is in support of wavelet scattering examples only. It may % change or be removed in a future release. % Make categorical arrays if the labels are not already categorical predLabels = categorical(predLabels); origLabels = categorical(origLabels); % Expects both predLabels and origLabels to be categorical vectors Npred = numel(predLabels); Norig = numel(origLabels); Nwin = Npred/Norig; predLabels = reshape(predLabels,Nwin,Norig); ClassCounts = countcats(predLabels); [mxcount,idx] = max(ClassCounts); ClassVotes = classes(idx); % Check for any ties in the maximum values and ensure they are marked as % error if the mode occurs more than once modecnt = modecount(ClassCounts,mxcount); ClassVotes(modecnt>1) = categorical({'NoUniqueMode'}); ClassVotes = ClassVotes(:); %------------------------------------------------------------------------- function modecnt = modecount(ClassCounts,mxcount) modecnt = Inf(size(ClassCounts,2),1); for nc = 1:size(ClassCounts,2) modecnt(nc) = histc(ClassCounts(:,nc),mxcount(nc)); end end end

**helperscatfeatures** - This function returns the wavelet time scattering feature matrix for a given input signal. In this case, we use the natural logarithm of the wavelet scattering coefficients. The scattering feature matrix is computed on 2^19 samples of a signal. The scattering features are subsampled by a factor of 8.

function features = helperscatfeatures(x,sf) % This function is in support of wavelet scattering examples only. It may % change or be removed in a future release. features = featureMatrix(sf,x(1:2^19),'Transform','log'); features = features(:,1:8:end)'; end