Isolated Digit Recognizer using GMM’s ECE5526 FINAL PROJECT SPRING 2011 JIM BRYAN

Isolated Digit Recognizer using GMMs ECE5526 FINAL PROJECT SPRING 2011 JIM BRYAN

Abstract Provide an in depth look at how GMMs can be used for word recognition based on Matlabs statistical toolbox. The isolated digit recognizer is based on a voice activity detector using energy thresholding and zero crossing detection. Moveover, the recognizer uses MFCCs as the basis for acoustic speech representation. These are standard voice processing techniques which it is assumed the reader is familiar with. The focus of this presentation is on the details the GMM implementation in Matlab, with the idea that a good understanding of the Matlab approach will yield insight to other system implementations such as Sphinx and HTK. Word recognition is comprised of two components, Model training and Model testing. The statistical toolbox functionGmmdistribution.fit is used for training The statistical toolbox Postpriori is used for testing The purpose of this effort is to train and run the recognizer, and to understand the basic functionality of functionGmmdistribution.fit and Postpriori funcion calls.

Introduction Based on MATLAB Digest - January 2010 Developing an Isolated Word Recognition System in MATLAB By Daryl NingDaryl Ning Describe the Matlab GUI base recognizer application Provide introductory material on GMMs using a simple 2 Mixture example with 2 models Discuss in detail the algorithms used to determine the best model match Show examples of Matlabs statistical toolbox representation of GMMs Run the simulation Discuss simulaton results and show possible improvements Summary Conclusions Areas for further study

Isolated digit recognizer overview Uses 8 GMMs per digit to train and recognize an individual users voice Matlab GUI based digit recognizer uses the following toolboxes Signal Processing toolbox provides a filtering and signal processing functions Statistics toolbox is used to implement a GMM Expectation Maximization algorithm to build the GMMs and to compute the Mahalnobis distance during recognition Data acquisition toolbox is used to stream the microphone input to Matlab for continous recognition Single digit recognizer implemented using dictionary of digits 0 9 Training is done with 30 second captures of repeated utterance of the given digit using the wavread function in Matlab Data is input continuously to Matlab via the data acquisition toolbox while the GUI recognizer is running The recognized digit is displayed on the GUI

Overview Continued Uses laptops internal microphone Sample rate is 8ksps Uses 20msec frames with a 10 msec overlap with a frame size of 160 samples per frame Uses a simple voice activity detector based on energy threshold and zero crossings per second for both training and the recognizer Voice activity energy and zero crossing thresholds are programmable and must be the same for training and recognition No model for silence or missed digit, so the recognizer displays the closest digit

GMM training and recognizer Matlab function calls The recognizer compute the posterior probabilities using the Statistics Toolbox function posterior Posterior accepts a gmm object/model as its input, along with an input data set, and returns a log-likelihood number that represents the data set match to the model The smallest log-likelihood has the highest posterior probability The recognizer computes the probability of the current word to each model in the dictionary. The model that has the lowest posterior probability is the recognized digit. A gmm object is created during training for each dictionary entry, in this case digits 0-9, using the function call gmdistribution.fit.

Example using 2 GMMs with 2 mixtures

Posterior Posterior extracts gmdistribution object parameters necessary to call Wdensity Wdensity performs the actual log-likely-hood calculation for the GMM, given the data set Wdensity returns two arrays log_lh is an array of size length(data)x order(GMM) mahalaD is an array of size length(data)x order(GMM), this is not the actual Mahalnoblis distance mahalaD = (x -) -1 (x -) T Estep calculates the loglikelihood based on the log_lh array and returns ll which is the loglikelihood of data x given the model

Wdensity function description Example funtioncall [log_lh,mahalaD]=wdensity(X, mu, Sigma, p, sharedCov, CovType) Where X is input data Mu is an array of means with(j,:) corresponding to jth mean vector Sigma is an array of arrays with (:,:,j) corresponding to the jth sigma in the model P are the mixture weights sharedCov indicates the covariance matrices may be common to all mixtures CovType may be either diagonal or full

Wdensity log-likelihood calculation,

Wdensity log-likelihood implementation details L = sqrt(Sigma(:,:,j)); % a vector xRinv = bsxfun(@times,Xcentered, (1./ L)); mahalaD(:,j) = sum(xRinv.^2, 2); log_lh(:,j) = -0.5 * mahalaD(:,j) +... (-0.5 *logDetSigma + log_prior(j)) - *log(2*pi)/2; Xcentered = bsxfun(@minus, X, mu(j,:));

estep [ll, post, logpdf]=estep(log_lh) Find the max of each row of log_lh matrix This represents the closest distance to the jth mixture for this data point. Convert log_ih distance probabilities by using post = exp(bsxfun(@minus, log_lh, maxll)), there will always be a 1 in the column of the maximum value, therefore this number is always >=1 Sum across the rows to normalize the relative probabilities density = sum(post,2); normalize posteriors post = bsxfun(@rdivide, post, density) Calculate the logpdf = log(density) + maxll; ll = sum(logpdf)

Estep example showing log_lh inputsfor two Gaussian Mixtures and the Maximum value of the log_lh P11 data from model log_lh = -18.6236 -3.0708 -36.2569 -3.0821 -24.1669 -2.2514 -33.8821 -3.2357 -18.4447 -3.2818 -5.8488 -4.2339 -18.4529 -2.5661 -14.7058 -3.5421 -2.7563 -19.3866 -3.0744 -21.2154 -2.4251 -14.8179 -4.1699 -12.7317 -2.5825 -16.8520 -4.4938 -8.5847 -3.7883 -13.7861 -2.8691 -7.2573 maxll = -3.0708 -3.0821 -2.2514 -3.2357 -3.2818 -4.2339 -2.5661 -3.5421 -2.7563 -3.0744 -2.4251 -4.1699 -2.5825 -4.4938 -3.7883 -2.8691

Estep example showing Post and density, density is used to normalize post P11 data from model post = exp(bsxfun(@minus, log_lh, maxll)); 1.0000 0.0000 0.0000 1.0000 1.0000 0.0000 1.0000 0.0001 0.0832 1.0000 1.0000 0.0109 1.0000 0.0008 0.0000 1.0000 0.0003 1.0000 0.0001 1.0000 0.0000 1.0000 density = sum(post,2) 1.0000 1.0001 1.0832 1.0109 1.0008 1.0000 1.0003 1.0001 1.0000

Estep example showing post after normalization and logpdf P11 data from model post = bsxfun(@rdivide, post, density) 1.0000 0.0000 0.0000 1.0000 1.0000 0.0000 0.9999 0.0001 0.0768 0.9232 0.9892 0.0108 0.9992 0.0008 0.0000 1.0000 0.0003 0.9997 0.0001 0.9999 0.0000 1.0000 logpdf = log(density) + maxll; ll = sum(logpdf) =-53.7464 -3.6490 -4.6937 -2.3765 -3.3219 -3.1317 -4.4911 -4.0361 -3.8076 -2.7171 -2.5739 -2.3359 -2.6023 -2.1502 -5.5963 -2.2777 -3.9857

Estep example showing log_lh inputs for two Gaussian Mixtures and the Maximum value of the log_lh P12 Data not from Model log_lh = -6.2916 -6.2281 -6.1189 -7.3603 -12.5238 -2.5414 -7.3336 -24.5710 -7.0679 -14.3058 -5.7049 -7.7255 -7.8564 -23.6082 -6.8128 -4.4655 -27.4139 -19.2832 -20.1139 -14.0730 -27.0048 -11.4791 -17.2614 -8.2714 -33.8912 -15.5351 -26.0666 -9.9934 -20.4353 -9.9218 -15.9387 -13.2732 maxll = -6.2281 -6.1189 -2.5414 -7.3336 -7.0679 -5.7049 -7.8564 -4.4655 -19.2832 -14.0730 -11.4791 -8.2714 -15.5351 -9.9934 -9.9218 -13.2732

Estep example showing Post and density, density is used to normalize post Data not from model P12 post = exp(bsxfun(@minus, log_lh, maxll)); 0.9384 1.0000 1.0000 0.2890 0.0000 1.0000 1.0000 0.0000 1.0000 0.0007 1.0000 0.1326 1.0000 0.0000 0.0956 1.0000 0.0003 1.0000 0.0024 1.0000 0.0000 1.0000 0.0001 1.0000 0.0000 1.0000 0.0696 1.0000 density = sum(post,2) 1.9384 1.2890 1.0000 1.0007 1.1326 1.0000 1.0956 1.0003 1.0024 1.0000 1.0001 1.0000 1.0696

Estep example showing post after normalization and logpdf P12 data not from model post = bsxfun(@rdivide, post, density) 0.4841 0.5159 0.7758 0.2242 0.0000 1.0000 1.0000 0.0000 0.9993 0.0007 0.8829 0.1171 1.0000 0.0000 0.0873 0.9127 0.0003 0.9997 0.0024 0.9976 0.0000 1.0000 0.0001 0.9999 0.0000 1.0000 0.0650 0.9350 logpdf = log(density) + maxll; ll = sum(logpdf) = -147.9445 -5.5662 -5.8650 -2.5414 -7.3336 -7.0671 -5.5804 -7.8564 -4.3742 -19.2829 -14.0706 -11.4791 -8.2713 -15.5351 -9.9934 -9.9218 -13.2060

Log-likelihood for 2 mixture example P =Nlogl = -ll 55.3416 109.3820 184.7868 42.8043 The diagonal term are the case where the data came from the model The off diagonal terms represent when the data came from the other model

Gaussian Models in Matlab

Model for one

Gaussian Mixture Distribution Structure one

8 Gaussian model means 8x39 one

Diagonal Covariance Matrix

Training the GMMs Before recording can begin it is necessary to set the laptops internal microphone Training involves finding a quiet environment and recording 30 seconds of utterance for each digit These are captured using Matlabs wavrecord y = wavrecord(30*8000,8000); There is a utility supplied that allows viewing the Voice Activity detection algorithm in order to determine correct captures of the training data speechdetect(y);

Trainmodels overview Generates Frames of speech base on 160 samples/frame with an 80 sample overlap Uses the same energy detect and zero crossing thresholds as the recognizer Determines portions of voiced speech based on these thresholds as well as a minimum of 250msec duration for each word A minimum of 100msec is required between each word Frames are marked as VA, voice active, and stored in a buffer call ALLdata. ALLdata is arranged so that the frames are in columns, the dimensions are 160xnumFRAMES Once all the words are captured, MFCC is called which is passed the ALLdata buffer for Mel cepstral coefficient processing MFCC returns MFCC vectors that are 39 coefficients per frame Gmmdistribution.fit is passed the MFCC vectors which runs an EM algorithm on the MFCC vectors to generate an 8 Mixture GMM for each digit

MFCC credits Derived from the original function 'mfcc.m' in the Auditory Toolbox % written by: % % Malcolm Slaney % Interval Research Corporation % [email protected] % http://cobweb.ecn.purdue.edu/~malcolm/interval/1998-010/ % % Also uses the 'deltacoeff.m' function written by: % % Olutope Foluso Omogbenigun % London Metropolitan University % http://www.mathworks.com/matlabcentral/fileexchange/19298

MFCC overview Pre-filter the data using a pre-emphasis filter preEmphasized = filter([1 -.97], 1, input); Window the data with a Hamming window preEmphasized = preEmphasized.*repmat(hamWindow(:),1,frames); fftMag = abs(fft(preEmphasized,fftSize)); earMag = log10(mfccFilterWeights * fftMag); ceps = mfccDCTMatrix * earMag; meanceps = mean(ceps,2); ceps = ceps - repmat(meanceps,1,frames); d = (deltacoeff(ceps')).*0.6; %Computes delta-mfcc d1 = (deltacoeff(d)).*0.4; %as above for delta-delta-mfcc ceps = [ceps; d'; d1']; %concatenates all together Return vector of 13 cep, 13 diff and 13 diff diff coefficients

Sound Settings for Microphone on Windows 7 laptop

Voice Activity Detector Overview Voice activity detection based on energy detection and zero crossing rate std_zxings: is the zero crossing threshold, default =.5 std_energy: is the energy detect threshold, default =.5 Energy and zero crossings thresholds are determined during the first 500msec of training to determine the background silence energy and zero crossing rate The same threshold settings must be used for all digit recordings Once a good recording has been made, save it to the hard drive using; wavwrite(y,8000,one.wav); Repeat for all the digits Run transcript and this will train the GMMs

Authors Ideal Voice Activity detector

Voice Detect using default thresholds digit = one

Voice Detect using default thresholds 1,1 digit = one

Voice Detect using default thresholds 1.5,1.5 digit = one

Transcript reads each model and calls trainmodels y = wavread('one.wav'); trainmodels(y,'one'); y = wavread('two.wav'); trainmodels(y,'two'); y = wavread('three.wav'); trainmodels(y,'three'); y = wavread('four.wav'); trainmodels(y,'four'); y = wavread('five.wav'); trainmodels(y,'five'); y = wavread('six.wav'); trainmodels(y,'six'); y = wavread('seven.wav'); trainmodels(y,'seven'); y = wavread('eight.wav'); trainmodels(y,'eight'); y = wavread('nine.wav'); trainmodels(y,'nine'); y = wavread('zero.wav'); trainmodels(y,'zero');

GMM dimensions for typical utterance Assume average digit length is 300 mSec Fs = 8000Hz 1/Fs = 125sec 160 samples/Fs = 20msec Since overlap and add using 50 % Hamming widow, 1 Frame occurs every 10msec Average number of frames per word 300/10 = 30 MFCC takes in 30x160 samples and produces 30x39 MFCC vectors on average Average size of log_lh vector per word for 8 Gaussian mixtures = 30x8 Log-likelihood based on average 30x8 matrix

Voice Activity detect filter implemented as a 128 tap FIR filter based on a Chebyschev window with 40 dB sidelobe attenation

Voice detector using 125-750 Hz 128 tap Chebyshev bandpass filter with 40 dB side lobe suppression and 20mse pre oneshot with 40msec post oneshot digit = one

Training Vector for digit one after modified VA detection

Scoring Difficult to score based on the real time recognizer. Recognizer fires on ambient noise Recognizer is slow as it has to perform GMM calculation for all dictionary entries Recorded test set of test set, counting from 1-9,0 produced 70% accuracy two and seven and eight did not correctly classify Had to lower zerocrossing threshold for test to collect all the utterances Accuracy might be due to insufficient training data Could have bad models for some of the classes Hand scoring difficult because must correctly label each utterance for the classifier. Seven had a null portion in the middle Lap top computers fan kicked on during training, this caused ambient noise during training so data set was not perfect

Test Set counting 1-9,0 and repeat frame based with silence removed

Summary An 8 mixture GMMs for speech recognition were demonstrated. Using only a small training set and an laptop microphone, digit recognition was demonstrated using only 8000Hz sample rate Care and feeding of the GMMs is very important for successful implementation. Garbage in, garbage out is especially true for speech recognition Background noise is a very big problem in accurate speech recognition. Adaptive noise cancellation using a second microphone for just the background noise should improve accuracy The voice activity detector is a critical component of the recognizer Scoring is also a difficult problem as the acoustic data must be synchronized with the dictionary to provide accurate results Marking the speech pattern and word isolation is not without difficulties as pauses between syllables occur during a single utterance

Conclusion GMMs are very powerful models for speech recognition. Scoring the models is difficult. The EM algorithm will produce different models based on the random seeding of the starting conditions. Simple utterances of ~15 repetitions is not sufficient for good GMM accuracy The voice activity detector plays a significant part in the training and testing of the data A new voice activity detector did not magically produce 100 percent scoring accuracy with a recorded test wav file Noise cancellation techniques and sophisticated voice detection algorithms are necessary for good performance as well as model optimization

Areas for further investigation Automate the scoring process Improve the Voice activity detector in the real time recognizer Add a second microphone for adaptive noise cancellation Convert GMMs to combination GMMs and HMMs so dictionary search isnt so computationally intensive Modify the number of mixtures of the GMMs with HMM phonetic implementation HMMs will allow for continuous digit recognition

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Isolated Digit Recognizer using GMM’s ECE5526 FINAL PROJECT SPRING 2011 JIM BRYAN