The aim of this paper is to evaluate the application of the wavelet packet transform (WP) and support vector machines (SVM) to transient evoked otoacoustic emissions (TEOAE) in order to achieve a detection of frequency-specific hearing loss. We introduce a system to determine detection rates between groups of persons with normal hearing, high frequency hearing loss, and pantonal hearing loss. The validity and use of our approach is verified on a different patient group

Dietl, H.

Weiss, S.

English

University of Strathclyde Institutional Repository

Strathprints Institutional RepositoryDietl, H. and Weiss, S. (2004) Detection of cochlear hearing loss applying wavelet packets andsupport vector machines. In: 38th Asilomar Conference on Signals, Systems and Computers,2004-11-07 - 2004-11-10, Pacific Grove, California.Strathprints is designed to allow users to access the research output of the University of Strathclyde.Copyright c© and Moral Rights for the papers on this site are retained by the individual authorsand/or other copyright owners. You may not engage in further distribution of the material for anyprofitmaking activities or any commercial gain. You may freely distribute both the url (http://strathprints.strath.ac.uk/) and the content of this paper for research or study, educational, ornot-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to Strathprints administrator:mailto:strathprints@strath.ac.ukhttp://strathprints.strath.ac.uk/Detection of Cochlear Hearing Loss Applying Wavelet Packets andSupport Vector MachinesHubert Dietl1, Stephan Weiss11 Dept. Electronics & Computer Science, University of Southampton, UKhwd,s.weiss@ecs.soton.ac.ukAbstract. The aim of this paper is to evaluate the ap-plication of the wavelet packet transform (WP) and sup-port vector machines (SVM) to transient evoked otoacous-tic emissions (TEOAE) in order to achieve a detection offrequency-speciﬁc hearing loss. We introduce a system todetermine detection rates between groups of persons withnormal hearing, high frequency hearing loss, and pantonalhearing loss. The validity and use of our approach is veriﬁedon a diﬀerent patient group.1. INTRODUCTIONTransient evoked otoacoustic emissions (TEOAE)are used as a clinical standard procedure to detectcochlear hearing loss [1], and measurement equip-ment [2] is widely available in hospitals. The analysis ofTEOAE is usually performed by an human expert. Re-cently, signal processing detection systems aiming at anautomated detection of cochlear hearing loss have beenmotivated to assist or replace the human expert. Thesestudies aiming at detection of TEOAE apply discretewavelet transform and neural networks [3],[4]. Here, weintroduce a system applying a WP for feature extrac-tion, a signal-to-noise (SNR)-like criterion for featureselection and support vector machines for classiﬁcation.Fig. 1 gives an overview of our system. For the fea-ture extraction, a WP is applied. To select the fea-tures of the data, an SNR-like criterion is applied tothe transformed data resulting in a reduction of co-eﬃcients to be used for classiﬁcation and aiming ata reduction of noisy coeﬃcients. This approach willbe outlined in more detail in Sec. 3, following a de-TF coefficients for trainingTF coefficients for testTraining data Feature selection:Selection of coefficients Classification: Trained SVM classifierDetection rates for test dataTest dataFeature extraction:Support vector machinesby SNR−like criterionWavelet Packet transformFig. 1. Overview of the detection system for cochlear hearing loss.scription of TEOAE data in Sec. 2. The classiﬁcationof the data is conducted by a support vector machine(SVM) classiﬁer explained in Sec. 4 more explicitly. InSec. 5, based on the training data, a support vectorclassiﬁcation network is found and applied to the testdata group yielding detection rates which describe theperformance of the system and can be compared withother studies. Finally, Sec. 6 draws the conclusions.2. TEOAE AND WAVELET PACKETTRANSFORMThe patient data consists of two sets measured atthe Universities of Homburg and Heidelberg, with eachconsisting of an evaluation of more than 200 ears. TheHomburg data represents the training data, the Heidel-berg data is addressed as test data. Both sets are classi-ﬁed to one of the three groups of normal hearing (NH),pantonal (PT), or high frequency (HF) hearing loss, asdeﬁned in Fig. 2. For each ear, the TEOAE equipmentmeasured a total of 520 responses, each for a period of20.48 ms, and calculated two partial averages (labelledA and B) alternatingly over 260 responses each.Due to the transient nature of the signals, previ-ous work on the qualitative analysis of TEOAE hasfocused on time-frequency (TF) methods, such as ﬁl-ter banks [5], matching pursuit [6], or discrete wavelettransforms (DWT) [3], whereby a quantitative studyw.r.t. the achievable distinction of frequency-speciﬁchearing loss has been performed in [3], based on theDWT.The wavelet packet transform (WP) can be seen as amore general transform compared to the DWT. There-fore, we brieﬂy describe the DWT here. The DWT is15750-7803-8622-1/04/$20.00 ©2004 IEEE0.125 2k 104kf/kHz/dBHL2030                                                                                                                                                                                                    0.125 2k 104kf/ kHz/dBHL2030                                                             ~~      ~~      ~~      ~~      ~~      ~~                                                0.125 2k 104kf/ kHz/dBHL2030Fig. 2. Characterisation of hearing loss for (left) normal hearing, (middle) pantonal HL, and (right) highfrequency HL.a ﬁxed transform based on a “mother wavelet” fromwhich the transformation coeﬃcients are derived byscaling, translation and sampling. Here, we have cho-sen the Mallat wavelet for which good results have beenreported in similar studies [3]. The transform coeﬃ-cients approximately cover TF tiles as illustrated inFig. 3 a).The WP transform is an adaptive transformation sim-ilar to the DWT but with a ﬂexible partitioning of theTF plane. The advantage of this approach comparedto the DWT is that the entropy of the transformeddata shall be minimised through variable levels of de-composition such that the energy is concentrated inas few coeﬃcients as possible. That minimisation isachieved by the reduction of the concentration accord-ing to Shannon’s entropy [7]. Fig. 3 b) shows a sampleWP decomposition.Based on a parameterisation of the data by the WP,representing the feature extraction of the data, the ap-plication of an SNR-like criterion for the feature selec-tion is conducted which will be described next.3. FEATURE SELECTIONTo quantify and exploit diﬀerences in the TEOAEWP coeﬃcients of the three groups of hearing abil-ity within the Homburg data, a signal-to-noise-ratio(SNR) based criterion is invoked. First, the SNR is es-timated for each of the 512 parameters in the TF-planebased on the WPs of the two partial averages, WPA(n)and WPB(n), n = 1, . . . , 512. The SNR of the nth co-eﬃcient is (coarsely) estimated by comparing the sumand the diﬀerence obtained from the partial averagesA and B:SNR(n) = 20 log10|WPA(n) + WPB(n)||WPA(n)−WPB(n)|+ . (1)This SNR is calculated for all measurements, and foreach of the 512 WP coeﬃcients within each of the threehearing ability groups, the distribution is recorded.The SNR value of a WP coeﬃcient is used to evaluatethe separability of any two groups with diﬀerent hear-ing status. The separability can be assessed indepen-dent of the selection of a speciﬁc threshold by meansof a socalled receiver operating characteristic (ROC)curve. The area underneath the ROC is a measure forthe separability of both groups, and independent of thedeﬁnition of SNR-thresholds [8].As single WP coeﬃcients yield a poor separabilitybetween any two groups, we pick the coeﬃcient thatgives the best separable SNR according to (1) as astarting value and iteratively grow a coeﬃcient set G toimprove separability. Further coeﬃcients are added toG from the neighbourhood of surrounding coeﬃcients.Adjacency is deﬁned by edge and corner connections inthe TF plane. The iteration is stopped when the ROCdoes not further improve for the SNR of the coeﬃcientscontained in G.4. SVM CLASSIFICATIONIn the following, we brieﬂy explain SVM, [9],[10].We consider a three class classiﬁcation problem for theclasses deﬁned by the groups NH, HF and PT, startingwith an explanation for a two class classiﬁcation. Thetraining data originates from the Homburg data, whilethe test data comprises the Heidelberg measurements.The training data is described as a set of trainingvectors {pi}i=1 ... M with corresponding binary labelsSi = 1 for the one class, e.g. NH, and Si = −1 forthe second class, e.g. HF. The SVM conducts a clas-siﬁcation of a test vector t by assigning a label Sˆ bycalculatingSˆ = sign(f(t)) with f(t) =∑iαiSiK(t,pi) + b.(2)The αi are called weights and b is the bias, which areSVM parameters and adopted during training by max-1576Wavelet PacketsTimeDWTa)b)FrequencyLevel 1Level 3Level 4Level 2FrequencyLevel 1Level 3TimeLevel 2Level 3Level 4Fig. 3. TF tiling comparison between a) a DWTand b) a sample WP decomposition.imisingLD =∑iαi −12∑i,jαiαjSiSjK(pi,pj) (3)under the constraints0 ≤ αi ≤ C and∑iαiSi = 0 (4)with C being a positive constant which weighs the in-ﬂuence of training errors. K(·, ·) is called kernel ofthe SVM. If there is a solution for αi, a value for bis determined. Usually αi = 0 for the majority of iand thus the summation in (2) is limited to a sub-net of the pi, which therefore is called the set of sup-port vectors. There are several commonly used kernelsfor SVM, which give some ﬂexibility for the underly-ing application. Many implementations of kernels canbe found in literature, whereby two popular ones areGaussian and polynomial kernels. If K(·, ·) is positivedeﬁnite, (3) and (4) is a convex quadratic optimisationproblem, which converges towards the global optimumassuringly. This optimisation can be quite demandingin terms of computation time for real-world problems,and therefore, sophisticated algorithms like sequentialminimal optimisation (SMO) [9] are used for the solu-tion.To ﬁnd a signiﬁcant value for the training error C,a leave-one-out (l-o-o) estimation of the error rate isapplied as follows: From the training samples, removethe ﬁrst example. Train the SVM on the remainingsamples. Then test the removed example. If the ex-ample is classiﬁed incorrectly, it is said to produce aleave-one-out error. In [9], an approach to estimatethe maximum l-o-o error is shown avoiding trainingthe SVM more than once, which is also used for ourstudy. By changing the value for C stepwise, the mini-mum for the l-o-o error is found determining the SVMclassiﬁcation network. For our application, a Gaussiankernel was used.So far, we have described the SVM for only twoclasses. As we aim at distinguishing 3, we need todeﬁne a multi-class method. In [11] a decision directedacyclic graph (DAG) for multi-class SVM is introduced.It is based on an 1-vs-1 classiﬁcation where the train-ing is conducted for all possible combinations of theclasses. Based on a trained SVM classiﬁer for each pos-sible class combination, a binary acyclic graph is usedfor testing. Fig. 4 shows the decision DAGSVM forour application to the the three classes with diﬀerenthearing ability.NH vs HFNot NHNH vs PTHF vs PTNot PTHF PTNHFig. 4. DAGSVM for TEOAE.5. RESULTS AND DISCUSSIONHaving described the detection methods and thedata used for our system, we present the results inthe following. Fig. 5 illustrates the average WP coeﬃ-cient energy for the training data showing the typicalTEOAE properties of high frequencies occurring earlyand low frequencies appearing late [6]. In Figure 6 theisolated coeﬃcients for each distinction case are shown.They were found by the search procedure based on theSNR criterion explained in Sec. 3 and appear to be rea-sonably located when compared to the average energiesin Fig. 5.Based on the coeﬃcient sets, a SVM classiﬁcation isconducted for each distinction case using the trainingdata. The test data is analysed by the determined clas-siﬁers according to the decision DAG in Fig. 4 yieldingthe detection rates in Tab. 1 for each class.The table shows that the HF can be detected moresigniﬁcantly than the NH group with the explained sys-tem. The PT group is the most diﬃcult to determine,just above half of the patients can be allocated cor-rectly. These results may not seem to be encouraging.However, when only considering the the case NH vs PT,89.9% of the NH group and 84.6% of the PT group are1577group detection ratefor test dataNH 68.1%HF 74.7%PT 56.4%Tab. 1. Detection rates yielded by DAGSVM.allocated correctly by the system which is well in therange of other studies.E.g in [12], a group of normal hearing is deﬁned byno hearing loss up to 30 dB and a hearing impairedgroup with a hearing loss over 30 dB. A separationmethod based on wavelet transforms, ensemble corre-lation, time window design and mean cross-correlationis introduced. The study concludes that by standardanalysis 90% of the normal hearing persons and 65%of the hearing impaired patients can be allocated cor-rectly. By applying the various methods, the value forthe hearing impaired group is increased by approxi-mately 17% to 83% in that study. Compared to ourstudy we achieve slightly better results when only con-sidering the case NH vs PT, which can be seen as equiv-alent to the case shown in [12]. One could also argue,that our methods lead to a better separation of hearingloss as our threshold for deﬁning the diﬀerence betweenNH and PT was 20 dB, and the worse the hearing lossgets, the weaker the TEOAE appear and therefore theeasier it should be to separate them. On the otherhand, we achieve the lowest value of 56% for the PTgroup, which shows that it is easier to separate whenclear TEOAE are present, which is more likely the casefor a threshold of hearing loss of 20 dB than for 30 dB.Recapitulating it can be said that our approach yieldsseparation results than can well compete with otherstudies so far.6. CONCLUSIONSWe have presented a WP analysis of TEOAE thataims at the detection of frequency speciﬁc hearing loss.We have motivated the use of TF methods, and pro-posed a method to optimise a set of distinctive WPcoeﬃcients. This maximisation represents the input toa SVM classiﬁer for the detection. We used two datasets for training and testing. The validity of the resultswas veriﬁed by a test group. Moreover, the obtainedresults proved to be competitive when they were com-pared to similar study which also aims at the detectionof TEOAE. Therefore, the results appear reasonablyrobust and encourage frequency speciﬁc hearing lossdetection via signal processing of TEOAE.7. ACKNOWLEDGEMENTSThe authors would like to acknowledge Prof. UlrichHoppe and Sebastian Hoth of the University of Erlan-gen, Germany, who kindly provided valuable expertiseand the data.REFERENCES[1] M.S. Robinette and T.J. Glattke, Otoacoustic Emis-sions: Clinical Applications, Thieme Medical Pub, 2.edition, 2001.[2] Otodynamics Ltd., Hatﬁeld, Herfortshire, UK, ILOOAE Instrument User Manual, 5a edition, October1997.[3] S. Weiss, U. Hoppe, M. Schabert, and U. Eysholdt,“Wavelet Analysis of Transient Evoked OtoacousticEmissions for Diﬀerential Diagnosis of Cochlear Hear-ing Loss,” in Asilomar Conference on Signals, Sys-tems, and Computers, Monterey, CA, November 2001.[4] G. Buller and M.E. Lutman, “Automatic classiﬁca-tion of transiently evoked otoacoustic emissions usingan artiﬁcial neural network,” British Journal of Audi-ology, vol. 32, pp. 235–247, 1998.[5] P. Ravazzani, G. Tognola, F. Grandori, and J. Ruoho-nen, “Two-Dimensional Filter to Facilitate Detectionof Transient-Evoked Otoacoustic Emissions,” IEEETransactions on Biomedical Engineering, vol. 45, pp.1089–1096, 1998.[6] K. J. Blinowska, P. J. Durka, A. Skierski, F. Grandori,and G. Tognola, “High Resolution Time-FrequencyAnalysis of Otoacoustic Emissions,” Technology andHealth Care, vol. 5, pp. 407–418, 1997.[7] A. Jensen and Anders la Cour Harbo, Ripples in Math-ematics, Springer-Verlag, Berlin, Heidelberg, NewYork, 2001.[8] J. A. Hanley and B. J. McNeil, “The Meaning and Useof the Area under a Receiver Operating Characteristic(ROC) Curve,” Radiology, vol. 143, pp. 26–36, 1982.[9] V.N. Vapnik, Statistical Learning Theory, CambridgeUniversity Press, New York: Wiley, 1998.[10] C. Bahlmann, B. Haasdonk, and H. Burkhardt, “On-line Handwriting Recognition with Support VectorMachines – A Kernel Approach,” in Proceedings of the8th Int. Workshop on Frontiers in Handwriting Recog-nition (IWFHR), pp. 49–54, 2002.[11] J. Platt, N. Cristianini, and J. Shawe-Taylor, “LargeMargin DAGs for Multiclass Classiﬁcation,” in Pro-ceedings of Advances in Neural Information ProcessingSystems, NIPS’99, MIT Press 2000, pp. 547–553.[12] A. Janusauskas, L. Sornmo, O. Svensson, and B. En-gdahl, “Detection of Transient-Evoked OtoacousticEmissions and the Design of Time Windows,” IEEETransactions on Biomedical Engineering, vol. 49, no.No.2, pp. 132–139, February 2002.1578average WP coefficient energy − normal hearing (Homburg)time / [ms]frequency / [Hz]0 2 4 6 8 10 12 14 16 18 2001000200030004000500060007000average WP coefficient energy − HF hearing loss (Homburg)time / [ms]frequency / [Hz]0 2 4 6 8 10 12 14 16 18 2001000200030004000500060007000average WP coefficient energy − pantonal hearing loss (Homburg)time / [ms]frequency / [Hz]0 2 4 6 8 10 12 14 16 18 2001000200030004000500060007000Fig. 5. Average WP coeﬃcient energy for the dif-ferent hearing ability groups for the training data.time / [ms]frequency / [Hz]WP mask: NH vs HF0 2 4 6 8 10 12 14 16 18 2001000200030004000500060007000time / [ms]frequency / [Hz]WP mask: NH vs PT0 2 4 6 8 10 12 14 16 18 2001000200030004000500060007000time / [ms]frequency / [Hz]WP mask: HF vs PT0 2 4 6 8 10 12 14 16 18 2001000200030004000500060007000Fig. 6. Selected feature coeﬃcients for the threedistinction cases.1579

1578average WP coefficient energy − normal hearing (Homburg) time / [ms] f r e q u e n c y /

Automatic classiﬁcation of transiently evoked otoacoustic emissions using an artiﬁcial neural network,”

average WP coefficient energy − normal hearing (Homburg) time / [ms] fre qu en cy /

High Resolution Time-Frequency Analysis

Jensen and Anders la Cour Harbo, Ripples in Mathematics,

Large Margin DAGs for Multiclass Classiﬁcation,” in

Online Handwriting Recognition with Support Vector Machines – A Kernel Approach,”

Otoacoustic Emissions: Clinical Applications,

Statistical Learning Theory,

The Meaning and Use of the Area under a Receiver Operating Characteristic (ROC)

Two-Dimensional Filter to Facilitate Detection of Transient-Evoked Otoacoustic Emissions,”

Wavelet Analysis of Transient Evoked Otoacoustic Emissions for Diﬀerential Diagnosis of Cochlear Hearing Loss,”

Detection of cochlear hearing loss applying wavelet packets and support vector machines

Name not available

Dietl, Hubert

Weiss, Stephan

Southampton (e-Prints Soton)

Detection of Cochlear Hearing Loss Applying Wavelet Packets andSupport Vector MachinesHubert Dietl1, Stephan Weiss11 Dept. Electronics & Computer Science, University of Southampton, UKhwd,s.weiss@ecs.soton.ac.ukAbstract. The aim of this paper is to evaluate the ap-plication of the wavelet packet transform (WP) and sup-port vector machines (SVM) to transient evoked otoacous-tic emissions (TEOAE) in order to achieve a detection offrequency-specic hearing loss. We introduce a system todetermine detection rates between groups of persons withnormal hearing, high frequency hearing loss, and pantonalhearing loss. The validity and use of our approach is veriedon a dierent patient group.1. INTRODUCTIONTransient evoked otoacoustic emissions (TEOAE)are used as a clinical standard procedure to detectcochlear hearing loss [1], and measurement equip-ment [2] is widely available in hospitals. The analysis ofTEOAE is usually performed by an human expert. Re-cently, signal processing detection systems aiming at anautomated detection of cochlear hearing loss have beenmotivated to assist or replace the human expert. Thesestudies aiming at detection of TEOAE apply discretewavelet transform and neural networks [3],[4]. Here, weintroduce a system applying a WP for feature extrac-tion, a signal-to-noise (SNR)-like criterion for featureselection and support vector machines for classication.Fig. 1 gives an overview of our system. For the fea-ture extraction, a WP is applied. To select the fea-tures of the data, an SNR-like criterion is applied tothe transformed data resulting in a reduction of co-ecients to be used for classication and aiming ata reduction of noisy coecients. This approach willbe outlined in more detail in Sec. 3, following a de-TF coefficients for trainingTF coefficients for testTraining data Feature selection:Selection of coefficients Classification: Trained SVM classifierDetection rates for test data Test dataFeature extraction:Support vector machines by SNR−like criterion Wavelet Packet transformFig. 1. Overview of the detection system for cochlear hearing loss.scription of TEOAE data in Sec. 2. The classicationof the data is conducted by a support vector machine(SVM) classier explained in Sec. 4 more explicitly. InSec. 5, based on the training data, a support vectorclassication network is found and applied to the testdata group yielding detection rates which describe theperformance of the system and can be compared withother studies. Finally, Sec. 6 draws the conclusions.2. TEOAE AND WAVELET PACKETTRANSFORMThe patient data consists of two sets measured atthe Universities of Homburg and Heidelberg, with eachconsisting of an evaluation of more than 200 ears. TheHomburg data represents the training data, the Heidel-berg data is addressed as test data. Both sets are classi-ed to one of the three groups of normal hearing (NH),pantonal (PT), or high frequency (HF) hearing loss, asdened in Fig. 2. For each ear, the TEOAE equipmentmeasured a total of 520 responses, each for a period of20.48 ms, and calculated two partial averages (labelledA and B) alternatingly over 260 responses each.Due to the transient nature of the signals, previ-ous work on the qualitative analysis of TEOAE hasfocused on time-frequency (TF) methods, such as l-ter banks [5], matching pursuit [6], or discrete wavelettransforms (DWT) [3], whereby a quantitative studyw.r.t. the achievable distinction of frequency-specichearing loss has been performed in [3], based on theDWT.The wavelet packet transform (WP) can be seen as amore general transform compared to the DWT. There-fore, we briey describe the DWT here. The DWT is0.125 2k 10 4kf/kHz/dBHL2030￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿0.125 2k 10 4kf/kHz/dBHL2030￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿￿0.125 2k 10 4kf/kHz/dBHL2030Fig. 2. Characterisation of hearing loss for (left) normal hearing, (middle) pantonal HL, and (right) highfrequency HL.a xed transform based on a \mother wavelet" fromwhich the transformation coecients are derived byscaling, translation and sampling. Here, we have cho-sen the Mallat wavelet for which good results have beenreported in similar studies [3]. The transform coe-cients approximately cover TF tiles as illustrated inFig. 3 a).The WP transform is an adaptive transformation sim-ilar to the DWT but with a exible partitioning of theTF plane. The advantage of this approach comparedto the DWT is that the entropy of the transformeddata shall be minimised through variable levels of de-composition such that the energy is concentrated inas few coecients as possible. That minimisation isachieved by the reduction of the concentration accord-ing to Shannon's entropy [7]. Fig. 3 b) shows a sampleWP decomposition.Based on a parameterisation of the data by the WP,representing the feature extraction of the data, the ap-plication of an SNR-like criterion for the feature selec-tion is conducted which will be described next.3. FEATURE SELECTIONTo quantify and exploit dierences in the TEOAEWP coecients of the three groups of hearing abil-ity within the Homburg data, a signal-to-noise-ratio(SNR) based criterion is invoked. First, the SNR is es-timated for each of the 512 parameters in the TF-planebased on the WPs of the two partial averages, WPA(n)and WPB(n), n = 1;:::;512. The SNR of the nth co-ecient is (coarsely) estimated by comparing the sumand the dierence obtained from the partial averagesA and B:SNR(n) = 20log10jWPA(n) + WPB(n)jjWPA(n)   WPB(n)j + : (1)This SNR is calculated for all measurements, and foreach of the 512 WP coecients within each of the threehearing ability groups, the distribution is recorded.The SNR value of a WP coecient is used to evaluatethe separability of any two groups with dierent hear-ing status. The separability can be assessed indepen-dent of the selection of a specic threshold by meansof a socalled receiver operating characteristic (ROC)curve. The area underneath the ROC is a measure forthe separability of both groups, and independent of thedenition of SNR-thresholds [8].As single WP coecients yield a poor separabilitybetween any two groups, we pick the coecient thatgives the best separable SNR according to (1) as astarting value and iteratively grow a coecient set G toimprove separability. Further coecients are added toG from the neighbourhood of surrounding coecients.Adjacency is dened by edge and corner connections inthe TF plane. The iteration is stopped when the ROCdoes not further improve for the SNR of the coecientscontained in G.4. SVM CLASSIFICATIONIn the following, we briey explain SVM, [9],[10].We consider a three class classication problem for theclasses dened by the groups NH, HF and PT, startingwith an explanation for a two class classication. Thetraining data originates from the Homburg data, whilethe test data comprises the Heidelberg measurements.The training data is described as a set of trainingvectors fpigi=1 ::: M with corresponding binary labelsSi = 1 for the one class, e.g. NH, and Si =  1 forthe second class, e.g. HF. The SVM conducts a clas-sication of a test vector t by assigning a label ^ S bycalculating^ S = sign(f(t)) with f(t) =XiiSiK(t;pi) + b:(2)The i are called weights and b is the bias, which areSVM parameters and adopted during training by max-Wavelet PacketsTimeDWT a) b)FrequencyLevel 1Level 3Level 4Level 2FrequencyLevel 1Level 3TimeLevel 2Level 3Level 4Fig. 3. TF tiling comparison between a) a DWTand b) a sample WP decomposition.imisingLD =Xii  12Xi;jijSiSjK(pi;pj) (3)under the constraints0  i  C andXiiSi = 0 (4)with C being a positive constant which weighs the in-uence of training errors. K(;) is called kernel ofthe SVM. If there is a solution for i, a value for bis determined. Usually i = 0 for the majority of iand thus the summation in (2) is limited to a sub-net of the pi, which therefore is called the set of sup-port vectors. There are several commonly used kernelsfor SVM, which give some exibility for the underly-ing application. Many implementations of kernels canbe found in literature, whereby two popular ones areGaussian and polynomial kernels. If K(;) is positivedenite, (3) and (4) is a convex quadratic optimisationproblem, which converges towards the global optimumassuringly. This optimisation can be quite demandingin terms of computation time for real-world problems,and therefore, sophisticated algorithms like sequentialminimal optimisation (SMO) [9] are used for the solu-tion.To nd a signicant value for the training error C,a leave-one-out (l-o-o) estimation of the error rate isapplied as follows: From the training samples, removethe rst example. Train the SVM on the remainingsamples. Then test the removed example. If the ex-ample is classied incorrectly, it is said to produce aleave-one-out error. In [9], an approach to estimatethe maximum l-o-o error is shown avoiding trainingthe SVM more than once, which is also used for ourstudy. By changing the value for C stepwise, the mini-mum for the l-o-o error is found determining the SVMclassication network. For our application, a Gaussiankernel was used.So far, we have described the SVM for only twoclasses. As we aim at distinguishing 3, we need todene a multi-class method. In [11] a decision directedacyclic graph (DAG) for multi-class SVM is introduced.It is based on an 1-vs-1 classication where the train-ing is conducted for all possible combinations of theclasses. Based on a trained SVM classier for each pos-sible class combination, a binary acyclic graph is usedfor testing. Fig. 4 shows the decision DAGSVM forour application to the the three classes with dierenthearing ability.NH vs HFNot NHNH vs PTHF vs PTNot PTHF PT NHFig. 4. DAGSVM for TEOAE.5. RESULTS AND DISCUSSIONHaving described the detection methods and thedata used for our system, we present the results inthe following. Fig. 5 illustrates the average WP coe-cient energy for the training data showing the typicalTEOAE properties of high frequencies occurring earlyand low frequencies appearing late [6]. In Figure 6 theisolated coecients for each distinction case are shown.They were found by the search procedure based on theSNR criterion explained in Sec. 3 and appear to be rea-sonably located when compared to the average energiesin Fig. 5.Based on the coecient sets, a SVM classication isconducted for each distinction case using the trainingdata. The test data is analysed by the determined clas-siers according to the decision DAG in Fig. 4 yieldingthe detection rates in Tab. 1 for each class.The table shows that the HF can be detected moresignicantly than the NH group with the explained sys-tem. The PT group is the most dicult to determine,just above half of the patients can be allocated cor-rectly. These results may not seem to be encouraging.However, when only considering the the case NH vs PT,89:9% of the NH group and 84:6% of the PT group aregroup detection ratefor test dataNH 68.1%HF 74.7%PT 56.4%Tab. 1. Detection rates yielded by DAGSVM.allocated correctly by the system which is well in therange of other studies.E.g in [12], a group of normal hearing is dened byno hearing loss up to 30 dB and a hearing impairedgroup with a hearing loss over 30 dB. A separationmethod based on wavelet transforms, ensemble corre-lation, time window design and mean cross-correlationis introduced. The study concludes that by standardanalysis 90% of the normal hearing persons and 65%of the hearing impaired patients can be allocated cor-rectly. By applying the various methods, the value forthe hearing impaired group is increased by approxi-mately 17% to 83% in that study. Compared to ourstudy we achieve slightly better results when only con-sidering the case NH vs PT, which can be seen as equiv-alent to the case shown in [12]. One could also argue,that our methods lead to a better separation of hearingloss as our threshold for dening the dierence betweenNH and PT was 20 dB, and the worse the hearing lossgets, the weaker the TEOAE appear and therefore theeasier it should be to separate them. On the otherhand, we achieve the lowest value of 56% for the PTgroup, which shows that it is easier to separate whenclear TEOAE are present, which is more likely the casefor a threshold of hearing loss of 20 dB than for 30 dB.Recapitulating it can be said that our approach yieldsseparation results than can well compete with otherstudies so far.6. CONCLUSIONSWe have presented a WP analysis of TEOAE thataims at the detection of frequency specic hearing loss.We have motivated the use of TF methods, and pro-posed a method to optimise a set of distinctive WPcoecients. This maximisation represents the input toa SVM classier for the detection. We used two datasets for training and testing. The validity of the resultswas veried by a test group. Moreover, the obtainedresults proved to be competitive when they were com-pared to similar study which also aims at the detectionof TEOAE. Therefore, the results appear reasonablyrobust and encourage frequency specic hearing lossdetection via signal processing of TEOAE.7. ACKNOWLEDGEMENTSThe authors would like to acknowledge Prof. UlrichHoppe and Sebastian Hoth of the University of Erlan-gen, Germany, who kindly provided valuable expertiseand the data.REFERENCES[1] M.S. Robinette and T.J. Glattke, Otoacoustic Emis-sions: Clinical Applications, Thieme Medical Pub, 2.edition, 2001.[2] Otodynamics Ltd., Hateld, Herfortshire, UK, ILOOAE Instrument User Manual, 5a edition, October1997.[3] S. Weiss, U. Hoppe, M. Schabert, and U. Eysholdt,\Wavelet Analysis of Transient Evoked OtoacousticEmissions for Dierential Diagnosis of Cochlear Hear-ing Loss," in Asilomar Conference on Signals, Sys-tems, and Computers, Monterey, CA, November 2001.[4] G. Buller and M.E. Lutman, \Automatic classica-tion of transiently evoked otoacoustic emissions usingan articial neural network," British Journal of Audi-ology, vol. 32, pp. 235{247, 1998.[5] P. Ravazzani, G. Tognola, F. Grandori, and J. Ruoho-nen, \Two-Dimensional Filter to Facilitate Detectionof Transient-Evoked Otoacoustic Emissions," IEEETransactions on Biomedical Engineering, vol. 45, pp.1089{1096, 1998.[6] K. J. Blinowska, P. J. Durka, A. Skierski, F. Grandori,and G. Tognola, \High Resolution Time-FrequencyAnalysis of Otoacoustic Emissions," Technology andHealth Care, vol. 5, pp. 407{418, 1997.[7] A. Jensen and Anders la Cour Harbo, Ripples in Math-ematics, Springer-Verlag, Berlin, Heidelberg, NewYork, 2001.[8] J. A. Hanley and B. J. McNeil, \The Meaning and Useof the Area under a Receiver Operating Characteristic(ROC) Curve," Radiology, vol. 143, pp. 26{36, 1982.[9] V.N. Vapnik, Statistical Learning Theory, CambridgeUniversity Press, New York: Wiley, 1998.[10] C. Bahlmann, B. Haasdonk, and H. Burkhardt, \On-line Handwriting Recognition with Support VectorMachines { A Kernel Approach," in Proceedings of the8th Int. Workshop on Frontiers in Handwriting Recog-nition (IWFHR), pp. 49{54, 2002.[11] J. Platt, N. Cristianini, and J. Shawe-Taylor, \LargeMargin DAGs for Multiclass Classication," in Pro-ceedings of Advances in Neural Information ProcessingSystems, NIPS'99, MIT Press 2000, pp. 547{553.[12] A. Janusauskas, L. Sornmo, O. Svensson, and B. En-gdahl, \Detection of Transient-Evoked OtoacousticEmissions and the Design of Time Windows," IEEETransactions on Biomedical Engineering, vol. 49, no.No.2, pp. 132{139, February 2002.average WP coefficient energy − normal hearing (Homburg)time / [ms]frequency / [Hz]0 2 4 6 8 10 12 14 16 18 2001000200030004000500060007000average WP coefficient energy − HF hearing loss (Homburg)time / [ms]frequency / [Hz]0 2 4 6 8 10 12 14 16 18 2001000200030004000500060007000average WP coefficient energy − pantonal hearing loss (Homburg)time / [ms]frequency / [Hz]0 2 4 6 8 10 12 14 16 18 2001000200030004000500060007000Fig. 5. Average WP coecient energy for the dif-ferent hearing ability groups for the training data.time / [ms]frequency / [Hz]WP mask: NH vs HF0 2 4 6 8 10 12 14 16 18 2001000200030004000500060007000time / [ms]frequency / [Hz]WP mask: NH vs PT0 2 4 6 8 10 12 14 16 18 2001000200030004000500060007000time / [ms]frequency / [Hz]WP mask: HF vs PT0 2 4 6 8 10 12 14 16 18 2001000200030004000500060007000Fig. 6. Selected feature coecients for the threedistinction cases.

Automatic classi of transiently evoked otoacoustic emissions using an arti neural network,&quot;

High Resolution Time-Frequency Analysis of Otoacoustic Emissions,&quot;

Large Margin DAGs for Multiclass Classi

Online Handwriting Recognition with Support Vector Machines { A Kernel Approach,&quot;

The Meaning and Use of the Area under a Receiver Operating Characteristic (ROC) Curve,&quot;

Two-Dimensional Filter to Facilitate Detection of Transient-Evoked Otoacoustic Emissions,&quot;

Wavelet Analysis of Transient Evoked Otoacoustic Emissions for Dierential Diagnosis of Cochlear Hearing Loss,&quot;

WP coefficient energy − normal hearing (Homburg) time / [ms] f r e q u e n c y /

Detection of Cochlear Hearing Loss Applying Wavelet Packets and Support Vector Machines

http://dx.doi.org/10.1109/ACSSC.2004.1399421

Detection of cochlear hearing loss applying wavelet packets and support vector machines

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