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= eS OSC ee eee ee ae The membership function of a fuzzy set is a generalization of the indicator function in classical sets. In fuzzy logic, it represents the degree of truth as an extension of valuation. Membership functions were introduced by Zadeh in the first paper on fuzzy sets [46]. The membership function which represents a fuzzy set A is usually denoted by 3. For an element x of set X, the value py (x) is called the membership degree of x in the fuzzy set A. The membership degree yw 4(x) quantifies the grade of membership of element x to the fuzzy set A. The value 0 means that x is not a

Figure 12 = eS OSC ee eee ee ae The membership function of a fuzzy set is a generalization of the indicator function in classical sets. In fuzzy logic, it represents the degree of truth as an extension of valuation. Membership functions were introduced by Zadeh in the first paper on fuzzy sets [46]. The membership function which represents a fuzzy set A is usually denoted by 3. For an element x of set X, the value py (x) is called the membership degree of x in the fuzzy set A. The membership degree yw 4(x) quantifies the grade of membership of element x to the fuzzy set A. The value 0 means that x is not a

Related Figures (31)

Fig. 2 FO estimate for a representative speech signal of 1 s. a Normalized waveform; b Estimated FO. The thick line corresponds to the segments that are “classified” as voiced by applying the 0.2 threshold to the aperiodicity (Ap0); ¢ Aperiodicity. The dashed line represents the boundary to “classify” the signal frames as voiced or unvoiced
Fig. 2 FO estimate for a representative speech signal of 1 s. a Normalized waveform; b Estimated FO. The thick line corresponds to the segments that are “classified” as voiced by applying the 0.2 threshold to the aperiodicity (Ap0); ¢ Aperiodicity. The dashed line represents the boundary to “classify” the signal frames as voiced or unvoiced
Fig. 3 FO estimate for a single instrument music signal of 1 s. a Normalized waveform; b Estimated FO. The thick line corresponds to the segments that are “classified” as voiced by applying the 0.2 threshold to the aperiodicity (Ap0); ¢ Aperiodicity. The dashed line represents the boundary to “classify” the signal frames as voiced or unvoiced
Fig. 3 FO estimate for a single instrument music signal of 1 s. a Normalized waveform; b Estimated FO. The thick line corresponds to the segments that are “classified” as voiced by applying the 0.2 threshold to the aperiodicity (Ap0); ¢ Aperiodicity. The dashed line represents the boundary to “classify” the signal frames as voiced or unvoiced
Table 1 Information concerning the signals in Figs. 2, 3 and 4
Table 1 Information concerning the signals in Figs. 2, 3 and 4
Fig. 4 FO estimate for a vocal (quartet) music signal of 1 s. a Normalized waveform; b Estimated FO. The thick line corresponds to the segments that are “classified” as voiced by applying the 0.2 threshold to the aperiodicity (Ap0); ¢ Aperiodicity. The dashed line represents the boundary to “classify” the signal frames as voiced or unvoiced
Fig. 4 FO estimate for a vocal (quartet) music signal of 1 s. a Normalized waveform; b Estimated FO. The thick line corresponds to the segments that are “classified” as voiced by applying the 0.2 threshold to the aperiodicity (Ap0); ¢ Aperiodicity. The dashed line represents the boundary to “classify” the signal frames as voiced or unvoiced
has good discrimination capability due to its different behavior for speech and music. As just stated, all histograms shown in Figures from 5 to 11 have been obtained ising a continuous 2-h audio signal representative of the audio classes (speech nd music) to be distinguished. The behavior of each feature is illustrated by two ormalized histograms (one for each audio class to be distinguished), which evidence he discrimination capability of the proposed FO0-derived features. The histograms n figures from 5 to 11 have been normalized so as to resemble probability density unctions.
has good discrimination capability due to its different behavior for speech and music. As just stated, all histograms shown in Figures from 5 to 11 have been obtained ising a continuous 2-h audio signal representative of the audio classes (speech nd music) to be distinguished. The behavior of each feature is illustrated by two ormalized histograms (one for each audio class to be distinguished), which evidence he discrimination capability of the proposed FO0-derived features. The histograms n figures from 5 to 11 have been normalized so as to resemble probability density unctions.
(MUSIC, SPEECH) for the output variable (see Fig. 14). When the obtained knowledge for the FRBS is not considered good enoug to be used, some kind of learning is needed. In such sense, automatic definitio: of FRBSs can be considered in many cases as an optimization or search proces: Genetic Algorithms are known to be capable of finding near optimal solutions i complex search spaces. In this work, the new rules added to the knowledge bas of the FRBS have been obtained using Genetic Algorithms-based evolutionar computation (genetic learning algorithms), giving rise to a Genetic Fuzzy Syster (GFS). This means that the FRBS is evolved by a genetic learning process. A goo review of GFS is found in [5]. The main genetic learning algorithms for FRBSs ar known as Michigan [1], Pittsburgh [40] and Iterative Rule Learning [43]. A bees eee beeen aa leas thews weed ta t4hito worrvele +e: axcanlere tha BODES to thw Ditte
(MUSIC, SPEECH) for the output variable (see Fig. 14). When the obtained knowledge for the FRBS is not considered good enoug to be used, some kind of learning is needed. In such sense, automatic definitio: of FRBSs can be considered in many cases as an optimization or search proces: Genetic Algorithms are known to be capable of finding near optimal solutions i complex search spaces. In this work, the new rules added to the knowledge bas of the FRBS have been obtained using Genetic Algorithms-based evolutionar computation (genetic learning algorithms), giving rise to a Genetic Fuzzy Syster (GFS). This means that the FRBS is evolved by a genetic learning process. A goo review of GFS is found in [5]. The main genetic learning algorithms for FRBSs ar known as Michigan [1], Pittsburgh [40] and Iterative Rule Learning [43]. A bees eee beeen aa leas thews weed ta t4hito worrvele +e: axcanlere tha BODES to thw Ditte
WILY IE AS dW Eat L4]> i flhouerset tT) CGALUIUE AIL ALIVe INUIL AW GLENS L Ph The genetic learning algorithm used in this work to evolve the FRBS is the Pitts- burgh algorithm. Next, the genetic learning process is described. In the Pittsburgh approach, each chromosome represents an entire base of rules and evolution is accomplished by means of genetic operators applied at the level of fuzzy rule sets. The fitness function evaluates the accuracy of the entire rule base encoded in the chromosome. The genetic learning process proposed in this work for SMD using the Pittsburgh approach is illustrated in Fig. 15.
WILY IE AS dW Eat L4]> i flhouerset tT) CGALUIUE AIL ALIVe INUIL AW GLENS L Ph The genetic learning algorithm used in this work to evolve the FRBS is the Pitts- burgh algorithm. Next, the genetic learning process is described. In the Pittsburgh approach, each chromosome represents an entire base of rules and evolution is accomplished by means of genetic operators applied at the level of fuzzy rule sets. The fitness function evaluates the accuracy of the entire rule base encoded in the chromosome. The genetic learning process proposed in this work for SMD using the Pittsburgh approach is illustrated in Fig. 15.
Fig. 16 ROC curves for all considered features when a k-NN classifier is used
Fig. 16 ROC curves for all considered features when a k-NN classifier is used
FO-based features vs. timbral features for different classifiers
FO-based features vs. timbral features for different classifiers
-NN SPR classifier. As can be seen in Table 4, the discrimination capability of the FO-derived features s related to the histograms shown in Figs. S—11. Given a FO-derived feature, the more eparated the feature histograms are, the higher the accuracy rate is. From Table 4, t also results that most of the meaningful information is provided by only three eatures: the average of the estimated FO (F0,,), the dynamic range of the estimated ‘0 (D ro) and the number of notes (Nnore). When the three features are combined, the lassification percentage goes up to about 90%, which is close to the value obtained vhen all F0-derived features are considered (93.30%). Further, we are interested in knowing the improvement (if any) due to the FO- Fig. 18 ROC curves for all considered features when a NN classifier is used
-NN SPR classifier. As can be seen in Table 4, the discrimination capability of the FO-derived features s related to the histograms shown in Figs. S—11. Given a FO-derived feature, the more eparated the feature histograms are, the higher the accuracy rate is. From Table 4, t also results that most of the meaningful information is provided by only three eatures: the average of the estimated FO (F0,,), the dynamic range of the estimated ‘0 (D ro) and the number of notes (Nnore). When the three features are combined, the lassification percentage goes up to about 90%, which is close to the value obtained vhen all F0-derived features are considered (93.30%). Further, we are interested in knowing the improvement (if any) due to the FO- Fig. 18 ROC curves for all considered features when a NN classifier is used
VUULGaIINU Vy MEAL LHe EDULIS OE AN VICODIN. As can be seen in Table 5, a great increase in the classification accuracy rate is always produced when combining each timbral feature with the FO-derived ones. Consequently, the F0-derived features (pitch features) constitute a good complement to the timbral features for SMD. Note that the results obtained when combining each timbral feature with the FO-derived ones are always above the reference (93.30%). The best results are obtained by combining MFCC and the FO-derived features, with an average classification percentage of about 97%. ye) aa “ $e in average classification percentage of about 97%. Now, we investigate the influence of the GFS on the classification accuracy rate or SMD. Table 6 shows the improvement in the accuracy rate (averaged results) lue to the inclusion of the GFS within the proposed two-stage classification scheme egarding the case of using only the classifier (first stage). The robustness of the SFS against different widely used classifiers (k-NN, GMM, NN and SVM) has also yeen assessed in Table 6. The results in Table 6 have been obtained when using the sroposed FO-based feature set, the Pittsburgh learning algorithm is applied to evolve he GFS, and the same audio database has been considered for testing the different lassification schemes.
VUULGaIINU Vy MEAL LHe EDULIS OE AN VICODIN. As can be seen in Table 5, a great increase in the classification accuracy rate is always produced when combining each timbral feature with the FO-derived ones. Consequently, the F0-derived features (pitch features) constitute a good complement to the timbral features for SMD. Note that the results obtained when combining each timbral feature with the FO-derived ones are always above the reference (93.30%). The best results are obtained by combining MFCC and the FO-derived features, with an average classification percentage of about 97%. ye) aa “ $e in average classification percentage of about 97%. Now, we investigate the influence of the GFS on the classification accuracy rate or SMD. Table 6 shows the improvement in the accuracy rate (averaged results) lue to the inclusion of the GFS within the proposed two-stage classification scheme egarding the case of using only the classifier (first stage). The robustness of the SFS against different widely used classifiers (k-NN, GMM, NN and SVM) has also yeen assessed in Table 6. The results in Table 6 have been obtained when using the sroposed FO-based feature set, the Pittsburgh learning algorithm is applied to evolve he GFS, and the same audio database has been considered for testing the different lassification schemes.
Multimed Tools Appl (2009) 41:253-286
Multimed Tools Appl (2009) 41:253-286
The results in Table 6 show the good behavior of the proposed two-stage classi- fication scheme for SMD, which implies that GFS can be an interesting component to be used in pattern recognition or classification tasks. As expected, the GFS always leads to a better performance of the speech/music discriminator. From results in Table 6, we can say that an average reduction about 2.35% in the total error rate has been achieved. The GFS leads to similar improvement in the accuracy rate for all considered classifiers, which evidences the robustness of the GFS against the
The results in Table 6 show the good behavior of the proposed two-stage classi- fication scheme for SMD, which implies that GFS can be an interesting component to be used in pattern recognition or classification tasks. As expected, the GFS always leads to a better performance of the speech/music discriminator. From results in Table 6, we can say that an average reduction about 2.35% in the total error rate has been achieved. The GFS leads to similar improvement in the accuracy rate for all considered classifiers, which evidences the robustness of the GFS against the
Table 7 Speech/rap music discrimination: comparison between FO features and MFCC type of classifier. The highest classification accuracy percentages correspond to the NN+GFS scheme. An average accuracy percentage above 97% is achieved by such classification scheme.
Table 7 Speech/rap music discrimination: comparison between FO features and MFCC type of classifier. The highest classification accuracy percentages correspond to the NN+GFS scheme. An average accuracy percentage above 97% is achieved by such classification scheme.
SCNLCG HI Lavie /, WdaVe OCCH OVIAHICG HI CWO Cas€s. WIL allG WITMOUL USE Ue CIPS 1 the classification scheme. In both cases, the k-NN SPR classifier has been considered As can be seen in Table 7, the proposed FO-derived features are especially well- suited to discriminate between speech and rap music, because they rely on the pitct rather than on the timbral texture. From Table 7, it results that the FO-derived features outperform MFCC for speech/rap music discrimination, the difference: being close to 4% and 3.5% for the first (k-NN) and second (k-NN+GFS) cases. respectively, which involves that the GFS does not give rise to further difference between the FO-derived features and MFCC. Note that the difference between the F0-derived features and MFCC is about 2% for the general case of SMD. Therefore the F0-derived features can be an interesting alternative to MFCC, especially for the particular case of speech/rap music discrimination. To corroborate the results in Table 7. the ROC curves shown in Fic. 20 have been
SCNLCG HI Lavie /, WdaVe OCCH OVIAHICG HI CWO Cas€s. WIL allG WITMOUL USE Ue CIPS 1 the classification scheme. In both cases, the k-NN SPR classifier has been considered As can be seen in Table 7, the proposed FO-derived features are especially well- suited to discriminate between speech and rap music, because they rely on the pitct rather than on the timbral texture. From Table 7, it results that the FO-derived features outperform MFCC for speech/rap music discrimination, the difference: being close to 4% and 3.5% for the first (k-NN) and second (k-NN+GFS) cases. respectively, which involves that the GFS does not give rise to further difference between the FO-derived features and MFCC. Note that the difference between the F0-derived features and MFCC is about 2% for the general case of SMD. Therefore the F0-derived features can be an interesting alternative to MFCC, especially for the particular case of speech/rap music discrimination. To corroborate the results in Table 7. the ROC curves shown in Fic. 20 have been
J. E. Muiioz was born in Estepona (Malaga), Spain, in 1970. He received the MSc degree in Telecommunication Engineering from the University of Malaga in 1995. Since 2003, he is assistant professor in Telematics at the Telecommunication Engineering Department of the University of Jaen. His area of research interest is Speech and Audio Analysis. He is involved in research projects of the Spanish Ministry of Science and Education.
J. E. Muiioz was born in Estepona (Malaga), Spain, in 1970. He received the MSc degree in Telecommunication Engineering from the University of Malaga in 1995. Since 2003, he is assistant professor in Telematics at the Telecommunication Engineering Department of the University of Jaen. His area of research interest is Speech and Audio Analysis. He is involved in research projects of the Spanish Ministry of Science and Education.
P. Vera-Candeas_ was born in Madrid, Spain, in 1976. He received the M.S. degree in Telecom- munication Engineering from the University of Malaga (UMA) in 2000 and a Ph.D. degree from the University of Alcala in 2006. Since 2000, he has worked at the Telecommunication Engineering Departament of the University of Jaén. Nowadays, he is an Associate Professor in Signal Processing and Communications Area. His areas of research interest are Signal Processing and its Applications to Audio Analysis and Ultrasonic NDT. He has been involved in research projects of the Spanish Ministry of Science and Education (MEC) and private companies.
P. Vera-Candeas_ was born in Madrid, Spain, in 1976. He received the M.S. degree in Telecom- munication Engineering from the University of Malaga (UMA) in 2000 and a Ph.D. degree from the University of Alcala in 2006. Since 2000, he has worked at the Telecommunication Engineering Departament of the University of Jaén. Nowadays, he is an Associate Professor in Signal Processing and Communications Area. His areas of research interest are Signal Processing and its Applications to Audio Analysis and Ultrasonic NDT. He has been involved in research projects of the Spanish Ministry of Science and Education (MEC) and private companies.
F. J. Cafiadas_ was born in Linares (Jaén), Spain, in 1977. He received the M.S. degree in Telecommunication Engineering from the University of Malaga (UMA) in 2004. During 2004- 2006, he worked as engineer in an Europe Research Project (INTUITION Network Excellence). Nowadays, he is an assistant professor at the Telecommunication Engineering Departament of the University of Jaén. His areas of research interests include automatic music transcription, multi-pitch estimation and sound source separation in polyphonic music signals. His PhD Thesis is focused on multi-pitch estimation techniques and single-channel source separation.
F. J. Cafiadas_ was born in Linares (Jaén), Spain, in 1977. He received the M.S. degree in Telecommunication Engineering from the University of Malaga (UMA) in 2004. During 2004- 2006, he worked as engineer in an Europe Research Project (INTUITION Network Excellence). Nowadays, he is an assistant professor at the Telecommunication Engineering Departament of the University of Jaén. His areas of research interests include automatic music transcription, multi-pitch estimation and sound source separation in polyphonic music signals. His PhD Thesis is focused on multi-pitch estimation techniques and single-channel source separation.
S. Garcia-Galan was born in Lahiguera (Jaen), Spain, in 1969. He received the MSc and PhD degrees in Telecommunication Engineering from the University of Malaga (UMA) and the Tech- nical University of Madrid (UPM), in 1995 and 2004, respectively. Since 1995, he is with the Telecommunication Engineering Department of the University of Jaen. His areas of research are engineering applications and artificial intelligence.
S. Garcia-Galan was born in Lahiguera (Jaen), Spain, in 1969. He received the MSc and PhD degrees in Telecommunication Engineering from the University of Malaga (UMA) and the Tech- nical University of Madrid (UPM), in 1995 and 2004, respectively. Since 1995, he is with the Telecommunication Engineering Department of the University of Jaen. His areas of research are engineering applications and artificial intelligence.
Related topics:
Information SystemsNew MusicAdaptive Network Based Fuzzy Inference SystemStatistical Pattern RecognitionMultimedia ApplicationAudio Classification
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