Computational Models of Music Similarity and their ... - OFAI

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38 2 Audio-based Similarity Measures the end of this section there are some paragraphs describing illustrations which help understand basic characteristics of the FPs. 2.2.4.1 Details The parameters used are: segment size 128 (about 3 seconds), hop size 64 (50% overlap). Instead of the 36 frequency bands of the Mel spectrum only 12 are used. The grouping of frequency bands is described below. The resolution of the modulation frequency in the range of 0 to 10Hz is 30. This results in 360 (12×30) dimensional FPs. The main reason for reducing the frequency resolution is to reduce the overall dimensionality of the FPs, and thus the required memory to store one pattern. Furthermore, a high frequency resolution is not necessary. For example, in [Pam01] 20 frequency bands were used. Analysis of the eigenvectors showed that especially higher frequency bands are very correlated. In [Pam05] only 12 frequency bands were used. In particular, the following mapping was used to group the 36 Mel bands into 12 frequency bands: 01 t = zeros(1,36); (2.21) 02 t(1) = 1; t( 7: 8) = 5; t(15:18) = 9; 03 t(2) = 2; t( 9:10) = 6; t(19:23) = 10; 04 t(3:4) = 3; t(11:12) = 7; t(24:29) = 11; 05 t(5:6) = 4; t(13:14) = 8; t(30:36) = 12; 06 07 mel2 = zeros(12,size(M_dB,2)); 08 for i=1:12, 09 mel2(i,:) = sum(M_dB(t==i,:),1); 10 end The actual values are more or less arbitrary. However, they are based on the observation that interesting details are often in lower frequency bands. Note that the energy is added up. Thus, the 12th frequency band of mel2 represents the sum of 7 M_db bands while the first and second band only represent one. This can be seen in Figure 2.16. In particular, the frequency bands 9-11 have higher values. The following defines the constants used for computations, in particular the fluctuation strength weights (flux), the filter which smoothes over the frequency bands (filt1), and the filter which smoothes over the modulation
2.2 Techniques 39 Relative Fluctuation Strength 1 0.8 0.6 0.4 0.2 0 0 4 8 12 16 20 24 Modulation Frequency [Hz] Figure 2.15: The relationship between the modulation frequency and the weighting factors of the fluctuation strength. frequencies (filt2): 11 f = linspace(0,22050/512/2,64+1); (2.22) 12 flux = repmat(1./(f(2:32)/4+4./f(2:32)),12,1); 13 w = [0.05, 0.1, 0.25, 0.5, 1, 0.5, 0.25, 0.1, 0.05]; 14 filt1 = filter2(w,eye(12)); %% 12x12 15 filt1 = filt1./repmat(sum(filt1,2),1,12); 16 filt2 = filter2(w,eye(30)); %% 30x30 17 filt2 = (filt2./repmat(sum(filt2,2),1,30))’; The weighting vector flux for the amplitude modulation is based on a model of perceived fluctuation strength [Fas82] and was primarily designed as a model for speech. The weights are shown in Figure 2.15. The filter is applied as shown in line 25 of Algorithm 2.24. From a practical point of view, the main purpose of the weighting is to reduce the influence of very low modulation frequencies which generally have higher energies. Alternatively, a weighting function based on preferred tempo could be used. For example, the periodicity histograms defined in [PDW03a] used a resonance model [Moe02] weighting function which has a maximum response around 120bpm (2Hz). The two filters (filt1 and filt2) are the same as used in [Pam01]. They are applied to smooth the patterns. The effect of the fluctuation strength weighting and the smoothing filters can be seen in Figure 2.16. In general, very short pieces (e.g. shorter than 15 seconds) should be excluded from the computations. However, if for some reason there is an interest in dealing with short pieces (e.g. when computing the similarity between segments) it is necessary to pad the Mel spectrogram with zeros.
Page 1: DISSERTATION Computational Models o
Page 5: Abstract This thesis aims at develo
Page 8 and 9: evaluate similarity measures for dr
Page 10 and 11: 2.2.7.3 Always Dissimilar . . . . .
Page 13 and 14: Chapter 1 Introduction This chapter
Page 15 and 16: 1.1 Outline of this Thesis 3 measur
Page 17 and 18: 1.2 Matlab Syntax 5 ◦ Development
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Page 23 and 24: 2.1 Introduction 11 Experts High qu
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Page 27 and 28: 2.2 Techniques 15 Amplitude 0 ZCR:
Page 29 and 30: 2.2 Techniques 17 MFCCs Mel Frequen
Page 31 and 32: 2.2 Techniques 19 Segment wav(idx)
Page 33 and 34: 2.2 Techniques 21 Triangular Filter
Page 35 and 36: 2.2 Techniques 23 num_coeffs = 5 nu
Page 37 and 38: 2.2 Techniques 25 2.2.2.5 Parameter
Page 39 and 40: 2.2 Techniques 27 used for clusteri
Page 41 and 42: 2.2 Techniques 29 FFT window size w
Page 43 and 44: 2.2 Techniques 31 Unlike G30 no ran
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Page 57 and 58: 2.2 Techniques 45 Alternatively, th
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2.5 Alternative: Web-based Similari
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2.6 Conclusions 91 2.5.3 Limitation
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Chapter 3 Applications This chapter
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3.2 Islands of Music 95 Figure 3.1:
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3.2 Islands of Music 97 they use to
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3.2 Islands of Music 99 a b c d Fig
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3.2 Islands of Music 101 AMBIENT CL
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3.2 Islands of Music 103 Figure 3.6
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3.2 Islands of Music 105 scribing a
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3.3 Fuzzy Hierarchical Organization
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3.4 Dynamic Playlist Generation 125
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3.5 Conclusions 137 + Punk / Bad Re
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Chapter 4 Conclusions In this thesi
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Bibliography [AHH + 03] Eric Allama
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[CKGB02] Pedro Cano, Martin Kaltenb
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[Got03] Masataka Goto, A Chorus-Sec
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[Lüb05] Dominik Lübbers, SoniXplo
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[PFW05b] , Improvements of Audio-Ba
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[SKW05a] Markus Schedl, Peter Knees
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Elias Pampalk I was born in 1978 in
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