Christensen, Mads Græsbøll

Ellis, Dan P. W.

Jensen, Jesper Højvang

Jensen, Søren Holdt

In the context of music, a cover version is a remake of a song, often with significant stylistic variation. In this paper we describe a distance measure between sampled audio files that is designed to be insensitive to instrumentation, time shift, temporal scaling and transpositions. The algorithm was submitted to the Music Information Retrieval eXchange (MIREX) 2007 audio cover song identification task, where it came fourth of the eight submitted algorithms

    Aalborg UniversitetA Chroma-based Tempo-insensitive Distance Measure for Cover Song IdentificationJensen, Jesper Højvang; Ellis, Dan P. W.; Christensen, Mads Græsbøll; Jensen, Søren HoldtPublication date:2007Document VersionPublisher's PDF, also known as Version of recordLink to publication from Aalborg UniversityCitation for published version (APA):Jensen, J. H., Ellis, D. P. W., Christensen, M. G., & Jensen, S. H. (2007). A Chroma-based Tempo-insensitiveDistance Measure for Cover Song Identification. Abstract from Third Music Information Retrieval EvaluationeXchange, .General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            ? Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            ? You may not further distribute the material or use it for any profit-making activity or commercial gain            ? You may freely distribute the URL identifying the publication in the public portal ?Take down policyIf you believe that this document breaches copyright please contact us at vbn@aub.aau.dk providing details, and we will remove access tothe work immediately and investigate your claim.Downloaded from vbn.aau.dk on: April 30, 2017A CHROMA-BASED TEMPO-INSENSITIVE DISTANCE MEASURE FORCOVER SONG IDENTIFICATIONJesper Højvang Jensen Daniel P.W. Ellis Mads G. Christensen Søren Holdt JensenAalborg University Columbia University Aalborg University Aalborg UniversityDept. Electron. Syst. LabROSA Dept. Electron. Syst. Dept. Electron. Syst.ABSTRACTIn the context of music, a cover version is a remake ofa song, often with significant stylistic variation. In thispaper we describe a distance measure between sampledaudio files that is designed to be insensitive to instrumen-tation, time shift, temporal scaling and transpositions. Thealgorithm was submitted to the Music Information Re-trieval eXchange (MIREX) 2007 audio cover song iden-tification task, where it came fourth of the eight submittedalgorithms.1 INTRODUCTIONAs the size of digital music collections increase, navigat-ing such collections become increasingly difficult. Oneof the goals of the music information retrieval commu-nity is to develop signal processing algorithms to facilitatesuch navigation, for instance by finding cover versions ofa song. Comparing different algorithms has been imprac-tical, as copyright issues have prevented the developmentof standard music collections. The annual MIREX evalu-ations overcome this problem by having participants sub-mit their algorithms which are then centrally evaluated.This way, distributing song data is avoided. If the testcollection will not come to the algorithms, the algorithmswill go to the test collection.The MIREX cover song retrieval contest was first heldin 2006, where the algorithm in [3] had the best retrievalperformance. This algorithm was especially developed forcover song identification and was computationally rela-tively expensive. It combined the chromagram with a beattracker in order to obtain a beat-synchronous chromagramthat was insensitive to temporal differences between dif-ferent versions of a song. Instead of beat tracking, thesubmission described in this paper uses a feature that isinsensitive to time shifting and temporal scaling.2 OVERVIEWIn Figure 1, a block diagram of the proposed algorithmis shown. The assumptions behind are that a song andThis research was supported by the Intelligent Sound project, Dan-ish Technical Research Council grant no. 26–04–0092, and the Paramet-ric Audio Processing project, Danish Research Council for Technologyand Production Sciences grant no. 274–06–0521.its cover versions share the same melody, but might dif-fer with respect to instrumentation, time shifts, tempo andtranspositions. The feature extracted as shown in Figure 1is insensitive to the former three properties, while the dis-tance computation ensures invariance to transpositions. InFigure 2 and 3, the output of different stages in the featureextraction is shown. Note that except a horizontal shift ofone band, Figure 2(c) and 3(c) are very similar.2.1 ChromagramThe chromagram is conceptually a frequency spectrumwhich has been folded into a single octave [1]. This singleoctave is divided into 12 logarithmically spaced frequencybins that each correspond to one semitone on the westernmusical scale. Although only an approximation, we willconsider the chromagram a soft decision activation pat-tern that tells whether a given note is playing. To computethe chromagram, we use the implementation described in[3]. Empirically, we found that using the logarithm of thechromagram increased performance. Let Y be a matrixcontaining the chromagram where element (Ylog)ij mea-sures the strength of semitone i, i ∈ 1, 2, · · · , 12, in framej. To avoid numerical problems, we then compute the log-arithm as(Ylog)ij = log(Y )ij + δδ, (1)where δ is a small constant.2.2 Power spectrumTo avoid time alignment problems, we remove all phaseinformation by computing the power spectrum for eachrow of Ylog, i.e., the activation pattern for each semitone.Empirically, the power spectrum performed better than theamplitude spectrum.2.3 Time-scale invarianceIf x(t) is a continuous signal and X(f) = F{x(t)} isits Fourier Transform, then a temporal scaling of x(t) willalso cause a scaling in the frequency domain: F{x(kt)} =X(f/k). For cover song detection, it is reasonable to as-sume that k is bounded, i.e., that two songs do not dif-fer in tempo more than e.g. a factor 1.4, in which case11.4 ≤ k ≤ 1.4. If either the time or frequency axis isviewed on a logarithmic scale, a time scaling (i.e., k 6= 1)Y =yT1yT2...yT12 ...Sampled audioChromagramSemitone 2y2Semitone 1y1Semitone 12y12log(·)log(·)log(·)......xT1xT2...xT12 =X|F{·}|2|F{·}|2|F{·}|2SemitonenynFigure 1. Block diagram of the feature extraction.(a) Chromagram after taking the logarithm.(b) Power spectrum of the chromagram rows.(c) Energy in the 25 exponentially spaced bandsFigure 2. Different stages of feature extraction fromMIDI song with duration 3:02.(a) Chromagram after taking the logarithm.(b) Power spectrum of the chromagram rows.(c) Energy in the 25 exponentially spaced bandsFigure 3. Feature extraction from the same MIDI song asin Figure 2, except it is stretched to have duration 3:38.Figure 4. Bandwidths of the 25 logarithmically spacedfilters.will show up as an offset. This is used in e.g. [5] to makethe distance between the fundamental frequency and itsharmonics independent of the fundamental frequency it-self. As we assume k is bounded, then so will the offsetbe. Thus, on the logarithmic scale, we could representthe signal by the output of a number of equally spacedbands with effective bandwidth corresponding to the po-tential offset. Alternatively, on the linear scale, a set ofexponentially spaced bands with relatively large effectivebandwidth would do the trick. In Figure 4, the 25 logarith-mically spaced bands with 50% overlap that we used areshown. The lowest band start at 0.017 Hz, and the highestband end at 0.667 Hz, thus capturing variations on a timescale between 1.5 s and 60 s. The amount of temporalscaling allowed is further increased when computing thedistance. The resulting feature is a 12 × 25 matrix wherecomponent i, j reflects the activity for semitone i in bandj.2.4 DistanceWe compute the distance between the two feature matri-ces X1 and X2 by normalizing them to unit norm andminimizing the Frobenius distance over the allowed trans-positions and frequency shifts. First, we normalize to unitFrobenius norm:X′1 =X1/‖X1‖F, (2)X′2 =X2/‖X2‖F. (3)Let T12 be the 12× 12 permutation matrix that transposesX′1 orX′2 by one semitone:(T12)i,j ={(I)i+1,j for i < 12,(I)1,j for i = 12,(4)where I is the identity matrix. To compensate for possibletranspositions, we minimize the Frobenius distance overall possible transpositions:d′(X′1,X′2) = mint∈{1,2,··· ,12}‖T t12X′1 −X′2‖F. (5)To allow even further time scaling than permitted by theeffective bandwidths, we also allow shifting the matrix:d(X′1,X′2) = mins∈{−2,−1,0,1,2}d′(X′(s)1 ,X′(−s)2 ), (6)Figure 5. Effect of transpositions on melody recognitionaccuracy.Figure 6. Effect of lengthening or shortening a song onmelody recognition accuracy. Duration is relative to orig-inal song.whereX′(s)l ={[0s X′l]if s ≥ 0,[X′l 0−s]if s < 0,(7)and where 0s is a 12× s matrix of zeros.3 RESULTSWe have evaluated the distance measure by using a nearestneighbor classifier on two different datasets, namely a setof MIDI files [4] and the covers80 set [2]. The basic set ofMIDI files consists of 900 MIDI songs that are the com-binations of 30 different melodies of length 180 secondsplayed with 30 different instruments. To measure the sen-sitivity to transpositions and variations in tempo, the set inwhich the nearest neighbor is found is replaced by trans-posed versions of the songs and lengthened/shortened ver-sions. In Figure 5 the effect of transpositions is shown,and in Figure 6 the effect of changing the tempo is shown.It is seen that transposing songs hardly affect performance,and that changing the tempo between a factor 0.7 and 1.4also does not affect performance too seriously.The covers80 dataset consists of 80 titles each in twodifferent versions, i.e., a total of 160 songs. With this set,a song’s nearest neighbor was the cover version in 36% ofthe cases. However, as parameters have been tweaked us-ing this dataset, some degree of overtraining is inevitable.The algorithm was also submitted for the MIREX 2007audio cover song identification task. The results of thisevaluation are shown in Table 1.Rank Participant Avg. Coversprec. in top 101 Serrà & Gómez 0.521 16532 Ellis & Cotton 0.330 12073 Bello, J. 0.267 8694 Jensen, Ellis, Christensen& Jensen0.238 7625 Lee, K. (1) 0.130 4256 Lee, K. (2) 0.086 2917 Kim & Perelstein 0.061 1908 IMIRSEL 0.017 34Table 1. MIREX 2007 Audio Cover Song Identificationresults. In comparison, the 2006 winner [3] identified 761cover songs in top 10.4 REFERENCES[1] M. A. Bartsch and G. H. Wakefield, “To catch a cho-rus: using chroma-based representations for audiothumbnailing,” in Proc. IEEE Workshop on Appl. ofSignal Process. to Aud. and Acoust., 2001, pp. 15 –18.[2] D. Ellis and G. Poliner, “Identifying cover songswith chroma features and dynamic programming beattracking,” in Proc. IEEE Int. Conf. Acoust., Speech,Signal Processing, 2007, pp. 1429–1432.[3] D. P. Ellis, “Identifying ‘cover songs’ with beat-synchronous chroma features,” in Music InformationRetrieval Evaluation eXchange, 2006.[4] J. H. Jensen, M. G. Christensen, and S. H. Jensen, “Aframework for analysis of music similarity measures,”in Proc. European Signal Processing Conf., 2007, pp.926–930.[5] S. Saito, H. Kameoka, T. Nishimoto, andS. Sagayama, “Specmurt analysis of multi-pitchmusic signals with adaptive estimation of commonharmonic structure,” in Proc. Int. Symp. on MusicInformation Retrieval, 2005, pp. 84–91.

A Chroma-based Tempo-insensitive Distance Measure for Cover Song Identification

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A Chroma-based Tempo-insensitive Distance Measure for Cover Song Identification

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