Research Article GPU Acceleration of Melody Accurate Matching in Query-by-Humming

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1 e Scentfc World Journal, Artcle ID , 7 pages Research Artcle GPU Acceleraton of Melody Accurate Matchng n Query-by-Hummng Lmn Xao, 1,2 Yao Zheng, 1,2,3 Wenq Tang, 1,2 Guangchao Yao, 1,2 and L Ruan 1,2 1 State Key Laboratory of Software Development Envronment, Behang Unversty, Bejng , Chna 2 School of Computer Scence and Engneerng, Behang Unversty, Bejng , Chna 3 Avaton Insttute, Bejng , Chna Correspondence should be addressed to Lmn Xao; xaolm@buaa.edu.cn and Yao Zheng; zyshren@163.com Receved 18 July 2013; Accepted 18 December 2013; Publshed 12 February 2014 Academc Edtors: Y. Chen and D. Wallom Copyrght 2014 Lmn Xao et al. Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted. Wth the ncreasng scale of the melody database, the query-by-hummng system faces the trade-offs between response speed and retreval accuracy. Melody accurate matchng s the key factor to restrct the response speed. In ths paper, we present a GPU acceleraton method for melody accurate matchng, n order to mprove the response speed wthout reducng retreval accuracy. The method develops two parallel strateges (ntra-task parallelsm and nter-task parallelsm) to obtan accelerated effects. The effcency of our method s valdated through extensve experments. Evaluaton results show that our sngle GPU mplementaton acheves 20x to 40x speedup rato, when compared to a typcal general purpose CPU s executon tme. 1. Introducton Wth the development of nformaton technology, musc retreval technology has been wdely appled. Query-byhummng (QBH) s an mportant applcaton for musc retreval, where users can hum a melody to retreve the song [1 3]. Dfferent from the tradtonal musc retreval engne, whch searches the song based on the descrpton of the musc such as the snger or the song name, QBH retreves the song based on the content. Musc retreval s becomng more natural, smple, and user-frendly wth the advancement of QBH. Thus, QBH wll gve broader applcaton prospects for musc retreval [4 6]. Typcal QBH systems consst of three modules, ncludng feature extracton, melody database, and melody matchng [7]. The feature extracton module ncludes ptch extract and note segmentaton. Ptch extract means that the acoustc nput s frst put nto frames; then we obtan the ptch frequences from the frames; fnally we use (1) totransform them nto the representaton of semtone. Note segmentaton means that the obtaned ptch sequence s cut nto dfferent notes. The melody database module s responsble for the management and ndex MIDI melody nformaton. Consder semtone =12 log 2 ( freq ) (1) 440 The core of QBH s the melody matchng between the hummng melody and the melody database. From the vew of practcal applcaton, melody matchng algorthms can be dvded nto fast match and accurate match [8, 9]. Fast match manly removed the less lkely canddates from the melody database, n order to reduce the computaton of accurate match and mprove the system s response tme; accurate match then calculated the more exact smlartes between thehummngmelodyandthecanddatemelodes,soasto obtan the fnal lst of smlar songs. Hence, we can see that the characterstcs of accurate match are a large amount of calculatonandprecsecalculatons. There has to be a trade-off between response speed and accuracy, f the QBH system wants to mprove the retreval accuracy wthn acceptable tmes. However, wth the ncreasng scale of the melody database, the sze of canddate

2 2 The Scentfc World Journal melodes s also growng, whch results n an extended response tme and poor user experence. The usual method formprovngtheresponsespeedstoreducetheszeofthe canddate melodes, but ths may cause low retreval accuracy [10]. Therefore, many efforts are made to develop methods and technques that execute the melody matchng n hgh performance platforms, allowng the producton of accurate results n a shorter tme. Graphc Processng Unt (GPU) s one of the recent trends n hgh performance platforms, whch has demonstrated sgnfcant speedups for many scentfc applcatons [11, 12]. Researchers also have studed the melody matchng on GPUs [13, 14]. However, exstng works choose to mplement a coarse-graned parallelzaton of the melody matchng algorthm, where multple problem nstances are smply replcated onto each multprocessor of a GPU. In ths paper, by analyzng the exstng accurate matchng algorthms, we propose a GPU-based parallelzaton for the accurate matchng algorthm. Our proposed method develops two parallel strateges (ntratask parallelsm and ntertask parallelsm). By takng full advantage of multcomputng unts of GPU, our method can greatly decrease the computaton tme of the accurate match algorthm and mprove the system s response speed wthout reducng the retreval accuracy. The rest of ths paper s organzed as follows. Secton 2 summarzes the melody accurate matchng. In Secton 3, an outlne of the CUDA-based GPU computng platform s gven. Secton 4 descrbes the detals of our parallelzaton strategy for melody accurate matchng usng CUDA. Expermental results are analyzed n Secton 5. The last secton concludes the whole paper and ponts out some future works. 2. Melody Accurate Matchng n QBH 2.1. Problem Defnton. In a QBH system, the hummng nput s frstly put nto a ptch tracker frame by frame and then the output ptch sequence s converted to a semtone scale accordng to (1). The MIDI man melody extracted from the multtrack melody s put nto a note sequence. Defnton 1. The hummng ptch sequence at semtone scale of length m s denoted by Q = (q 1,q 2,...,q m ),where q represents the ptch correspondng to the th frame of hummng. Defnton 2. The MIDI note sequence matched wth Q s denoted by P = {(p 1,d 1 ), (p 2,d 2 ),...,(p n,d n )}, wherep and d represent the ptch and duraton of the th note, respectvely. Defnton 3. The dstance functon between the hummng sequence and the MIDI note sequence s denoted by dst(q,p j ),whereq and p j represent the ptch of hummng sequence and MIDI melody. Therefore, based on the above defntons, the problem of melody accurate matchng could be expressed, gven hummng sequence Q, MIDI note sequence P, and dstance functon,howtocalculatethemnmumdstancebetweenthe two sequences Melody Accurate Matchng Algorthms. In practcal hummng applcatons, dfferent people have dfferent vocal ranges, resultng n tonal nconsstency between hummng melody and standard melody but tonal change consstency; smlarly, dfferent people have dfferent sngng speed, resultng n sngng speed rato nconsstency between the two melodes. Thus, there exst speed change and ptch offset between hummng melody and standard MIDI melody. How toevaluatethespeedchangeandptchoffsetbeforeaccurate matchng s the dffculty of melody accurate matchng algorthms. Exstng matchng algorthms, ncludng lnear scalng (LS) [15], recursve algnment (RA) [9], and dynamc tme warpng (DTW) [16], take dfferent approaches to resolve the above dffculty and mprove retreval accuracy. Lnear scalng (LS) s a smple, ntutve, and effectve melody matchng algorthm. LS chooses dfferent scalng factors to stretch or compress the ptch contour of the hummng melody to more accurately match the MIDI melody. The defcency of LS s also qute obvous: local msmatch may deterorate the global matchng; the selecton of sutable stretchng coeffcent or ptch offset s dffcult; the length of hummng melody may affect the retreval accuracy. Recursve algnment (RA) uses recursve lnear scalng match to explore the optmal matchng results. Although t s derved from the LS, ths method overcomes the dsadvantage of usng sngle stretch factor or ptch offset throughout the entre melody matchng. Hence, RA s capable of capturng long dstance nformaton n human sngng. The drawbacks of ths approach are matchng the fner, hgher tme complexty; the segmentaton fragments based on mdpont, and the MIDI melodes do not necessarly satsfy the lnear relatonshp. Dynamc tme warpng (DTW) s one of the most effectve approaches to melody accurate matchng, whch s a frame-based dynamc programmng algorthm. In DTW, the canddate note sequences should be expanded to frame sequences. Compared to LS and RA, DTW has hgher accuracy but hgher complexty. The detals of DTW-based melody accuracy matchng are descrbed n followng secton. 3. GPU Computng wth CUDA Over the past few years, GPU has ganed sgnfcant popularty as a powerful tool for hgh performance computng. Wth the development of general programmng toolkts, such as Compute Unfed Devce Archtecture (CUDA), GPU becomes a general-purpose shared-memory many-core computng platform and plays mportant roles n applcatons such as computer vson, search, and sortng [17, 18]. CUDA s an extenson of C/C++ whch enables users to wrte scalable multthreaded programs for CUDA-enabled GPUs [19]. In the CUDA programmng model, an applcaton conssts of a sequental host program, whch can execute parallel programs known as kernels on GPUs. A kernel s

3 The Scentfc World Journal 3 Input: Hummng ptch sequence Q=(q 1,q 2,...,q m ) MIDI note sequence P = {(p 1,d 1 ), (p 2,d 2 ),...,(p n,d n )} Scalng factor set S=(sc 1, sc 2,...,sc k ) Output: Mnmum dstance s mn (1) T =LS(Q, P, S)//T s the best scalng hummng ptch sequence (2) Standardze hummng ptch sequence T (3) Transform note sequence P nto frame-based ptch sequence P =(p 1,p 2,...,p t ) (4) Standardze canddate ptch sequence P (5) Intalze ptch offset s pan (6) whle (s pan > 0.01) then (7) s left =dtw(t, P s pan ) (8) s mddle =dtw(t, P ) (9) s rght =dtw(t, P +s pan ) (10) s mn = mn{s left,s mddle,s rght } (11) s pan = s pan /2 (12) end whle (13) return s mn Algorthm 1: DTW-based match (Q, P, S). executed usng potentally large number of parallel threads. Thus, GPU acheves massve parallelsm through executng a large number of lghtweght threads concurrently. These threads are organzed n thread blocks and grds of thread blocks. Each thread runs the same sequental program and has a thread ID wthn ts thread block. The herarchcal organzaton nto blocks and grds has mplcatons for thread communcaton and synchronzaton. Threads wthn a thread block can communcate through a per-block shared memory and may synchronze usng barrers. However, threads located n dfferent blocks cannot communcate or synchronze drectly. The memory model n CUDA has fve types of memory: each thread has prvate local memory; each thread block has shared memory vsble to all threads of the block; all threads have access to the same global memory; there are also two addtonal read-only memores accessble by all threads: the constant, and texture memory. Thread creaton, schedulng, and management are performed entrely n hardware. In order to manage large number of threads, the GPU employs the SIMT (Sngle Instructon Multple Thread) archtecture [20] n whch the threads of ablockareexecutedngroupsof32calledwarps.thewarp can greatly mprove performance by havng threads n a warp execute the same code path and access memory n nearby addresses. 4. GPU-Parallel Melody Accurate Matchng As descrbed n Secton 2.2, DTW s an effcent melody matchng algorthm; however, the tme complexty s O(mt). Ths s the motvaton for our research, hopng that we can accelerate DTW computaton usng GPU wthout reducng the accuracy Melody Accurate Matchng Based on DTW. The melody accurate matchng based on DTW s outlned n Algorthm 1. Suppose that the query ptch sequence s denoted by Q = (q 1,q 2,...,q m ), and the note sequence s denoted by P = {(p 1,d 1 ), (p 2,d 2 ),...,(p n,d n )}.Thenwecanconstructam t DTW matrx D accordng to (2). D(, j) s the mnmum dstance startng from the left-most sde ( = 1) of the matrx to the current poston (, j). Consder D (, j) = dst (q,p j )+mn { D ( 2, j 1) D ( 1, j 1) { { D ( 1, j 2). The correspondng boundary condtons for the above recurson can be expressed as D (, 1) =, D(1,j)=dst (1,j), D (, 0) =, D(0,j)=, D (0, 0) =0. =2,...,m j=1,...,t =1,...,m j=1,...,t The cost of the optmal DTW path s defned as (2) (3) mn j=1 to t D(m,j). (4) After fndng the optmzng j,the optmal DTW path can be obtaned by back trackng. As prevously descrbed, tempo varaton and ptch transposton should be consdered before the accurate matchng. For most users, tempo varaton s attrbuted to lnear varaton. Researchers apply the LS algorthm to the hummngptchsequencebeforecomparngttothecanddate melody. The recurrent relaton shows that the optmal path exsts only when the hummng nput s wthn half to twce the sze of the canddate melody. Hence, the hummng

4 4 The Scentfc World Journal Input: Hummng ptch sequence Q=(q 1,q 2,...,q m ) Frame-based canddate ptch sequence P =(p 1,p 2,...,p t ) Output:CostmatrxD (1) Intalze the frst two rows and columns of the matrx D (2) for j=2to t do (3) for =2to m parallel do (4) calculate D(, j) (5) end for (6) synchronze( ) (7) end for (8) return D Algorthm 2: Parallel mplementaton for calculatng the matrx D PDTW (Q, P). sequencecanbescaledseveraltmes,rangngfrom0.5to 2 tmes the orgnal length and compared to the canddate melody n order to acheve the best scalng factor. For ptch transposton, a heurstc method can be appled that shfts the entre hummng ptch sequence to a sutable poston n order to generate the mnmum DTW dstance. m 4.2. Parallelzaton Strategy for Melody Accurate Matchng. In ths secton, our proposed parallelzaton strateges for melody accurate matchng based on DTW are explaned. We nvestgate two approaches for parallelzng the melody accurate matchng usng CUDA: ntra-task parallelzaton and nter-task parallelzaton. Intra-task parallelzaton ndcates that each task s assgned to one thread block and all threads n the thread block cooperate to perform the task n parallel. Inter-task parallelzaton ndcates that each task s assgned to exactly one thread and all threads n a thread block perform the tasks n parallel. 0 0 j t Intra-Task Parallelzaton. As descrbed n the above secton, the DTW algorthm has quadratc tme complexty that lmts ts usefulness. The purpose of computaton durng the DTW algorthm s to fll the matrx D,whchcanbeeasly mplemented as a smple two nested loops. Accordng to (2), agvend(, j) can be computed only f D( 2,j 1),D( 1, j 1), andd( 1, j 2) have already been computed. For nstance, as shown n Fgure 1, D(2, 2) (red cell locates) depends on D(0, 1), D(1, 1), and D(1, 0) (green cells locate). Ths ndcates that all elements n column two are computable smultaneouslyftheelementsncolumnzeroandcolumn one have already been computed. Thus, every entry of the same column s computable and elements wthn the column canbecomputednparallel. Based on ths dea, we present an effcent parallel mplementaton for calculatng matrx D,as shown n Algorthm 2. The nput to the algorthm s two ptch sequences. The output of the algorthm s matrx D. Lnes3 5arethecoreofour parallel algorthm, whch calculates each element of a column n parallel. After calculatng all elements of each column, synchronzaton operaton s performed to ensure that all processors have fnshed current computaton (lne 6). Fgure 1: Column-wse fashon for computng matrx D. We can easly determne the tme complexty of Algorthm 2. Assume that there are p processors for computng smultaneously. Based on Algorthm 2, the total executon tme can be expressed as T (m, t) = t j=2 m 1 p =O( 1 mt). (5) p Inter-Task Parallelzaton. As descrbed n above the secton, nter-task parallelzaton ndcates that we compute n parallel all the scores of a hummng query wth every peceofmelodynthecanddatemelodyset.fornstance, f the canddate set contans N peces of melodes, we can launch N threads executng Algorthm 2 n parallel. The man challenges are the optmzaton of resource allocatons and memory operatons. Westorethehummngptchsequencentexturememory, whch s the cached, fast memory and shared among all threads. Because of the ncreasng scale of the melody

5 The Scentfc World Journal 5 Input: Hummng ptch sequence Q Canddate melody set N=(P 1,P 2,...,P l ) Scalng factor set S=(sc 1, sc 2,...,sc k ) Output: Melody smlarty lst (1) Load Q, N to GPU devce (2) for =1to l parallel do (3) T =LS(Q, P,S) (4) Standardze hummng ptch sequence T (5) Transform P nto frame-based ptch sequence P (6) Standardze canddate ptch sequence P (7) Intalze ptch offset s pan (8) whle (s pan > 0.01) then (9) s left =PDTW(T, P s pan ) (11) s mddle =PDTW(T, P ) (12) s rght =PDTW(T, P +s pan ) (13) s mn = mn{s left,s mddle,s rght } (14) s pan =s pan /2 (15) end whle (16) end for (17) Load the matrces back to host (18) Calculate the melody smlarty lst Algorthm 3: GPU-based parallel melody accurate matchng. database,thecanddatemelodysetusuallycontanstoomany peces of melodes to be stored n any of the cached memores (texture, constant and shared memory). Therefore, we store the canddate melody set n the global memory. To gan maxmum bandwdth and best performance, all threads n a half-warpshouldaccessthenotesequencesnglobalmemory n a coalesced pattern. In order to adopt the coalesced pattern, everynotesequencesstorednanarrayofdouble-float, a CUDA structure contanng two 32-bt floats storng the ptch and duraton of each note. Then we organze all note sequences n memory as a one-dmensonal array, such that ts frst N entres correspond to the frst note of each sequence; the next N entres correspond to the second note of each sequence, and so forth. Each thread performs the computatons on ts own matrx D. In order to mnmze the amount of requred memory, we only store the current column and forward two columns of each matrx n shared memory. Fnally, n order to allow smultaneous read/wrte operatons by the actve threads, we store the matrces usng the same strategy as the note sequences Implementaton wth CUDA. Basedontheaboveparallelzaton strateges, we present an acceleraton method for melody accurate matchng, as shown n Algorthm3. Specfcally, ntra-task parallelzaton s performed n a thread block; nter-task parallelzaton s performed among thread blocks. 5. Performance Evaluaton In order to evaluate the performance of our GPU-parallel melody accurate matchng algorthm, several experments Table 1: Evaluaton envronment. CPU (AthlonII X4) GTX285 GTX480 Number of Core (30SM) 480 (15SM) SP clock 3.2 GHz GHz GHz Compler GCC CUDA SDK 4.0 CUDA SDK 4.0 were carred out. We frst ntroduce the sngng corpus used n ths study. Then, we compare the performance and accuracy between our parallel mplementaton and the exstng sequental mplementaton Evaluaton Envronment. Evaluaton envronment s shown n Table 1. We use an AMD AthlonII X4 3.2 GHz for CPU, NVIDIA GTX285 wth 240 SPs (Stream processor), and GTX480 wth 480 SPs for GPUs. To evaluate our proposed acceleraton method, we used the publcly avalable MIREX (musc nformaton retreval evaluaton exchange) QBSH corpus [21], whch has been used for the evaluaton of QBSH for many tmes. The corpus ncludes 48 MIDI fles and 4431 sngng or hummng clps. Each clp has duraton of 8 s, wth an 8 khz samplng rate and 8 bt resoluton. The frame sze s 256 and the overlap s 0, resultng n a ptch rate of 8000/256 = Hence, an 8 s sngng clp s converted to a ptch vector of =250 elements n semtones. We add MIDI fles to MIREX corpus to compose the MIDI database. These MIDI fles are collectedfrommidiarchvesonthenternet.

6 6 The Scentfc World Journal Tme (s) CPU GTX GTX K 5 K 10 K Scale of MIDI database (1K = 1000) Fgure 2: Comparson of executon tmes wth dfferent scale of MIDI database. Speedup rato K 5 K 10K Scale of MIDI database (1K = 1000) GTX285 GTX480 Fgure 3: Speedup rato obtaned wth the usage of GPUs Performance Results. We ntroduce the speedup rato to evaluate the performance of GPU-parallel melody accurate matchng algorthm. Top-M ht rate and mean recprocal rank(mrr)areusedtoevaluatetheaccuracyofourproposed algorthm. MRR s a standard metrcs n MIREX, whch can be denoted as n MRR = 1 1, (6) n rank where rank means the rank of the correct song for the th query. Fgure2 shows the executon tmes of dfferent hardware settngs wth respect to the varyng scale of MIDI database. We observe that the performance s senstve to the problem sze and hardware settngs. The results ndcate that the more cores are on GPU, the greater the performance s mproved. As shown n Fgure 3, the speedup rato over CPU seral versonrangesfrom20to40ongpus.theresultsalso ndcate that the fluctuaton of speedup rato s very small as the scale of MIDI database ncreases. To verfy whether the accelerated strategy affects the retreval accuracy, we evaluate the accuracy of our proposed parallel algorthm smultaneously. We selected 829 sngng clps from the corpus to test the performance. As shown =1 Table 2: Retreval results for dfferent methods. Method MRR Top-1 Top-3 Top-5 Top-10 Seral verson Parallel verson n Table 2, our proposed parallel algorthm almost does not affect the retreval accuracy. 6. Concluson and Future Work Ths paper presents a GPU-parallel melody accurate matchng method for query-by-hummng. The method uses two parallelzaton strateges (ntra-task parallelzaton and ntertask parallelzaton) to accelerate melody matchng. The expermental results show that our proposed method can obtan 20x to 40x speedups wthout reducng retreval accuracy. For future work, we wll further optmze the parallel program to mprove the performance. Second, we wll perform exhaustve comparson wth other QBH acceleraton methods. Conflct of Interests The authors declare that there s no conflct of nterests regardng the publcaton of ths paper. Acknowledgments Ths research was funded by the H-tech Research and Development Program of Chna (863 Program) under Grant no. 2011AA01A205, the Natonal Natural Scence Foundaton of Chna under Grant nos , , and , the Doctoral Fund of Mnstry of Educaton of Chna under Grant no , Bejng Natural Scence Foundaton undergrantno ,andthefundofthestatekey Laboratory of Software Development Envronment under Grant no. SKLSDE-2012ZX-23. References [1] A. Ghas, J. Logan, D. Chamberln, and B. C. Smth, Query by hummng: muscal nformaton retreval n an audo database, n Proceedngs of the 3rd Internatonal Multmeda Conference and Exhbton (MULTIMEDIA 95), pp , November [2] G.P.Nam,T.T.T.Luong,andH.H.Nam, Intellgentquery by hummng system based on score level fuson of multple classfers, EURASIP Journal on Sgnal Processng, vol. 2011, no. 21, pp. 1 11, [3] Q. Wang, Z. Guo, G. Lu, J. Guo, and Y. Lu, Query by hummng by usng localty senstve hashng based on combnaton of ptch and note, n Proceedngs of the IEEE Internatonal Conference on Multmeda and Expo, pp , [4] K. Km, K. R. Park, S.-J. Park, S.-P. Lee, and M. Y. Km, Robust query-by-sngng/hummng system aganst background nose envronments, IEEE Transactons on Consumer Electroncs,vol. 57, no. 2, pp , 2011.

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