Music Retrieval and Analysis

Music Retrieval and Analysis
Part I: Music Retrieval Arbee L.P. Chen National Tsing Hua University ISMIR’03 Tutorial III

Outline Technologies Systems and evaluation Future research directions
Architecture for Music Retrieval Music Representations Music query processing Music indexing Similarity measures Systems and evaluation Existing systems Meldex Themefinder SEMEX PROMS OMRAS System evaluation Future research directions

Architecture for Music Retrieval
Users Music Player Music Query Interface Query result Result music objects Music query Music Storage manager Music Feature Extractor Music Query Processor Music objects Music features Result music objects Music Database Music Index

Music Representations

Styles of Music Composition
Monophony Monophonic music has at most one note playing at any given time; before a new note starts the previous note must have ended Homophony Homophonic music has at most one set of notes playing at the same time. For any set of notes that start at the same time, no new note or notes may begin until every note in that set has ended Polyphony Polyphonic music has no such restrictions. Any note or set of notes may begin before any previous note or set of notes has ended

Monophony Representations
Absolute measure Absolute pitch C5 C5 D5 A5 G5 G5 G5 F5 G5 Absolute duration Absolute pitch and duration (C5,1)(C5,1)(D5,1)(A5,1)(G5,1)(G5,0.5)(G5,0.5)(F5,1)(G5,1) Relative measure Contour (in semitones) IOI (Inter onset interval) ratio Contour and IOI ratio (0,1)(+2,1)(+7,1)(-2,1)(0,0.5)(0,1)(-2,2)(+2,1)

Polyphony Representations
All information preservation Keep all information of absolute pitch and duration (start_time, pitch, duration) (1,C5,1)(2,C5,1)(3,D5,1)(3,A5,1)(4,F5,4)(5,C6,1)(6,G5,0.5)(6.5,G5,0.5)… Relative note representation Record difference of start times and contour (ignore duration) (1,0)(1,+2)(0,+7)(1,-4)… Monophonic reduction Select one note at every time step (main melody selection) (C5,1)(C5,1)(A5,1)(F5,1)(C6,1)... Homophonic reduction (chord reduction) Select every note at every time step (C5)(C5)(D5,A5)(F5)(C6)(G5)(G5)…

Music Representation - Theme
A short tune that is repeated or developed in a piece of music A small part of a musical work Efficient retrieval A highly semantic representation Effective retrieval Automatic theme extraction Exact repeating patterns Approximate repeating patterns

Music Representation – Markov Models
Capture global information for a music piece Repeating patterns Sequential patterns A lossy representation Good for music classification

Markov Model Representation
[Pickens and Crawford, CIKM‘02] Homophonic reduction For each chord, compute its distance with the 24 lexical chords Capture statistical properties by Markov models The representation of each song is reduced into a matrix

Markov Model Representation (Cont.)
Chord Markov model representation Lexical chords

Music Query Processing
On-line methods (string matching algorithms) Exact string matching Brute-force method KMP algorithm Boyer-Moore algorithm Shift-Or algorithm Partial string matching Approximate string matching Dynamic programming

Brute-Force Method T: A5 B5 A5 C5 A5 B5 A5 B5 P: A5 B5 A5 B5
Time complexity O(mn) A5 B5 C5 A5 B5 A5 B5 A5 B5 A5 B5 A5 B5

KMP Algorithm Left-to-right scan Failure function shift rule O(m+n) A5
B5 C5 A5 B5 Failure function f(i) A5 B5 Skip this step A5 B5 A5 B5 A5 B5

Boyer-Moore Algorithm
If the pattern P is relatively long and the alphabet is reasonably large, this algorithm is likely to be the most efficient string matching algorithm Right-to-left scan Bad character shift rule Good suffix shift rule O(m+n)

Bad Character Shift Rule
Right to left scan A5 B5 A5 B5 skip these steps A5 B5 A5 B5 A5 B5

Good Suffix Shift Rule Good suffix A5 C5 B5 A5 B5 A5 B5 Skip this step

Shift-Or Algorithm An example of the shift-or algorithm for p=aab and s=abcaaab T a b c a a b E S(E) T[a] E S(E) T[b] E S(E) T[c] E S(E) T[a] E S(E) T[a] E S(E) T[a] E S(E) T[b] E a b 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Shift-Or Algorithm for Partial Matching [Lemstrom and Perttu, ISMIR’00]
An example of the shift-or algorithm for p=aab and s=(ab)(ca)(aab) T a b c a a b E S(E) T[a]^T[b] E S(E) T[c]^T[a] E S(E) T[a]^T[a]^T[b] E a b 1 1 1 1 1 1

Approximate Matching In practical pattern matching applications, exact matching is not always suitable In the field of MIR, approximation is measured mainly by the edit distance: the minimal number of local edit operations needed to transform one music object into another Dynamic programming method serves this purpose

Edit Distance Unit cost edit distance
W(ab)=1, ab (Replacement) W(a   )=W( b)=1 (Deletion and Insertion) Non-unit cost edit distance (Content-sensitive) The costs of replacement, deletion and insertion can be any values which depend on the cost function E.g., W(mn)=0.2 and W(a  )=0.8

Dynamic Programming Method
Given any two strings S1=abac, S2=aaccb The edit distance evaluated by DP The edit distance is 3 a b c 1 2 3 4 5 a b a c c b (1 deletion, 2 insertions) a a c c b

Music Indexing Tree-based index (Suffix tree)
List-based index (1D-list) N-gram index Indexing Markov models?

Tree-Based Index [Chen, et al., ICME‘00]
Music objects are coded as strings of music segments Four segment types to model music contour Pitch and duration are considered Index structures Augmented suffix tree Both incipit/partial and exact/approximate matching can be handled

Tree-Based Index (Cont.)
Four segment types type A type B type C type D

Tree-Based Index (Cont.)
$ 3 $ B 2 $ An example suffix tree A 1-D augmented suffix tree 1 The suffix tree of the string S=“ABCAB”

List-Based Index [Liu, Hsu and Chen, ICMCS‘99]
Music objects are coded as melody strings “so-mi-mi-fa-re-re-do-re-mi-fa-so-so-so” Melody strings are organized as linked lists Both incipit/partial and exact/approximate matching can be handled Exact link, insertion link, dropout link, transposition link

List-Based Index (Cont.)

N-Gram Index A widely used technique in music databases
Target strings are cut into index terms by a sliding window with length N Index can be implemented by various methods, e.g., inverted file Queries are also cut into index terms with length N Searching and joining are then performed

N-Gram Index [Doraisamy and Ruger, ISMIR’02]
Query=bbca Cut into 2-grams S=aabbcaab bb, ca 2-Gram Position aa 1,6 ab 2,7 bb 3 bc 4 ca 5 Position: 3 Position: 5 Join Inverted file The substring is found from position 3 to position 6

Similarity Measures The effectiveness of MIR depends on the similarity measure Edit distance (Suitable for short queries) Difference between two probability matrices Note shift distance [Typke, et al., ISMIR‘03]

Probability Matrix Distance
0.5 1 0.25 S1: CCCAABCB S2: CCAAABCB A B C 0.7 0.3 1 Kullback-Liebler (KL) divergence: The value is 0 when two matrices are the same q: Query probability matrix d: Data probability matrix i: row x: column D(S1||S2)=0.1092

Probability Matrix Distance (Cont.)
Ineffective for MIR with short queries 0-entries in the query model mean unknown values? 0-entries in the corpus model means facts? Performance comparison with string matching needed

Note Shift Distance Sum of the two dimensional distance between the notes of the query and the notes of the answer

Music Retrieval Systems
Music Representations Music Query processing Special features

Meldex [McNab, et al., D-Lib Magazine‘97]
"melodic contour" or "pitch profile“  RUUDD (R:Repeat, U:Up, D:Down) Approximate string matching Dynamic programming Query by humming

Themefinder [Kornstadt, Computing in Musicology‘98]
Select themes manually Allow different query types Pitch Interval Contour Provide exact matching only

SEMEX [Lemstrom and Perttu, ISMIR’00]
The pattern is monophonic; the musical source is polyphonic Finding all positions of S (source) that have an occurrence of p p=bca S=<a, b, c><a, b><b, c><a, b> Shift-or algorithm No similarity function

PROMS [Clausen, et al., ISMIR‘00]
Representation by pitch and onset time (ignore duration) Index by inverted file Fault-tolerant music search Allow missing notes Allow fuzzy notes Query=(b, (d or c), a, b)

OMRAS [Dovey, ISMIR‘01] Searching in a “piano roll” model
Gaps based dynamic programming Example (gap = 2): Data T0=<64,72,76>, T1=<60>, T2=<59,67,79>, T3=<55,63>, T4=<55,67,79> Query S0=<59,67>, S1=<55,67> Piano roll T0 T1 T2 T3 T4 S0 2 1 S1

System Evaluation Traditional measures of effectiveness are precision and recall

The Recall-Precision Curve

A Platform for Evaluating MIR Systems
Evaluation of various music retrieval approaches Efficiency response time Effectiveness recall-precision curve The Ultima project builds such a platform [Hsu, Chen and Chen, CIKM’01] Same data set and query set for various approaches Compare recall-precision curves

The Ultima Project Data store Query generation module
Query processing module Result summarization module Report module Mediator

Future Research Directions
Music Retrieval based on music structure Music retrieval based on user’s perceptiveness Similarity measure for polyphonic music A novel index structure for polyphony Fair evaluation method

Music Retrieval and Analysis
Part II: Music Analysis

Outline Music Segmentation and Structure Analysis
Local Boundary Detection Repeating Pattern Discovery Phrase Extraction Music Classification Music Recommendation Systems Future Research Directions

Local Boundary Detection
[Cambouropoulos, ICMC’01] Segment music by local discontinuities between notes Calculate boundary strength values for each interval of a melodic surface, i.e., pitch, IOI, and rest, according to the strength of local discontinuities

Local Boundary Detection (Cont.)
A music object m has a parametric profile Pk, which is represented as a sequence of n intervals Pk = [x1, x2, …, xn] where k{pitch, IOI, rest} Pitch interval measured in semitones IOI and rest intervals measured in milliseconds or numerical duration values IOI (Inter onset interval) The amount of time between the onset of one note and the onset of the next note Rest The amount of time between the offset of one note and the onset of the next note IOI pitch rest

The degree of change r between two successive interval values xi and xi+1 is: The strength of the boundary si for interval xi is: Overall local boundary strength based on the three intervals wp*si(p)+wd*si(d)+wr*si(r)

Repeating Pattern Discovery
A repeating pattern in music data is defined as a sequence of notes which appears more than once in a music object The themes or motives are typical kinds of repeating patterns Exact repeating patterns [Hsu, Liu and Chen, TMM’01] By the string-join operator Approximate repeating patterns [Lartillot, ISMIR’03] By detecting when their successive notes are sufficiently close and their borders contrast sufficiently with the outer environment

Exact Repeating Pattern Discovery
{ 12(2), 23(3), 34(4), 45(3), 56(2) } 234(3) 345(3) 456(2) 123(2) { 1234(2), (2), (2) } Nontrivial repeating patterns S = 1234A2345B3456C123456 { }

Approximate Repeating Pattern Discovery
Stpe1 Find all note pairs (n1, n2) which satisfy the pitch distance constraint Step 2 Group the similar note pairs D((n1, n2), (n1’, n2’)) Step 3 Merge the adjacent note pairs for approximate repeating patterns (n1, n2)(n2,n3) : (n1,n2,n3) (n1’,n2’)(n2’,n3’) : (n1’,n2’,n3’)

Approximate Repeating Pattern Discovery (Cont.)
n1, n2 p1, p2 o1, o2 n1’, n2’ p1’, p2’ o1’, o2’  p = p2 – p1  p’ = p’2 – p’1  o = o2 – o1  o’ = o’2 – o’1 pi is the pitch value of ni oi is the onset time of ni D((n1, n2), (n1’, n2’)) = ( | p -  p’| + 1 ) * (max { o/  o’,  o’/  o }) 0.7

Phrase Extraction Two features used for phrase extraction
Duration and rest Melodic Shapes [Huron, Computing in Musicology’95] Statistics Information in Western Folksongs The most common length of a phrase is 8 notes Half of all phrases are between 7 and 9 notes in length Three-quarters of all phrases are between 6 and 10 notes in length

Phrase Extraction (Cont.)
A: the pitch value of the first note in the target phrase B: the pitch value of the last note in the target phrase C: the average pitch value of the remaining notes in the target phrase Contour Type Number of Phrases Percentage Arch Shape Definition Convex 13926 38.6% A<C  B<C Descending 10376 28.8% A>C>B Ascending 6983 19.4% ACB Concave 3496 9.7% A>C  B>C Others 1294 3.5%

Identify the positions of all the terminative notes Extract the music pieces according to the terminative notes Select the candidate music pieces for decomposition based on the length information If the length  12, the music piece is marked as a phrase If the length > 12, decompose the music piece into phrases convex > descending > ascending > concave

y z Here is an example to illustrate the process of phrase-based segmentation. Three terminative notes are identified in this example. The note Y is marked as a terminative note because a rest follows it. The note X and Z are marked as a terminative note because their duration exceed the given threshold. Then we can extract three music pieces. The length of the first music piece is equal to 12, so it is directly marked as a phrase. The length of the second music piece is 28, so we have to decompose this music piece into phrases. Since the length of a music phrase is limited from 6 to 12, we examine the prefix music fragments of the second music piece with length from 6 to 12, as shown in the following table. We check these prefix music fragments according to their length. First, we check whether the first fragment with length 6 has the convex shape. In the first fragment, the pitch values of the first note and last note are 64, and 67, respectively. The average pitch value of the remaining notes is 58.5. Recall the definition of the convex shape. The average pitch value of the remaining notes must larger than the pitches of the first note and the last note. Therefore, the first fragment does not have a convex shape. Then, we check the same condition for the fragments with length 7, 8 … to 12 until we find a fragment has a convex shape. After that, we find none of these fragments has the convex shape. So we start over again to check if any fragment in the table has the descending shape. Finally, we find that the last fragment satisfy the definition of the descending shape. As a result, the last fragment is marked as a phrase and is removed from this music piece. Here we can see that the these two phrases are similar which demonstrate that our approach is practical than others. Because the length of the remaining music piece is sixteen which is still longer than 122, we decompose it into phrases by using the same process. At last, three phrases are then extracted from the second music piece. The first two phrases have the descending shapes and the last one has the ascending shape. Order The Length of the Prefix Fragment The Pitch of the First Note The Pitches of the Remaining Notes The Pitch of the Last Note 1 6 64 62, 60, 57, 55 67 2 7 62, 60, 57, 55, 67 3 8 62, 60, 57, 55, 67, 67 69 4 9 62, 60, 57, 55, 67, 67, 69 5 10 62, 60, 57, 55, 67, 67, 69, 67 11 62, 60, 57, 55, 67, 67, 69, 67, 69 12 62, 60, 57, 55, 67, 67, 69, 67, 69, 64 62 Convex? No Descending? Length = 12, A = 64, B = 62, C = 63.7

Music Classification After music segmentation, different kinds of music units can be extracted from music objects, such as repeating patterns and phrases Different kinds of music units may have different semantics in musicology These extracted music units can be used in music classification, retrieval, and analysis

Music Recommendation Systems
[Chen and Chen, CIKM’01] The results of music classification can be used for music-related services By analyzing the user access histories, we can discover which music classes the users may be interested in and which users belonging to the same group By using different kinds of recommendation mechanisms, we can recommend the users the music objects

Architecture A polyphonic music object one melody track
other accompaniment tracks

Recommendation Mechanisms
Content-based filtering approach Similarity between music objects and user profiles Recommend the music objects that belong to the music groups the user is recently interested in Collaborative filtering approach Similarity between user profiles Provide unexpected recommendations to the users in the same user group Statistical approach Recommend “hot” music objects

Future Research Directions
Polyphonic Music Segmentation Efficient Approximate Repeating Pattern Discovery Representation and Similarity Measure for Musical Structures Musical Style/Form Detection

References [Camb01] Cambouropoulos, E., “The Local Boundary Detection Model (LBDM) and its Application in the Study of Expressive Timing,” Proc. International Computer Music Conference, 2001. [Chen00] Chen, A.L.P., M. Chang, J. Chen, J.L. Hsu, C.H. Hsu, and S.Y.S. Hua, "Query by Music Segments: An Efficient Approach for Song Retrieval," Proc. IEEE International Conference on Multimedia and Expo, 2000. [Chen01] Chen, H.C. and A.L.P. Chen, "A Music Recommendation System Based on Music Data Grouping and User Interests grouping and user interests," Proc. ACM International Conference on Information and Knowledge Management, 2001 [Clau00] Clausen, M., R. Engelbrecht, D. Meyer, and J. Schmitz, “PROMS: A Web-based Tool for Searching in Polyphonic Music,” Proc. International Symposium on Music Information Retrieval, 2000. [Dove01] Dovey, M.J., “A Technique for Regular Expression Style Searching in Polyphonic Music,” Proc. International Symposium on Music Information Retrieval, 2001.

References (Cont.) [Korn98] Kornstadt, A., “Themefinder: A Web-based Melodic Search Tool,” Computing in Musicology, 11: , 1998. [Dora02] Doraisamy, S. and S.M. Ruger, “A comparative and fault-tolerance study of the use of n-grams with polyphonic music,” Proc. International Symposium on Music Information Retrieval, 2002. [Hsu01] Hsu, J.L., C.C. Liu and A.L.P. Chen, "Discovering Nontrivial Repeating Patterns in Music Data," IEEE Transactions on Multimedia, Vol. 3, No. 3, 2001. [Hsu02] Hsu, J.L., A.L.P. Chen and H.C. Chen, "The Effectiveness Study of Various Music Information Retrieval Approaches," Proc. ACM International Conference on Information and Knowledge Management, 2002. [Huro95] Huron, D., “The Melodic Arch in Western Folksongs,” Computing in Musicology, Volume 10, 1995.

References (Cont.) [Lart03] Lartillot, O., “Discovering musical patterns through perceptive heuristics,” Proc. International Symposium on Music Information Retrieval, 2003. [Lems00]Lemstrom, K. and Sami Perttu, “SEMEX-An Efficient Music Retrieval Prototype,” Proc. International Symposium on Music Information Retrieval, 2000. [Liu99] Liu, C.C., J.L. Hsu, and A.L.P. Chen, "An Approximate String Matching Algorithm for Content-Based Music Data Retrieval," Proc. IEEE International Conference on Multimedia Computing and Systems, 1999. [Mcna97] McNab, R.J., L.A. Smith, D. Bainbridge, and I.H. Witten, “The New Zealand Digital Library: MELody inDEX,” D-Lib Magazine, 1997. [Pick02] Pickens, J., and T. Crawford, “Harmonic Models for Polyphonic Music Retrieval,” Proc. ACM Conference on Information and Knowledge Management, 2002.

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