Spring-2008MMDB-Audio 1 Audio Databases

Spring-2008 MMDB-Audio 2 Metadata Using metadata to represent audio content is done in a very similar way as we did for video. The metadata used to represent audio content may be viewed as a set of objects spread out cover a time line. We may index the metadata associated with audio in exactly the same way as we indexed video, and the same query-processing techniques may be used over again.

Spring-2008 MMDB-Audio 3 Example: The following figure shows the line segments associated with part of an opera. Activity1 may be Act 1 of the opera, activity2 may be Act 1, Scene 1, and so on.

Spring-2008 MMDB-Audio 4 Example: (conti.) Each activity may have an associated set of fields.  Singers: It may be a set valued field containing records having a Role, SingerType and SingerName. If the triple (Lohengrin, Tenor, Rene Kollo) appears in the segment [50, 100), Rene Kollo, a tenor, is singing the role of Lohengrin during the time segment [50, 100) of the opera.  Score: It may be a field of type music_doc which points to a relevant part of the music score associated with the time segment [50, 100).  Transcript: It may be a field of type document that points to the relevant part of the libretto during the time segment [50, 100).

Spring-2008 MMDB-Audio 5 Signal-Based Audio Content In some applications, creation of metadata is somewhat complex, speaker unknown or content unclear. Audio data is considered as a signal,  (x), over time x. Different features of the signal  are extracted, indexed and stored for efficient retrieval. Metadata may still be used to complement the signal data.

Spring-2008 MMDB-Audio 6 Sample Audio Signals

Spring-2008 MMDB-Audio 7 Signal Period of vibration, T = time taken for a “particle” in the wave to return to its starting position, ex. from point A to point B. Frequency of vibration, f = number of vibrations per second. f = 1/T. Velocity, v = the speed of the crests and troughs move to the right. v= w/T = w  f, where w denotes the wavelength of the wave. Amplitude, a = the maximum intensity of the signal associated with the wave.

Spring-2008 MMDB-Audio 8 Indexing by Segmentation Split up the audio signal into relatively homogeneous “windows.” This may be done in one of two ways:  Application developer can specify, a priori, a window size w (in sec. or min.), and assume that the wave’s properties within that window are obtained by averaging.  Use a homogeneity predicate as in the case of images, except that this homogeneity predicate applies to the one-dimensional case..

Spring-2008 MMDB-Audio 9 Windowing Using audio signal The following figure shows a nonhomogeneous audio signal. After split into five windows, each window is homogeneous in the sense that it has a constant amplitude, wavelength, and wave velocity.

Spring-2008 MMDB-Audio 10 Indexing Using Feature Extraction After segmentation, the audio signal may be viewed as a sequence of n windows, w 1, …, w n. For each window, we extract some features associated with the audio signal. If k features are extracted, then an audio signal may be considered to be a sequence of n points in a k-dimensional space.

Spring-2008 MMDB-Audio 11 Example Features Intensity(I): the power of the signal generated by the wave (in Watts per square meters). Where  is the density of the material through which the sound is being propagated. Loudness(L): Where L 0 denotes the loudness with the lowest frequency (about 15Hz) that a human ear can detect.

Spring-2008 MMDB-Audio 12 Content Index In general, to index the content of an audio signal, we proceed with the following two step: 1.Find a set w 1, …, w n of window segments. 2.For each window w i, store a vector consisting of K acoustical attributes. An audio database may be viewed as a set of (K+3)-tuples consisting of the audio source (audio file), the window (within that audio file), the duration of the window, and the K feature values associated with that window. A k-d tree can be used to index audio data.

Spring-2008MMDB-Audio 13 Content-based Retrieval for Music Databases

Spring-2008 MMDB-Audio 14 Introduction The management of large collections of music data in a multimedia database has received much attention in the past few years. For music content-based retrieval, we can extract the features, such as melodies, rhythms and chords, from the music data and develop indices that will help to retrieve the relevant music data quickly.

Spring-2008 MMDB-Audio 15 Music Feature string Ex: “ sol-do-re-mi-mi-mi-mi-re-mi-do-do” Melody feature string:eabccccbaa Rhythm string: Music feature sting:e 1 a 1 b 1 c 2 c 2 c 1 c 1 b 1 a 2 a 2 A sample of “You Are My Sunshine”

Spring-2008 MMDB-Audio 16 Features of Music Data Coding scheme: a music object  a sequence of music segments  music segment = (segment type, segment duration, segment pitch)  four segment types: ┌┐(type A), └┘(type B), ┌┘(type C), and └┐(type D)

Spring-2008 MMDB-Audio 17 Features of Music Data For example, the sequence of music segments: (B,3,-3) (A,1,+1) (D,3,-3) (B,1,-2) (C,1,+2) (C,1,+2) (C,1,+1)

Spring-2008 MMDB-Audio 18 music segment = (type, duration, pitch)

Spring-2008 MMDB-Audio 19 Music Data Retrieval: System Architecture

Spring-2008 MMDB-Audio 20 Indexing String Indexing for music data  Suffix tree Numeric Indexing for music data  R-tree

Spring-2008 MMDB-Audio 21 Suffix tree A suffix tree is an index structure that has been proposed to locate strings that are exactly matched to a target string. No two edges out of a node can have edge-labels beginning with the same character. For any leaf i, the concatenation of the edge-labels on the path from the root to leaf i exactly spells out the suffix of string that starts at position i.

Spring-2008 MMDB-Audio 22  1 ababc 1 2 babc Ex:ababc {ababc,babc,abc,bc,c}  ab 2 babc 1 abcc 3  b 1 ab c 3 abc 4 2 c  14 abb c 3 abc 2 c 5 c

Spring-2008 MMDB-Audio 23 Ex:”Do Re Do Re Mi” →ababc a b a a c c b c

Spring-2008 MMDB-Audio 24 Numeric Mapping Numeric Mapping Function  v(m):the integer value of segment of m adjacent notes  m: adjacent notes from melody feature string  P(x i ):the integer value of each note  1  i  m

Spring-2008 MMDB-Audio 25 Numeric Mapping (Con.) For example: A music feature string denoted by ‘bcdbc’, n=10, m=4 b c d b c =   b c d b =   c d b c

Spring-2008 MMDB-Audio 26 Example: two tigers (S 1 : Do Re Mi Do Do Re Mi Do) MelodyMusic SegmentV(4)Integer value abcaabcaabca 0* * * *  bcaa 1* * * * caab 2* * * * aabc 0* * * * abca 0* * * *  The integer value of music of two tigers.

Spring-2008 MMDB-Audio 27 Numeric Indexing Structure (R-Tree) (21,2110) s12 NULL s11 3 NULL s14 NULL s15 NULL Non-leaf Node Leaf Node Link List

Spring-2008 MMDB-Audio 28 Pitch Change abca→bcdb─ 》 1,1,-2  m: adjacent notes from melody feature string  Adj: the maximum value of distance of two pitches  D: the total number of distances of pitches

Spring-2008 MMDB-Audio 29 Example: “abcaabca” Suppose: m=10, Adj=9, D=19 Music Segment valueV(4) Integer value ,10, 710* * *  , 7, 910* * * ,9,107* * * ,10, 109* * * ,10, 710* * * 

Spring-2008 MMDB-Audio 30 Numeric Index  2726,2727)  3392,3809) s22 NULL s NULL s15 NULL s23 NULL s21 NULL

Spring-2008 MMDB-Audio 31 Searching in Numeric Index Exact Matching  For example: Music query segment is ‘ccdbb’  {ccdbb}→{ccdb} →{cdbb} V(4) {1322} V(4) {1132}

Spring-2008 MMDB-Audio 32  21,1002)  1132,1322)  2110,3224) s12 NULL s11 3 NULL s23s33 NULL s22s14 NULL s32 NULL s21 NULL s31 NULL s34 NULL s15 NULL 1132 s23 s34 NULL 1322 s22 s31 NULL Non-leaf Node Leaf Node Link List  1132,1322) {s2,s3}  {s2,s3}→ {s2,s3} position_s2  2,3),position_s3  1,4) →s2.

Spring-2008 MMDB-Audio 33 Approximate Searching <= h  n 0 <= h  n 1  a multiple of n 1 <= h  n 2  a multiple of n 2 … <= h  n m-1  a multiple of n m-1 n: the number of pitches m: adjacent notes from melody feature string h: the distance of two pitches We can examine the difference between the transformed value of the query string and existing data.

Spring-2008 MMDB-Audio 34 Example:  1) <= 1  10 0  2) <= 1  10 1  a multiple of 10 1  3) <= 1  10 2  a multiple of 10 2  4) <= 1  10 3  a multiple of 10 3 Approximate matching conditions for m=4, n=10,h=1 Ex: b b c d a b c d

Spring-2008 MMDB-Audio 35 Multi-Feature indexing Combine Suffix tree Independent Suffix tree Twin Suffix tree Grid-Twin Suffix tree Numeric Index Hybrid Multi-feature Index

Spring-2008 MMDB-Audio 36 Combine Suffix Tree Ex:”a 1 a 2 b 1 →{12,7}” “121→{12,7,1,6…}” The feature strings are directly used to construct the index in the index structure Combined Suffix Tree.

Spring-2008 MMDB-Audio 37 Independent Suffix Tree constructed from “a 1 b 2 a 1 b 2 c 2 ” (Melody:ababc) (Rhythm:12122) The Independent Suffix Trees separates the feature strings into a melody and a rhythm string and stores them in two independent suffix trees.

Spring-2008 MMDB-Audio 38 Twin Suffix Tree Twin Suffix Tree is constructed by adding additional information to the Independent Tree. This index structure consists of a melody and a rhythm suffix tree with links pointing.

Spring-2008 MMDB-Audio 39 Twin Suffix Tree The Twin Suffix Tree constructed from “a 1 b 2 a 2 b 1 a 2 b 2 c 2 ”

Spring-2008 MMDB-Audio 40 Grid-Twin Suffix Tree Use a hash function to map each suffix of the feature string into a specific bucket of a 2D grid. The hash function uses the first n symbols of the suffix to map it into a specific bucket.

Spring-2008 MMDB-Audio 41 Grid-Twin Suffix Tree ”a1b2a2c1a3””a1b2a2c1a3”

Spring-2008 MMDB-Audio 42 Condensed Grid-Twin Suffix Tree

Spring-2008 MMDB-Audio 43 Condensed Grid-Twin Suffix Tree “abaca” “caaca” entry Music ID entry Music ID

Spring-2008 MMDB-Audio 44 Multi-Feature Numeric Indexing for Music Data rhythm Melody:“a 1 b 1 c 1 a 1 ” melody

Spring-2008 MMDB-Audio 45 Multi-Feature Numeric Indexing for Music Data Non- Leaf Node Leaf Node Link List

Spring-2008 MMDB-Audio 46 Multi-Feature Numeric Indexing for Music Data melody rhythm chord 500

Spring-2008 MMDB-Audio 47 Hybrid Multi-Feature Index Using a multi-feature tree structure instead of grid structure in GTST. (2, 3) (3, 5) (6, 2) (5, 5) (4, 3.75) (1, 1) (1.5, 2 )

Spring-2008 MMDB-Audio 48 Suffix Trees with Bit Arrays Instead of the links between corresponding feature nodes in Twin Suffix Tree, the bit arrays are created to indicate the relationships between suffix trees.

Spring-2008 MMDB-Audio 49 Feature Extraction of Music Data We can find some sequence of notes appeared more than one time in a music object, which are called the repeating patterns. A lot of researches in musicology and music psychology consent that the repeating pattern is one of general features in music structure modeling.

Spring-2008 MMDB-Audio 50 Repeating Patterns of Music Data Repeating patterns: In string S, there is a sub-string appearing more than once and its length being equal to or greater than 2. Non-trivial repeating patterns: The frequency of the repeating pattern X appearing in the string S is more than it is appearing in any other repeating patterns. Fault tolerant non-trivial repeating patterns: It allows the sequences with partial different notes being as in the same non-trivial repeating pattern.

Spring-2008 MMDB-Audio 51 Example: RP C-D-E-FC-D-ED-E-F C-DD-E Freq23233 RPE-FCDEF Freq23332 non-trivial: freq(“C-D-E-F”) = freq(“D-E-F”) = freq(“E-F”) = freq(“F”) =2 freq(“C-D-E”) = freq(“C-D”) = freq(“D-E”) = freq(“C”) =freq(“D”) = freq(“E”) = 3. ===>only “C-D-E-F” and “C-D-E” are non-trivial. Consider the melody string “C-D-E-F-C-D-E-C-D-E-F”, this melody string has ten repeating patterns

Spring-2008 MMDB-Audio 52 Music Feature Extractions Correlative Matrix FastPET RP-Tree 2RC Similar Non-trivial Repeating Pattern Fault Tolerance Non-trivial Repeating Patterns

Spring-2008 MMDB-Audio 53 CORRELATIVE MATRIX The correlative matrix of the string S=“CAACCAACDCBC" There are four cases to set CS : 1.T i,j =1 and T (i+1),(j+1) = 0 T 1,4 =1 and T 2,5 =0 ---> insert CS=("C",1,0) 2.T i,j =1 and T (i+1),(j+1) ≠ 0 T 1,5 =1 and T 2,6 ≠0 ---> modify to CS=("C",2,1) 3.T i,j >1 and T (i+1),(j+1) ≠ 0 T 2,6 =2 and T 3,7 ≠0 --> insert CS=("CA",1,1),("A",1,1) 4.T i,j >1 and T (i+1),(j+1) = 0 T 4,8 =4 and T 5,9 =0 ---> insert CS=("CAAC",1,0),("AAC",1,1),("AC",1,1) change ("C",6,1) into ("C",7,2) CS=candidate set ==> CS(pattern,rep_count,sub_count)

Spring-2008 MMDB-Audio 54 CORRELATIVE MATRIX (cont.) There are two more tasks we have to do : 1.If a repeating pattern is a substring of another repeating pattern, and their repeating are the same, it will be removed from the candidate set CS. EX:("CA",1,1),("CAA",1,1),("AA",1,1),("AAC",1,1) and ("AC",1,1) are be moved since they are all the substring of the repeating pattern ("CAAC",1,0) 2.We should calculate the real repeating frequency for every repeating pattern found. EX: "C" = rep_count= f =

Spring-2008 MMDB-Audio 55 RP-TREE The RP-tree for the music feature string S=“ABCDEFGHABCDEFGHIJABC” {ABCDEFGH,2,(1,9)} {ABCD,2,(1,9)}{BCDE,2,(2,10)}{CDEF,2,(3,11)}{DEFG,2,(4,12)}{EFGH,2,(5,13)} {AB,3,(1,9,19)}{BC,3,(2,10,20)}{CD,2,(3,11)}{DE,2,(4,12)}{EF,2,(5,13)}{FG,2,(6,14)}{GH,2,(7,15)} {A,3,(1,9,19)}{B,3,(2,10,20)}{C,3,(3,11,21)}{D,2,(4,12)}{E,2,(5,13)}{F,2,(6,14)}{G,2,(7,15)}{H,2,(8,16)}

Spring-2008 MMDB-Audio 56 RP-TREE (cont.) {ABCDEFGH,2,(1,9)} {AB,3,(1,9,19)} {BC,3,(2,10,20)} (a) {AB,3,(1,9,19)} {BC,3,(2,10,20)} {ABCDEFGH,2,(1,9)} {ABC,3,(1,9,19)} (b) {ABCDEFGH,2,(1,9)} {ABC,3,(1,9,19)} (c)

Spring-2008 MMDB-Audio 57 FastPET: Fast Pattern Extracting Technique abcdbcdabcabcd a- 1 1 b c d b c d - 3 a - 1 b - 2 c - 3 a - b - c - d - Correlative Matrix for “abcdbcdabcabcd” i j

Spring-2008 MMDB-Audio 58 FastPET (cont.) abcdbcdabcabcd a- 1 1 b c d … d ‘abc’ P[8] = {3},P[11] = {3} PatternSet = {{‘abc’,3}}

Spring-2008 MMDB-Audio 59 FastPET (cont.) abcdbcdabcabcd a- b c d b … … d P[8] = {3},P[11] = {3, 4} PatternSet = {{‘abc’,3},{‘abcd’, 2}}

Spring-2008 MMDB-Audio 60 FastPET (cont.) i Non-trivial repeating pattern bcabcbcdabcd Frequency4332 Pattern Length2334 Starting position 2,5,9,121,8,112,5,121,11 P[5] = {3}, P[8] = {3},P[9] = {2}, P[11] = {3, 4},P[12] = {3} PatternSet = {{‘bc’, 4}, {‘abc’,3}, {‘bcd’, 3}, {‘abcd’, 2}} j Non-trivial RP for ’abcdbcdabcabcd’

Spring-2008 MMDB-Audio 61 2RC (Two-Row Comparsion) abcdbcdabcabcd a111  2RC can provide memory saving, O(n).  Example ： S=“abcdbcdabcabcd” Row A i=

Spring-2008 MMDB-Audio 62 2RC (cont.) abcdbcdabcabcd a111 b2122 Row A Row B i=2

Spring-2008 MMDB-Audio 63 abcdbcdabcabcd b2122 c3233 Row A Row B i=3 2RC (cont.)

Spring-2008 MMDB-Audio 64 abcdbcdabcabcd c3233 d434 Row A Row B PatternSet={{“abc”,3}} i=4 2RC (cont.)

Spring-2008 MMDB-Audio 65 True suffix tree approach for non-trivial repeating pattern discovering (TRP) Step 1. constructing suffix tree by adding a stop symbol ‘#’ into the tail of string S. Step 2. finding out repeating patterns. Step 3. pattern sweeping..

Spring-2008 MMDB-Audio 66 Example 1 - Step 1 of TRP 3 root 2bcdabcabcd# 12# 5 abcabcd# d 9 abcd# bc 6 abcabcd# bcdabcabcd# 13 # d 10 abcd# c 4 bcdabcabcd# 7 abcabcd# 14 # d 8 1 bcdabcabcd# 11 # abcd# dabc True suffix tree of S=“abcdbcdabcabcd#”.

Spring-2008 MMDB-Audio 67 Example 1 - Step 2 of TRP Repeating patternsabcdabcbcdcdbc Frequency23334 Pattern Length43322 Starting position1,111,8,112,5,123,6,132,5,9,12 All repeating patterns of music object S – “abcdbcdabcabcd”.

Spring-2008 MMDB-Audio 68 Example 1 - Step 3 of TRP Repeating patternabcdabcbcdcdbc Pattern Length43322 Starting position1,111,8,112,5,123,6,132,5,9,12 Ending positions4, 143, 10, 134, 7, 14 3, 6, 10, 13 Scopes of repeating pattern 1~4 11~14 1~3 8~10 11~13 2~4 5~7 12~14 3~4 6~7 13~14 2~3 5~6 9~10 12~13 Pattern sweeping for music object S – “abcdbcdabcabcd”. Non-trivial repeating patterns

Spring-2008 MMDB-Audio 69 Example 2 - TRP Repeating patternsLengthFrequency Scope aa29 1~2 aaa38 1~3 aaaa47 1~4 aaaaa56 1~5 aaaaaa65 1~6 aaaaaaa74 1~7 aaaaaaaa83 1~8 aaaaaaaaa92 1~9 Non-trivial repeating pattern Pattern sweeping for repeating patterns of S = “aaaaaaaaaa”.

Spring-2008 MMDB-Audio 70 Fault Tolerant Non-trivial Repeating Pattern Discovering Step 1. Constructing Suffix Tree Step 2. Creating Repeating Pattern Table Step 3. Greedy Concatenating Repeating Patterns Step 4. Exacting Fault Tolerant Non-trivial Repeating Patterns

Spring-2008 MMDB-Audio 71 Step 2 of FTRP RP Table RP abcbcbcbccbc Length 543 Start 1,62,73,8 End 1+5-1= = = = = =10 Scope 1~5 6~10 2~5 7~10 3~5 8~10 Creating Repeating Pattern Table

Spring-2008 MMDB-Audio 72 Step 3 of FTRP Greedy Concatenating Repeating Patterns Position Notebcfdaehgbcdae RP fault 1fault 0 bc?dae RP bcdae Scope 1~2, 9~10 4~6, 11~13

Spring-2008 MMDB-Audio 73 Step 4 of FTRP FTRPbc?dae Scope1~69~13 RPbcdae Scope1~2,9~104~6,11~13 “bc” and “dae” are all in “bc?dae” Exacting Fault Tolerant Non-trivial Repeating Patterns

Spring-2008 MMDB-Audio 74 Performance Study The Effect on Repeating Pattern Found

Spring-2008 MMDB-Audio 75 Hit Ratio Improvement