Machine Perception of Music & Audio. Topic 9: Measuring Distance
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1 Machne Percepton of Musc & Audo Topc 9: Measurng Dstance Bran Pardo EECS 352 Wnter
2 Wh measure dstance? Clusterng requres dstance measures. Local methods requre a measure of localt Search engnes requre a measure of smlart Bran Pardo EECS 352 Wnter 2010
3 Dmenson 2 Eucldean Dstance What people ntutvel thnk of as dstance d Dmenson 1 Bran Pardo EECS 352 Wnter 2010
4 Generalzed Eucldean Dstance n = the number of dmensons d where n n n 1/ 2 } and Bran Pardo EECS 352 Wnter 2010
5 L p norms L p norms are all specal cases of ths: d n 1 p 1/ p p changes the norm 1 L 1 norm Manhattan Dstance: p 1 2 L 2 norm Eucldean Dstance: p 2 Hammng Dstance: p 1and 01 Bran Pardo EECS 352 Wnter 2010
6 Weghtng Dmensons Put pont n the cluster wth the closest center of gravt Whch cluster should the red pont go n? How do I measure dstance n a wa that gves the rght answer for both stuatons? Bran Pardo EECS 352 Wnter 2010
7 Weghted Norms You can compensate b weghtng our dmensons. d n 1/ w p 1 p Ths lets ou turn our crcle of equal-dstance nto an elpse wth aes parallel to the dmensons of the vectors. Bran Pardo EECS 352 Wnter 2010
8 What s a metrc? A metrc has these four qualtes. otherwse call t a measure nequalt trangle smmetr non - negatve 0 reflev t ff 0 z d z d d d d d d Bran Pardo EECS 352 Wnter 2010
9 Metrc or not? Drvng dstance wth 1-wa streets Categorcal Stuff : Is dstance Jazz to Blues to Rock no less than dstance Jazz to Rock? Bran Pardo EECS 352 Wnter 2010
10 Categorcal Varables Consder feature vectors for genre & vocals: Genre: {Blues Jazz Rock Zdeco} Vocals: {vocalsno vocals} s1 = {rock vocals} s2 = {azz no vocals} s3 = { rock no vocals} Whch two songs are more smlar? Bran Pardo EECS 352 Wnter 2010
11 One Soluton:Hammng dstance Blues Jazz Rock Zdeco Vocals s1 = {rock vocals} s2 = {azz no_vocals} s3 = { rock no_vocals} Hammng Dstance = number of bts dfferent between bnar vectors Bran Pardo EECS 352 Wnter 2010
12 Hammng Dstance Bran Pardo EECS 352 Wnter 2010 {01} and } where n n n d
13 Defnng our own dstance an eample How often does artst quote artst? Quote Frequenc Beethoven Beatles Lz Phar Beethoven Beatles Lz Phar? 1 2 Let s buld a dstance measure! Bran Pardo EECS 352 Wnter 2010
14 Defnng our own dstance an eample Beethoven Beatles Lz Phar Beethoven Beatles Lz Phar? 1 2 Quotefrequenc Q Dstance d 1 f value n table Q f Q zartsts f z Bran Pardo EECS 352 Wnter 2010
15 Mssng data What f for some categor on some eamples there s no value gven? Approaches: Dscard all eamples mssng the categor Fll n the blanks wth the mean value Onl use a categor n the dstance measure f both eamples gve a value Bran Pardo EECS 352 Wnter 2010
16 Dealng wth mssng data n n w n n d w 1 1 else 1 are defned and both f 0 Bran Pardo EECS 352 Wnter 2010
17 Edt Dstance Quer = strng from fnte alphabet Target = strng from fnte alphabet Cost of Edts = Dstance Target: C A G E D - - Quer: C E A E D
18 Tpcal Melodc Search Sstem Quer Database Themes Targets Sgt. Pepper s Smlart Ranker Yesterda Ranked Lst
19 Wh Monophonc Themes? Audo Document Theme 1 Theme 3 Theme 2 PROBLEM Smlart rankers tpcall requre monophonc nput
20 Smlart Rankng b Edt Dstance Quer = strng Target = strng Cost of Edts = Dstance Target: C A G E D - - Quer: C E A E D
21 Local Strng Algnment 0 ma q s M s M q M M M -1-1 M -1 M -1 M Insert Delete Match Restart
22 Local Strng Algnment S Q ma M SIMILARITY THEME QUERY G A B B G D A C B
23 Md Ptch Melod Transcrpton Sung quer Segmented quer Short Gltch Notes Seconds Ptch Quantzaton Errors musc.
24 Melod Encodng Transcrpton Encodng up 2 half-steps { } 2 nd s ½ length of 1 st note Ptch nterval and rhthm rato Tempo and transposton nvarant Smplfes error modelng musc.cs.northwestern.edu
25 Response Ptch Interval Modelng Snger Varaton se I nterval Respon Ascendng Maor 6 th 50 stmulus-response pars Stmulus Ptch Interval In ½ steps 12 to an octave Stmulus 1 Response 1 Stmulus 2 Response 2
26 Ma sngle-part smlart S Q ma P Q Song Smlart = MAXPart Smlart QUERY PS SCORE
27 Oops! QUERY Cheap Knock-off To God on Hgh Glor Be
28 Oops! QUERY Cheap Knock-off To God on Hgh Glor Be
29 Oops! QUERY Cheap Knock-off To God on Hgh Glor Be
30 Homophonc Smlart SCORE QUERY M -1-1 M -1 M -1 M
31 Homophonc Algnment 0 ma q s M s M q M M Insert Delete Match Restart ma n C n C H REPLACES
32 Skppng Between Parts Quer Score To God On Hgh All Glor Be
33 Polphonc Algnment Part k+1 L -1-1k+1 Part k L -1-1k L L -1lk+1-1k Part k-1 L -1-1k-1 L -1k L k L -1k-1
34 Polphonc Algnment 0 ma k l k l p q L k l k l p L p q L p L q L L k l k l k k k k k k Insert Delete Match Restart Shft Shft CHANGE-PART COST
35 Makng monophonc parts Part 1 notebt Part 2 note
36 Makng monophonc parts Part 1a Part 1b Part 2a Part 2b Part 2c
37 TARGET DATABASE Eperment 300 Bach 4-part vocal chorale harmonzatons QUERIES 5 to 25 notes n length Skp between parts wth a probablt of: Queres per condton COMPARE Mamal sngle-part smlart Polphonc smlart
38 Mean rank of correct target Results Mamum sngle-part smlart Polphonc algnment Per-note probablt of changng parts n quer
39 Number of queres Number of queres Ppart change = Polphonc algnment Mamum sngle-part smlart Rank of correct target rght rank
40 Conclusons Standard sequence algnment fals when queres skp from part to part We etend strng-matchng to handle ths case Ths mproves search performance
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