Setting shape rules for handprinted character recognition

IScIDE 2013Beijing

Syntactic sensitive complexity for symbol-free sequenceBo-Shiang Huang, Daw-Ran Liou, Alex A. SimakCheng-Yuan LiouNational Taiwan UniversityDept. of Computer Science and Information Engineering Symbols Piano Sonata No. 16 in C major, K.545, by Mozart mov 2

Influenza A virus H7N9 5MEQEQDTPWTQSTEHINTQKKESGQRTQRLEHPNSIQLMDHYLRTTSRVGMHKRIVYWKQWLSLKNLTQGSLKTRVSKRWKLFSKQEWIN

(A/Shanghai/02/2013(H7N9))Segment: PB1-F2 proteinProtein ID: AGL44435 Length: 90 AA

Languages6 ,

Transmission bits7 .. 01110010010101

Time series A: maximal V: minimal U: up D: down

Oil price (Dubai, 52 week records of 2012)AVUDSymbols9BitsCharactersWordsFeaturesMeaningsConcepts..

Introduction and review Complexity of L-system (2011)

Complexity of symbol sequence

10Lindenmayer system (1968)Powerful system used to model the growth processes of plants.11Lindenmayer system (1968)G=(V, , P) V: alphabets: the initial state of systemP: parallel rewriting rules; mapping P: V V* .

12variables: A , Bstart: Arules: (A AB), (B A)

n= 0: A n= 1: AB n= 2: ABA n= 3: ABAAB A / \ A B / | \ A B A / | | | \ A B A A BKoch snowflake graphVariables: F, +, - Start: F--F--FRules: FF+F--F+F 14 n=0 n=1 n=2Lindenmayer systemContext-free grammar can be used to build a tree.15Context-free grammartreeFF+F--F+F (bracket strings)

Lindenmayer systemCan we deconstruct a tree to context-free grammars?16treeContext-free grammar?Deconstruction of tree

17Rewriting rules P [-FTL][+FTR]TR [-FTRL][+FTRR]TL nullTRL nullTRR nullPTL TRTRL TRRBracketed strings of tree19[ FP ][-FTL] [+FTR][-FTRL] [+FTRR] [FP[-FTL][+FTR [-FTRL][+FTRR]]]Context-free grammar20 [FP[-FTL][+FTR [-FTRL][+FTRR]]]P [-FTL][+FTR]TR [-FTRL][+FTRR]TL nullTRL nullTRR null[ FP ][-FTL] [+FTR][-FTRL] [+FTRR]Every non-terminal node can be rewritten as: PLRAbbreviation21 [FP[-FTL[-FTLL][-FTLR]][+FTR [-FTRL][+FTRR[-FTRRL][+FTRRR[-FTRRRL]]]]]P [-FTL][+FTR]TL [-FTLL][+FTLR]TR [-FTRL][+FTRR]TRR [-FTRRL][+FTRRR]TRRR [-FTRRRL]TLL nullTLR nullTRL nullTRRL nullTRRRL null [-F][+F] [-F][+F] [-F][+F] [-F][+F] [-F] null null null null nullClassificationReasonThere are too many rules.Some of them are similar to each other.22P [-FTL][+FTR] [-F][+F]TL [-FTLL][+FTLR] [-F][+F]TR [-FTRL][+FTRR] [-F][+F]TRR [-FTRRL][+FTRRR] [-F][+F]TRRR [-FTRRRL] [-F]TLL null nullTLR null nullTRL null nullTRRL null nullTRRRL null nullClassification method 1Homomorphism

23P [-FTL][+FTR] [-F][+F]TL [-FTLL][+FTLR] [-F][+F]TR [-FTRL][+FTRR] [-F][+F]TRR [-FTRRL][+FTRRR] [-F][+F]TRRR [-FTRRRL] [-F]TLL null nullTLR null nullTRL null nullTRRL null nullTRRRL null nullIsomorphismClassification method 2Isomorphism Level 0 Level 1 Level 2

25ClassificationCombine homomorphism and isomorphism26P [-FTL][+FTR] [-F][+F]TL [-FTLL][+FTLR] [-F][+F]TR [-FTRL][+FTRR] [-F][+F]TRR [-FTRRL][+FTRRR] [-F][+F]TRRR [-FTRRRL] [-F]TLL null nullTLR null nullTRL null nullTRRL null nullTRRRL null null (1)Class 3 C3C34 (1)Class 3 C1C1 (1)Class 3 C1C3 (1)Class 3 C1C2 (1)Class 2 C1 (5)Class 1 nullComplexity formula (2011) 1String to context-free grammar28 [FP[-FTL][+FTR [-TRL][+FTRR]]]V1 V2V3V4V2 V2V3V3 V1V4 V3V2V3

Deconstruction procedure29Symbol sequenceTree Context-free grammar (bracketed strings)

Classification (levels)Complexity

Psychological complexity

30

Complexity of Music (2011)31One musical note can be divided into two or three sub units.

A half note can be rewritten into dierent notes.

Musical tree of Beethoven's Piano Sonata No. 6, Mov. 3.

Music tree of Rachmaninos piano concerto No.3 mov.

Bracketed strings for two trees.

Bracketed String of Beethoven Piano Sonata no 6. mov. 3

Bracketed strings for each node of rhythmic tree in Beethoven Piano Sonata no 6. mov. 3. (2 bracketed strings omitted)

Bracketed string of Rachmaninos piano concerto No.3 mov.1

Mozarts 19 Piano Sonatas, using isomorphic level 1

Mozarts 19 Piano Sonatas, using isomorphic level 2

Mozarts 19 Piano Sonatas, using isomorphic level 3

Beethovens 32 Piano Sonatas, using isomorphic level 1

Beethovens 32 Piano Sonatas, using isomorphic level 2

Beethovens 32 Piano Sonatas, using isomorphic level 3

Complexity of DNA sequence(2013)46Computation procedure47DNA sequenceDNA treeContext-free grammarClassificationComplexityTree representation48AATTCCGGACTGCAGT?Tree representation49A C T GBuilding tree50A A T T C CG G A C T G C A G TA C T GClassification tableClassification of RulesIsomorphic Level #0Isomorphic Level #1Class #1(19) C1 C1C1( 8) C1 C1C1( 4) C1 C1C2( 1) C1 C1C3( 4) C1 C2C1( 1) C1 C2C2(20) C1 C2C2( 1) C1 C2C4( 1) C1 C3C1( 1) C1 C3C3( 1) C1 C4C2( 5) C1 C4C4Class #2(48) C2 null( 4) C2 C4C5Class #3( 4) C3 C5C4Class #4(20) C4 C5C5Class #5(48) C5 null51Classification of RulesCountIsomorphic Depth #1Class #119( 8) C1 C1C1( 1) C1 C1C3( 1) C1 C2C2( 1) C1 C2C4( 1) C1 C3C1( 1) C1 C3C3( 1) C1 C4C2( 5) C1 C4C4Class #24( 4) C2 C4C5Class #34( 4) C3 C5C4Class #420(20) C4 C5C5Class #548(48) C5 nullComplexity V5(z) = 1 (definition) V4(z) = (z x ((20 x V5(z) x V5(z)))) / 20 = z V3(z) = (z x (( 4 x V5(z) x V4(z)))) / 4 = z2 V2(z) = (z x (( 4 x V4(z) x V5(z)))) / 4 = z2 V1(z) = (z x (( 8 x V1(z) x V1(z)) + ( 1 x V1(z) x V3(z)) + ( 1 x V2(z) x V2(z)) + ( 1 x V2(z) x V4(z)) + ( 1 x V3(z) x V1(z)) + ( 1 x V3(z) x V3(z)) + ( 1 x V4(z) x V2(z)) + ( 5 x V4(z) x V4(z)))) / 1952Ebola virus53

Complexity of H7N9 PB1-F2 Complexity of text sequence Using 1 to 27 (5 bits) to represent alphabets plus space character. (BIN)

Constructing binary tree. Building tree for text sequence56 00 00 10 10 01 01 11 11 00 01 10 11 01 00 11 1000 01 10 11Procedure57Text sequenceTree structureRewriting rulesClassificationComplexityComplexity of Declaration of IndependenceCalculated every 256 bits. (July 4, 1776)Complexity of Declaration of IndependenceCalculated every 512 bits. (July 4, 1776)Complexity of Declaration of Independence60Calculated every 1024 bits. (July 4, 1776)Dream of Red Chamber,1754?, 61Unicode + ASCII

32 bits for each Character and punctuation

Complexity (tree) for each 1024 bitsComplexity of 1~10 62 Dream of the Red Chamber 1754, Unicode

Complexity of 11~20 Dream of the Red Chamber 1754 11~20Complexity of 21~30

64Complexity of 31~40

65Complexity of 41~50

66Complexity of 51~60

67Low complexity sections in 68

(lowest complexity)Quasi-regular structure69 To our knowledge, there is no other method can pick such quasi-regular sections in arts, music, DNA, literatures, and transmission bits ...Complexity of 1~10

Romance of the Three Kingdoms, Complexity of 11~20

Romance of the Three Kingdoms Complexity of 21~30

Romance of the Three Kingdoms Low complexity sections in Three Kindom73

SummaryRepresentation is not unique.Study of ancient languages.Transmission anomaly different from Kullback-Leibler divergence Measure of structural complexity. 74Thanks for listening.75