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Transposition invariant string matching
, 2003
"... Given strings A = a1a2...am and B = b1b2...bn over an alphabet Σ ⊆ U, whereU is some numerical universe closed under addition and subtraction, and a distance function d(A,B) that gives the score of the best (partial) matching of A and B, the transposition invariant distance is ..."
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Cited by 29 (8 self)
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Given strings A = a1a2...am and B = b1b2...bn over an alphabet Σ ⊆ U, whereU is some numerical universe closed under addition and subtraction, and a distance function d(A,B) that gives the score of the best (partial) matching of A and B, the transposition invariant distance is
Transposition invariant words
"... www.elsevier.com/locate/tcs We define an operation called transposition on words of fixed length. This operation arises naturally when the letters of a word are considered as entries of a matrix. Words that are invariant with respect to transposition are of special interest. It turns out that transp ..."
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www.elsevier.com/locate/tcs We define an operation called transposition on words of fixed length. This operation arises naturally when the letters of a word are considered as entries of a matrix. Words that are invariant with respect to transposition are of special interest. It turns out
TRANSPOSITIONINVARIANT SELFSIMILARITY MATRICES
"... Selfsimilarity matrices have become an important tool for visualizing the repetitive structure of a music recording. Transforming an audio data stream into a feature sequence, one obtains a selfsimilarity matrix by pairwise comparing all features of the sequence with respect to a local cost measur ..."
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transpositioninvariant selfsimilarity matrix, which reveals the repetitive structure even in the presence of key transpositions. Furthermore, we introduce an associated transposition index matrix displaying harmonic relations within the music recording. As an application, we sketch how our concept can be used
Speeding up TranspositionInvariant String Matching
"... Finding the longest common subsequence (LCS) of two given sequences A = a0a1... am−1 and B = b0b1... bn−1 is an important and well studied problem. We consider its generalization, transpositioninvariant LCS (LCTS), which has recently arisen in the field of music information retrieval. In LCTS, we l ..."
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Cited by 2 (0 self)
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Finding the longest common subsequence (LCS) of two given sequences A = a0a1... am−1 and B = b0b1... bn−1 is an important and well studied problem. We consider its generalization, transpositioninvariant LCS (LCTS), which has recently arisen in the field of music information retrieval. In LCTS, we
Practical Algorithms for TranspositionInvariant StringMatching ⋆
"... We consider the problems of (1) longest common subsequence (LCS) of two given strings in the case where the first may be shifted by some constant (that is, transposed) to match the second, and (2) transpositioninvariant text searching using indel distance. These problems have applications in music ..."
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We consider the problems of (1) longest common subsequence (LCS) of two given strings in the case where the first may be shifted by some constant (that is, transposed) to match the second, and (2) transpositioninvariant text searching using indel distance. These problems have applications in music
TEMPO AND TRANSPOSITIONINVARIANT IDENTIFICATION OF PIECE AND SCORE POSITION
"... We present an algorithm that, given a very small snippet of an audio performance and a database of musical scores, quickly identifies the piece and the position in the score. The algorithm is both tempo and transpositioninvariant. We approach the problem by extending an existing tempoinvariant sy ..."
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We present an algorithm that, given a very small snippet of an audio performance and a database of musical scores, quickly identifies the piece and the position in the score. The algorithm is both tempo and transpositioninvariant. We approach the problem by extending an existing tempoinvariant
Practical Algorithms for TranspositionInvariant StringMatching
"... We consider the problems of (1) longest common subsequence (LCS) of two given strings in the case where the first may be shifted by some constant (that is, transposed) to match the second, and (2) transpositioninvariant text searching using indel distance. These problems have applications in music ..."
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Cited by 11 (4 self)
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We consider the problems of (1) longest common subsequence (LCS) of two given strings in the case where the first may be shifted by some constant (that is, transposed) to match the second, and (2) transpositioninvariant text searching using indel distance. These problems have applications in music
Restricted Transposition Invariant Approximate String Matching Under Edit Distance
"... Abstract. Let A and B be strings with lengths m and n, respectively, over a finite integer alphabet. Two classic string mathing problems are computing the edit distance between A and B, and searching for approximate occurrences of A inside B. We consider the classic Levenshtein distance, but the dis ..."
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, but the discussion is applicable also to indel distance. A relatively new variant [8] of string matching, motivated initially by the nature of string matching in music, is to allow transposition invariance for A. This means allowing A to be “shifted ” by adding some fixed integer t to the values of all its
Algorithms for Transposition Invariant String Matching (Extended Abstract)
 Journal of Algorithms
, 2002
"... Given strings A and B over an alphabet Σ ⊆ U, where U is some numerical universe closed... ..."
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Cited by 9 (6 self)
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Given strings A and B over an alphabet Σ ⊆ U, where U is some numerical universe closed...
Geometric Algorithms for Transposition Invariant ContentBased Music Retrieval
, 2003
"... We represent music as sets of points or sets of horizontal line segments in the Euclidean plane. Via this geometric representation we cast transposition invariant contentbased music retrieval problems as ones of matching sets of points or sets of horizontal line segments in plane under translations ..."
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Cited by 45 (6 self)
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We represent music as sets of points or sets of horizontal line segments in the Euclidean plane. Via this geometric representation we cast transposition invariant contentbased music retrieval problems as ones of matching sets of points or sets of horizontal line segments in plane under
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