On hidden Markov models and cyclic strings for shape recognition

Palazón-González, Vicente; Marzal, Andrés; Vilar, Juan Miguel

doi:10.1016/j.patcog.2014.01.018

Cited by 7 publications

(4 citation statements)

References 27 publications

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“…For instance, in bioinformatics [3,6,35,42], the position where a sequence starts can be totally arbitrary due to arbitrariness in the sequencing of a circular molecular structure or due to inconsistencies introduced into sequence databases as a result of different linearization standards [3]. In image processing [2,56,57,58], the contours of a shape may be represented through a directional chain code; the latter can be interpreted as a cyclic sequence if the orientation of the image is not important [2].…”

Section: Introductionmentioning

confidence: 99%

Approximate Circular Pattern Matching

Charalampopoulos¹,

Kociumaka²,

Radoszewski³

et al. 2022

Preprint

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We consider approximate circular pattern matching (CPM, in short) under the Hamming and edit distance, in which we are given a length-n text T , a length-m pattern P , and a threshold k > 0, and we are to report all starting positions of fragments of T (called occurrences) that are at distance at most k from some cyclic rotation of P . In the decision version of the problem, we are to check if any such occurrence exists. All previous results for approximate CPM were either average-case upper bounds or heuristics, except for the work of Charalampopoulos et al. [CKP + , JCSS'21], who considered only the Hamming distance. For the reporting version of the approximate CPM problem, under the Hamming distance we improve upon the main algorithm of [CKP + , JCSS'21] from O(n + (n/m) • k 4 ) to O(n + (n/m) • k 3 log log k) time; for the edit distance, we give an O(nk 2 )-time algorithm. We also consider the decision version of the approximate CPM problem. Under the Hamming distance, we obtain an O(n + (n/m) • k 2 log k/ log log k)-time algorithm, which nearly matches the algorithm by Chan et al. [CGKKP, STOC'20] for the standard counterpart of the problem. Under the edit distance, the O(nk log 3 k) runtime of our algorithm nearly matches the O(nk) runtime of the Landau-Vishkin algorithm [LV, J. Algorithms'89]. As a stepping stone, we propose an O(nk log 3 k)-time algorithm for the Longest Prefix k -Approximate Match problem, proposed by Landau et al. [LMS, SICOMP'98], for all k ∈ {1, . . . , k}.We give a conditional lower bound that suggests a polynomial separation between approximate CPM under the Hamming distance over the binary alphabet and its non-circular counterpart. We also show that a strongly subquadratic-time algorithm for the decision version of approximate CPM under edit distance would refute the Strong ETH.

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Section: Introductionmentioning

confidence: 99%

Approximate Circular Pattern Matching

Charalampopoulos¹,

Kociumaka²,

Radoszewski³

et al. 2022

Preprint

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“…In many real-world applications, such as in bioinformatics [4,22,25,7] or in image processing [3,33,34,32], any cyclic shift (rotation) of P is a relevant pattern, and thus one is interested in computing the minimal distance of every length-m substring of T and any cyclic shift of P , if this distance is no more than k. This is the circular pattern matching with k mismatches (k-CPM) problem. A multitude of papers [17,8,6,5,9,24] have thus been devoted to solving the k-CPM problem but, to the best of our knowledge, only average-case upper bounds are known; i.e.…”

Section: Introductionmentioning

confidence: 99%

“…The CPM problem can also be solved in O(n) time [15]. Applications where circular strings are considered include the comparison of DNA sequences in bioinformatics [24,4] as well as the comparison of shapes represented through directional chain codes in image processing [37,36]. In both applications, it is not sufficient to look for exact (circular) matches.…”

Section: Introductionmentioning

confidence: 99%

Circular Pattern Matching with k Mismatches

Charalampopoulos

Kociumaka

Pissis

et al. 2019

Fundamentals of Computation Theory

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The k-mismatch problem consists in computing the Hamming distance between a pattern P of length m and every length-m substring of a text T of length n, if this distance is no more than k. In many real-world applications, any cyclic shift of P is a relevant pattern, and thus one is interested in computing the minimal distance of every length-m substring of T and any cyclic shift of P . This is the circular pattern matching with k mismatches (k-CPM) problem. A multitude of papers have been devoted to solving this problem but, to the best of our knowledge, only average-case upper bounds are known. In this paper, we present the first non-trivial worst-case upper bounds for the k-CPM problem. Specifically, we show an O(nk)-time algorithm and an O(n + n m k 5 )-time algorithm. The latter algorithm applies in an extended way a technique that was very recently developed for the k-mismatch problem [Bringmann et al., SODA 2019].

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“…They are strings or sequences where the last element is followed by the first element, that is, there is no beginning or end [17,18]. For example, contours of shapes can be represented by cyclic chain-codes [1,26].…”

Section: Introductionmentioning

confidence: 99%

Speeding up the cyclic edit distance using LAESA with early abandon

Palazón-González

Marzal

2015

Pattern Recognition Letters

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The cyclic edit distance between two strings is the minimum edit distance between one of this strings and every possible cyclic shift of the other. This can be useful, for example, in image analysis where strings describe the contour of shapes or in computational biology for classifying circular permuted proteins or circular DNA/RNA molecules.The cyclic edit distance can be computed in O(mn log m) time, however, in real recognition tasks this is a high computational cost because of the size of databases. A method to reduce the number of comparisons and avoid an exhaustive search is convenient. In this work, we present a new algorithm based on a modification of LAESA (Linear Approximating and Eliminating Search Algorithm) for applying pruning in the computation of distances. It is an efficient procedure for classification and retrieval of cyclic strings. Experimental results show that our proposal considerably outperforms LAESA.

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On hidden Markov models and cyclic strings for shape recognition

Abstract: Cita bibliográfica / Cita bibliogràfica (ISO 690):PALAZÓN-GONZÁLEZ, Vicente; MARZAL, Andrés; VILAR, Juan M. On hidden Markov models and cyclic strings for shape recognition. Pattern Recognition, 2014Recognition, , vol. 47, no 7, p. 2490Recognition, -2504

Cited by 7 publications

References 27 publications

Approximate Circular Pattern Matching

Approximate Circular Pattern Matching

Circular Pattern Matching with k Mismatches

Speeding up the cyclic edit distance using LAESA with early abandon

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