Use of median string for classification

Martínez-Hinarejos, Carlos D.; Juan, Alfons; Casacuberta, Francisco

doi:10.1109/icpr.2000.906220

Cited by 22 publications

(14 citation statements)

References 6 publications

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“…Kohonen, in 1985 [4], proposed an approximation algorithm to find the generalized median based on a process of perturbation of the set median in order to modify it in the direction of the generalized median string. This results was improved in 2000 by Martínez-Hinarejos et al [5] [6]. Moreover, their experiments showed that using the generalized median instead of the set median improved their results.…”

Section: Introductionmentioning

confidence: 88%

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A Stochastic Approach to Median String Computation

Olivares-Rodríguez

Oncina

2008

Lecture Notes in Computer Science

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Abstract. Due to its robustness to outliers, many Pattern Recognition algorithms use the median as a representative of a set of points. A special case arises in Syntactical Pattern Recognition when the points (prototypes) are represented by strings. However, when the edit distance is used, finding the median becomes a NP-Hard problem. Then, either the search is restricted to strings in the data (set-median) or some heuristic approach is applied. In this work we use the (conditional) stochastic edit distance instead of the plain edit distance. It is not yet known if in this case the problem is also NP-Hard so an approximation algorithm is described. The algorithm is based on the extension of the string structure to multistrings (strings of stochastic vectors where each element represents the probability of each symbol) to allow the use of the Expectation Maximization technique. We carry out some experiments over a chromosomes corpus to check the efficiency of the algorithm.

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Section: Introductionmentioning

confidence: 88%

“…Unfortunately, Martínez-Hinarejos et al [5] [10] showed that the median string is better representative of a given set than the set median. In their work [11], they proposed several approximation methods to find the median.…”

Section: Median String and Set Medianmentioning

confidence: 99%

A Stochastic Approach to Median String Computation

Olivares-Rodríguez

Oncina

2008

Lecture Notes in Computer Science

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“…Thus, it is reasonable to think that we could improve the precision by mining the neighbourhood of the learnt centre, using local edit modifications. This kind of approaches has been pioneered by Kohonen in [16] and is surveyed in [17]. Suppose that the learnt ball is B k (u).…”

Section: Improving the Precision With A Posteriori Heuristicsmentioning

confidence: 99%

Learning Balls of Strings with Correction Queries

Bonache

Higuera

Janodet

et al. 2007

Machine Learning: ECML 2007

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Abstract. During the 80's, Angluin introduced an active learning paradigm, using an Oracle, capable of answering both membership and equivalence queries. However, practical evidence tends to show that if the former are often available, this is usually not the case of the latter. We propose new queries, called correction queries, which we study in the framework of Grammatical Inference. When a string is submitted to the Oracle, either she validates it if it belongs to the target language, or she proposes a correction, i.e., a string of the language close to the query with respect to the edit distance. We also introduce a non-standard class of languages: The topological balls of strings. We show that this class is not learnable in Angluin's Mat model, but is with a linear number of correction queries. We conduct several experiments with an Oracle simulating a human Expert, and show that our algorithm is resistant to approximate answers.

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“…Approximation Although centre string and median string are NPcomplete, there exist approximation algorithms with bounded errors [7] and heuristic algorithms [9], [18]. For example, given a finite language W over Σ, set center (resp.…”

Section: Open Problemsmentioning

confidence: 99%

“…Its importance is reflected by the wide use of a polynomial time approximation, the set median string ( [9,18,17,7,6,8]). In this restricted version of the problem, the solution string must be taken in the input set W (it is also termed the "center string" in [7, p. 349]).…”

Section: Introductionmentioning

confidence: 99%

Complexities of the Centre and Median String Problems

Nicolas

Rivals

2003

Combinatorial Pattern Matching

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Abstract. Given a finite set of strings, the median string problem consists in finding a string that minimizes the sum of the distances to the strings in the set. Approximations of the median string are used in a very broad range of applications where one needs a representative string that summarizes common information to the strings of the set. It is the case in Classification, in Speech and Pattern Recognition, and in Computational Biology. In the latter, median string is related to the key problem of Multiple Alignment. In the recent literature, one finds a theorem stating the NP-completeness of the median string for unbounded alphabets. However, in the above mentioned areas, the alphabet is often finite. Thus, it remains a crucial question whether the median string problem is NP-complete for finite and even binary alphabets. In this work, we provide an answer to this question and also give the complexity of the related centre string problem. Moreover, we study the parametrized complexity of both problems with respect to the number of input strings.

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Use of median string for classification

Cited by 22 publications

References 6 publications

A Stochastic Approach to Median String Computation

A Stochastic Approach to Median String Computation

Learning Balls of Strings with Correction Queries

Complexities of the Centre and Median String Problems

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