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258
Finding motifs using random projections
, 2001
"... Pevzner and Sze [23] considered a precise version of the motif discovery problem and simultaneously issued an algorithmic challenge: find a motif Å of length 15, where each planted instance differs from Å in 4 positions. Whereas previous algorithms all failed to solve this (15,4)-motif problem, Pevz ..."
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Cited by 285 (6 self)
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Pevzner and Sze [23] considered a precise version of the motif discovery problem and simultaneously issued an algorithmic challenge: find a motif Å of length 15, where each planted instance differs from Å in 4 positions. Whereas previous algorithms all failed to solve this (15,4)-motif problem, Pevzner and Sze introduced algorithms that succeeded. However, their algorithms failed to solve the considerably more difficult (14,4)-, (16,5)-, and (18,6)motif problems. We introduce a novel motif discovery algorithm based on the use of random projections of the input’s substrings. Experiments on simulated data demonstrate that this algorithm performs better than existing algorithms and, in particular, typically solves the difficult (14,4)-, (16,5)-, and (18,6)-motif problems quite efficiently. A probabilistic estimate shows that the small values of � for which the algorithm fails to recover the planted Ð � �-motif are in all likelihood inherently impossible to solve. We also present experimental results on realistic biological data by identifying ribosome binding sites in prokaryotes as well as a number of known transcriptional regulatory motifs in eukaryotes. 1. CHALLENGING MOTIF PROBLEMS Pevzner and Sze [23] considered a very precise version of the motif discovery problem of computational biology, which had also been considered by Sagot [26]. Based on this formulation, they issued an algorithmic challenge: Planted Ð � �-Motif Problem: Suppose there is a fixed but unknown nucleotide sequence Å (the motif) of length Ð. The problem is to determine Å, givenØ nucleotide sequences each of length Ò, and each containing a planted variant of Å. More precisely, each such planted variant is a substring that is Å with exactly � point substitutions. One instantiation that they labeled “The Challenge Problem ” was parameterized as finding a planted (15,4)-motif in Ø � sequences each of length Ò � �. These values of Ò, Ø, andÐ are
Probabilistic discovery of time series motifs
, 2003
"... Several important time series data mining problems reduce to the core task of finding approximately repeated subsequences in a longer time series. In an earlier work, we formalized the idea of approximately repeated subsequences by introducing the notion of time series motifs. Two limitations of thi ..."
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Cited by 185 (26 self)
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Several important time series data mining problems reduce to the core task of finding approximately repeated subsequences in a longer time series. In an earlier work, we formalized the idea of approximately repeated subsequences by introducing the notion of time series motifs. Two limitations of this work were the poor scalability of the motif discovery algorithm, and the inability to discover motifs in the presence of noise. Here we address these limitations by introducing a novel algorithm inspired by recent advances in the problem of pattern discovery in biosequences. Our algorithm is probabilistic in nature, but as we show empirically and theoretically, it can find time series motifs with very high probability even in the presence of noise or “don’t care ” symbols. Not only is the algorithm fast, but it is an anytime algorithm, producing likely candidate motifs almost immediately, and gradually improving the quality of results over time.
Comining phylogenetic data with co-regulated genes to identify regulatory motif
- BIOINFORMATICS
, 2003
"... Motivation: Discovery of regulatory motifs in unaligned DNA sequences remains a fundamental problem in computational biology. Two categories of algorithms have been developed to identify common motifs from a set of DNA sequences. The first can be called a ‘multiple genes, single species’approach. It ..."
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Cited by 136 (11 self)
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Motivation: Discovery of regulatory motifs in unaligned DNA sequences remains a fundamental problem in computational biology. Two categories of algorithms have been developed to identify common motifs from a set of DNA sequences. The first can be called a ‘multiple genes, single species’approach. It proposes that a degenerate motif is embedded in some or all of the otherwise unrelated input sequences and tries to describe a consensus motif and identify its occurrences. It is often used for co-regulated genes identified through experimental approaches. The second approach can be called ‘single gene, multiple species’. It requires orthologous input sequences and tries to identify unusually well conserved regions by phylogen-etic footprinting. Both approaches perform well, but each has some limitations. It is tempting to combine the knowledge of co-regulation among different genes and conservation among orthologous genes to improve our ability to identify motifs. Results: Based on the Consensus algorithm previously established by our group, we introduce a new algorithm called PhyloCon (Phylogenetic Consensus) that takes into account both conservation among orthologous genes and co-regulation of genes within a species. This algorithm first aligns conserved regions of orthologous sequences into multiple sequence alignments, or profiles, then compares profiles representing non-orthologous sequences. Motifs emerge as common regions in these profiles. Here we present a novel statistic to compare profiles of DNA sequences and a greedy approach to search for common subprofiles. We demonstrate that PhyloCon performs well on both synthetic and biological data. Availability: Software available upon request from the authors.
Finding Motifs in Time Series
, 2002
"... The problem of efficiently locating previously known patterns in a time series database (i.e., query by content) has received much attention and may now largely be regarded as a solved problem. However, from a knowledge discovery viewpoint, a more interesting problem is the enumeration of previously ..."
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Cited by 111 (20 self)
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The problem of efficiently locating previously known patterns in a time series database (i.e., query by content) has received much attention and may now largely be regarded as a solved problem. However, from a knowledge discovery viewpoint, a more interesting problem is the enumeration of previously unknown, frequently occurring patterns. We call such patterns "motifs," because of their close analogy to their discrete counterparts in computation biology. An efficient motif discovery algorithm for time series would be useful as a tool for summarizing and visualizing massive time series databases. In addition, it could be used as a subroutine in various other data mining tasks, including the discovery of association rules, clustering and classification. In this work we carefully motivate, then introduce, a non-trivial definition of time series motifs. We propose an efficient algorithm to discover them, and we demonstrate the utility and efficiency of our approach on several real world datasets.
Finding composite regulatory patterns in DNA sequences
- Bioinformatics
, 2002
"... Pattern discovery in unaligned DNA sequences is a fundamental problem in computational biology with important applications in finding regulatory signals. Current approaches to pattern discovery focus on monad patterns that correspond to relatively short contiguous strings. However, many of the actua ..."
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Cited by 108 (4 self)
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Pattern discovery in unaligned DNA sequences is a fundamental problem in computational biology with important applications in finding regulatory signals. Current approaches to pattern discovery focus on monad patterns that correspond to relatively short contiguous strings. However, many of the actual regulatory signals are composite patterns that are groups of monad patterns that occur near each other. A difficulty in discovering composite patterns is that one or both of the component monad patterns in the group may be “too weak”. Since the traditional monad-based motif finding algorithms usually output one (or a few) high scoring patterns, they often fail to find composite regulatory signals consisting of weak monad parts. In this paper, we present a MITRA (MIsmatch TRee Algorithm) approach for discovering composite signals. We demonstrate that MITRA performs well for both monad and composite patterns by presenting experiments over biological and synthetic data. Availability: MITRA is available at
Limitations and potentials of current motif discovery algorithms.
- Nucleic Acids Res
, 2005
"... ABSTRACT Computational methods for de novo identification of gene regulation elements, such as transcription factor binding sites, have proved to be useful for deciphering genetic regulatory networks. However, despite the availability of a large number of algorithms, their strengths and weaknesses ..."
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Cited by 88 (0 self)
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ABSTRACT Computational methods for de novo identification of gene regulation elements, such as transcription factor binding sites, have proved to be useful for deciphering genetic regulatory networks. However, despite the availability of a large number of algorithms, their strengths and weaknesses are not sufficiently understood. Here, we designed a comprehensive set of performance measures and benchmarked five modern sequence-based motif discovery algorithms using large datasets generated from Escherichia coli RegulonDB. Factors that affect the prediction accuracy, scalability and reliability are characterized. It is revealed that the nucleotide and the binding site level accuracy are very low, while the motif level accuracy is relatively high, which indicates that the algorithms can usually capture at least one correct motif in an input sequence. To exploit diverse predictions from multiple runs of one or more algorithms, a consensus ensemble algorithm has been developed, which achieved 6-45% improvement over the base algorithms by increasing both the sensitivity and specificity. Our study illustrates limitations and potentials of existing sequence-based motif discovery algorithms. Taking advantage of the revealed potentials, several promising directions for further improvements are discussed. Since the sequence-based algorithms are the baseline of most of the modern motif discovery algorithms, this paper suggests substantial improvements would be possible for them.
Tight lower bounds for certain parameterized NP-hard problems
- Proc. 19th Annual IEEE Conference on Computational Complexity (CCC’04
, 2004
"... Based on the framework of parameterized complexity theory, we derive tight lower bounds on the computational complexity for a number of well-known NP-hard problems. We start by proving a general result, namely that the parameterized weighted satisfiability problem on depth-t circuits cannot be solve ..."
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Cited by 62 (10 self)
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Based on the framework of parameterized complexity theory, we derive tight lower bounds on the computational complexity for a number of well-known NP-hard problems. We start by proving a general result, namely that the parameterized weighted satisfiability problem on depth-t circuits cannot be solved in time no(k) poly(m), where n is the circuit input length, m is the circuit size, and k is the parameter, unless the (t − 1)-st level W [t − 1] of the W-hierarchy collapses to FPT. By refining this technique, we prove that a group of parameterized NP-hard problems, including weighted sat, dominating set, hitting set, set cover, and feature set, cannot be solved in time no(k) poly(m), where n is the size of the universal set from which the k elements are to be selected and m is the instance size, unless the first level W [1] of the W-hierarchy collapses to FPT. We also prove that another group of parameterized problems which includes weighted q-sat (for any fixed q ≥ 2), clique, and independent set, cannot be solved in time no(k) unless all search problems in the syntactic class SNP, introduced by Papadimitriou and Yannakakis, are solvable in subexponential time. Note that all these parameterized problems have trivial algorithms of running time either n k poly(m) or O(n k). 1
A graph theoretical approach for predicting common RNA secondary structure motifs including pseudoknots in unaligned sequences
, 2004
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Computational identification of transcriptional regulatory elements in DNA sequence
, 2006
"... Identification and annotation of all the functional elements in the genome, including genes and the regulatory sequences, is a fundamental challenge in genomics and computational biology. Since regulatory elements are frequently short and variable, their identification and discovery using computatio ..."
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Cited by 55 (0 self)
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Identification and annotation of all the functional elements in the genome, including genes and the regulatory sequences, is a fundamental challenge in genomics and computational biology. Since regulatory elements are frequently short and variable, their identification and discovery using computational algorithms is difficult. However, significant advances have been made in the computational methods for modeling and detection of DNA regulatory elements. The availability of complete genome sequence from multiple organisms, as well as mRNA profiling and high-throughput experimental methods for mapping protein-binding sites in DNA, have contributed to the development of methods that utilize these auxiliary data to inform the detection of transcriptional regulatory elements. Progress is also being made in the identification of cis-regulatory modules and higher order structures of the regulatory sequences, which is essential to the understanding of transcription regulation in the metazoan genomes. This article reviews the computational approaches for modeling and identification of genomic regulatory elements, with an emphasis on the recent developments, and current challenges.
Mining Motifs in Massive Time Series Databases
- In Proceedings of IEEE International Conference on Data Mining (ICDM’02
, 2002
"... The problem of efficiently locating previously known patterns in a time series database (i.e., query by content) has received much attention and may now largely be regarded as a solved problem. However, from a knowledge discovery viewpoint, a more interesting problem is the enumeration of previously ..."
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Cited by 49 (3 self)
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The problem of efficiently locating previously known patterns in a time series database (i.e., query by content) has received much attention and may now largely be regarded as a solved problem. However, from a knowledge discovery viewpoint, a more interesting problem is the enumeration of previously unknown, frequently occurring patterns. We call such patterns "motifs", because of their close analogy to their discrete counterparts in computation biology. An efficient motif discovery algorithm for time series would be useful as a tool for summarizing and visualizing massive time series databases. In addition it could be used as a subroutine in various other data mining tasks, including the discovery of association rules, clustering and classification.
