-
Algorithmica. 01/2012; 62:951-981.
-
J. Comb. Optim. 01/2010; 19:217-240.
-
[show abstract]
[hide abstract]
ABSTRACT: In this article, we studied the tag single-nucleotide polymorphism (tagSNP) selection problem on multiple populations using the pairwise r(2) linkage disequilibrium criterion. We proposed a novel combinatorial optimization model for the tagSNP selection problem, called the minimum common tagSNP selection (MCTS) problem, and presented efficient solutions for MCTS. Our approach consists of the following three main steps: (i) partitioning the SNP markers into small disjoint components, (ii) applying some data reduction rules to simplify the problem, and (iii) applying either a fast greedy algorithm or a Lagrangian relaxation algorithm to solve the remaining (general) MCTS. These algorithms also provide lower bounds on tagging (i.e., the minimum number of tagSNPs needed). The lower bounds allow us to evaluate how far our solution is from the optimum. To the best of our knowledge, it is the first time the tagging lower bounds are discussed in the literature. We assessed the performance of our algorithms on real HapMap data for genome-wide tagging. The experiments demonstrated that our algorithms run 3-4 orders of magnitude faster than the existing single-population tagging programs such as FESTA, LD-Select, and the multiple-population tagging method MultiPop-TagSelect. Our method also greatly reduced the required tagSNPs compared with LD-Select on a single population and MultiPop-TagSelect on multiple populations. Moreover, the numbers of tagSNPs selected by our algorithms are almost optimal because they are very close to the corresponding lower bounds obtained by our method.
Journal of computational biology: a journal of computational molecular cell biology 01/2010; 17(1):21-37. · 1.69 Impact Factor
-
SIAM J. Comput. 01/2009; 38:2198-2219.
-
ACM Transactions on Algorithms. 01/2008; 5.
-
[show abstract]
[hide abstract]
ABSTRACT: The assignment of orthologous genes between a pair of genomes is a fundamental and challenging problem in comparative genomics, since many computational methods for solving various biological problems critically rely on bona fide orthologs as input. While it is usually done using sequence similarity search, we recently proposed a new combinatorial approach that combines sequence similarity and genome rearrangement. This paper continues the development of the approach and unites genome rearrangement events and (post-speciation) duplication events in a single framework under the parsimony principle. In this framework, orthologous genes are assumed to correspond to each other in the most parsimonious evolutionary scenario involving both genome rearrangement and (post-speciation) gene duplication. Besides several original algorithmic contributions, the enhanced method allows for the detection of inparalogs. Following this approach, we have implemented a high-throughput system for ortholog assignment on a genome scale, called MSOAR, and applied it to human and mouse genomes. As the result will show, MSOAR is able to find 99 more true orthologs than the INPARANOID program did. In comparison to the iterated exemplar algorithm on simulated data, MSOAR performed favorably in terms of assignment accuracy. We also validated our predicted main ortholog pairs between human and mouse using public ortholog assignment datasets, synteny information, and gene function classification. These test results indicate that our approach is very promising for genome-wide ortholog assignment. Supplemental material and MSOAR program are available at http://msoar.cs.ucr.edu.
Journal of Computational Biology 12/2007; 14(9):1160-75. · 1.55 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: The total order of genes or markers on a chromosome is crucial for most comparative genomics studies. However, current gene mapping efforts might only suffice to provide a partial order of the genes on a chromosome. Several different genes or markers might be mapped at the same position due to the low resolution of gene mapping or missing data. Moreover, conflicting datasets might give rise to the ambiguity of gene order. In this paper, we consider the reversal distance and breakpoint distance problems for partially ordered genomes. We first prove that these problems are nondeterministic polynomial-time (NP)-hard, and then give an efficient heuristic algorithm to compute the breakpoint distance between partially ordered genomes. The algorithm is based on an efficient approximation algorithm for a natural generalization of the well-known feedback vertex set problem, and has been tested on both simulated and real biological datasets. The experimental results demonstrate that our algorithm is quite effective for estimating the breakpoint distance between partially ordered genomes and for inferring the gene (total) order.
Journal of Bioinformatics and Computational Biology 11/2007; 5(5):1087-101.
-
[show abstract]
[hide abstract]
ABSTRACT: With the launch of the international HapMap project, the haplotype inference problem has attracted a great deal of attention in the computational biology community recently. In this paper, we study the question of how to efficiently infer haplotypes from genotypes of individuals related by a pedigree without mating loops, assuming that the hereditary process was free of mutations (i.e. the Mendelian law of inheritance) and recombinants. We model the haplotype inference problem as a system of linear equations as in [10] and present an (optimal) linear-time (i.e. O(mn) time) algorithm to generate a particular solution (A particular solution of any linear system is an assignment of numerical values to the variables in the system which satisfies the equations in the system.) to the haplotype inference problem, where m is the number of loci (or markers) in a genotype and n is the number of individuals in the pedigree. Moreover, the algorithm also provides a general solution (A general solution of any linear system is denoted by the span of a basis in the solution space to its associated homogeneous system, offset from the origin by a vector, namely by any particular solution. A general solution for ZRHC is very useful in practice because it allows the end user to efficiently enumerate all solutions for ZRHC and performs tasks such as random sampling.) in O(mn2) time, which is optimal because the size of a general solution could be as large as Theta(mn2). The key ingredients of our construction are (i) a fast consistency checking procedure for the system of linear equations introduced in [10] based on a careful investigation of the relationship between the equations (ii) a novel linear-time method for solving linear equations without invoking the Gaussian elimination method. Although such a fast method for solving equations is not known for general systems of linear equations, we take advantage of the underlying loop-free pedigree graph and some special properties of the linear equations.
Genome informatics. International Conference on Genome Informatics 02/2007; 19:95-106.
-
[show abstract]
[hide abstract]
ABSTRACT: In this paper, we study the tagSNP selection problem on multiple populations using the pairwise r(2) linkage disequilibrium criterion. We propose a novel combinatorial optimization model for the tagSNP selection problem, called the minimum common tagSNP selection (MCTS) problem, and present efficient solutions for MCTS. Our approach consists of three main steps including (i) partitioning the SNP markers into small disjoint components, (ii) applying some data reduction rules to simplify the problem, and (iii) applying either a fast greedy algorithm or a Lagrangian relaxation algorithm to solve the remaining (general) MCTS. These algorithms also provide lower bounds on tagging (i.e. the minimum number of tagSNPs needed). The lower bounds allow us to evaluate how far our solution is from the optimum. To the best of our knowledge, it is the first time tagging lower bounds are discussed in the literature. We assess the performance of our algorithms on real HapMap data for genome-wide tagging. The experiments demonstrate that our algorithms run 3 to 4 orders of magnitude faster than the existing single-population tagging programs like FESTA, LD-Select and the multiple-population tagging method MultiPop-TagSelect. Our method also greatly reduces the required tagSNPs compared to LD-Select on a single population and MultiPop-TagSelect on multiple populations. Moreover, the numbers of tagSNPs selected by our algorithms are almost optimal since they are very close to the corresponding lower bounds obtained by our method.
Computational systems bioinformatics / Life Sciences Society. Computational Systems Bioinformatics Conference 02/2007; 6:67-78.
-
Theor. Comput. Sci. 01/2007; 378:316-330.
-
Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007, New Orleans, Louisiana, USA, January 7-9, 2007; 01/2007
-
[show abstract]
[hide abstract]
ABSTRACT: A large number of biclustering methods have been proposed to detect patterns in gene expression data. All these methods try to find some type of biclusters but no one can discover all the types of patterns in the data. Furthermore, researchers have to design new algorithms in order to find new types of biclusters/patterns that interest biologists. In this paper, we propose a novel approach for biclustering that, in general, can be used to discover all computable patterns in gene expression data. The method is based on the theory of Kolmogorov complexity. More precisely, we use Kolmogorov complexity to measure the randomness of submatrices as the merit of biclusters because randomness naturally consists in a lack of regularity, which is a common property of all types of patterns. On the basis of algorithmic probability measure, we develop a Markov Chain Monte Carlo algorithm to search for biclusters. Our method can also be easily extended to solve the problems of conventional clustering and checkerboard type biclustering. The preliminary experiments on simulated as well as real data show that our approach is very versatile and promising.
Journal of Bioinformatics and Computational Biology 09/2006; 4(4):911-33.
-
[show abstract]
[hide abstract]
ABSTRACT: We introduce a new combinatorial optimization problem in this paper, called the Minimum Common Integer Partition (MCIP) problem, which was inspired by computational biology applications including ortholog assignment and DNA fingerprint
assembly. A partition of a positive integer n is a multiset of positive integers that add up to exactly n, and an integer partition of a multiset S of integers is defined as the multiset union of partitions of integers in S. Given a sequence of multisets S
1, ⋯, S
k
of integers, where k ≥ 2, we say that a multiset is a common integer partition if it is an integer partition of every multiset S
i
, 1≤ i≤ k. The MCIP problem is thus defined as to find a common integer partition of S
1, ⋯, S
k
with the minimum cardinality. It is easy to see that the MCIP problem is NP-hard since it generalizes the well-known Set
Partition problem. We can in fact show that it is APX-hard. We will also present a
\frac54\frac{5}{4}-approximation algorithm for the MCIP problem when k = 2, and a
\frac3k(k-1)3k-2\frac{3k(k-1)}{3k-2}-approximation algorithm for k ≥ 3.
06/2006: pages 236-247;
-
[show abstract]
[hide abstract]
ABSTRACT: Expressed sequence tag (EST) datasets represent perhaps the largest collection of genetic information. ESTs can be exploited in a variety of biological experiments and analysis. Here we are interested in the design of overlapping oligonucleotide (overgo) probes from large unigene (EST-contigs) datasets.
OLIGOSPAWN is a suite of software tools that offers two complementary services, namely (1) the selection of "unique" oligos each of which appears in one unigene but does not occur (exactly or approximately) in any other and (2) the selection of "popular" oligos each of which occurs (exactly or approximately) in as many unigenes as possible. In this paper, we describe the functionalities of OLIGOSPAWN and the computational methods it employs, and we report on experimental results for the overgo probes designed with it.
The algorithms we designed are highly efficient and capable of processing unigene datasets of sizes on the order of several tens of Mb in a few hours on a regular PC. The software has been used to design overgo probes employed to screen a barley BAC library (Hordeum vulgare). OLIGOSPAWN is freely available at http://oligospawn.ucr.edu/.
BMC Bioinformatics 02/2006; 7:7. · 2.75 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: In pattern recognition, feature extraction techniques are widely employed to reduce the dimensionality of data and to enhance the discriminatory information. Principal component analysis (PCA) and linear discriminant analysis (LDA) are the two most popular linear dimensionality reduction methods. However, PCA is not very effective for the extraction of the most discriminant features, and LDA is not stable due to the small sample size problem. In this paper, we propose some new (linear and nonlinear) feature extractors based on maximum margin criterion (MMC). Geometrically, feature extractors based on MMC maximize the (average) margin between classes after dimensionality reduction. It is shown that MMC can represent class separability better than PCA. As a connection to LDA, we may also derive LDA from MMC by incorporating some constraints. By using some other constraints, we establish a new linear feature extractor that does not suffer from the small sample size problem, which is known to cause serious stability problems for LDA. The kernelized (nonlinear) counterpart of this linear feature extractor is also established in the paper. Our extensive experiments demonstrate that the new feature extractors are effective, stable, and efficient.
IEEE Transactions on Neural Networks 02/2006; 17(1):157-65. · 2.95 Impact Factor
-
Research in Computational Molecular Biology, 10th Annual International Conference, RECOMB 2006, Venice, Italy, April 2-5, 2006, Proceedings; 01/2006
-
Algorithms and Complexity, 6th Italian Conference, CIAC 2006, Rome, Italy, May 29-31, 2006, Proceedings; 01/2006
-
[show abstract]
[hide abstract]
ABSTRACT: Abstract
Background
Expressed sequence tag (EST) datasets represent perhaps the largest collection of genetic information. ESTs can be exploited in a variety of biological experiments and analysis. Here we are interested in the design of overlapping oligonucleotide ( overgo ) probes from large unigene (EST-contigs) datasets.
Results
OLIGOSPAWN is a suite of software tools that offers two complementary services, namely (1) the selection of "unique" oligos each of which appears in one unigene but does not occur (exactly or approximately) in any other and (2) the selection of "popular" oligos each of which occurs (exactly or approximately) in as many unigenes as possible. In this paper, we describe the functionalities of OLIGOSPAWN and the computational methods it employs, and we report on experimental results for the overgo probes designed with it.
Conclusion
The algorithms we designed are highly efficient and capable of processing unigene datasets of sizes on the order of several tens of Mb in a few hours on a regular PC. The software has been used to design overgo probes employed to screen a barley BAC library ( Hordeum vulgare ). OLIGOSPAWN is freely available at http://oligospawn.ucr.edu/ .
BMC Bioinformatics. 01/2006;
-
[show abstract]
[hide abstract]
ABSTRACT: Robust and accurate cancer classification is critical in cancer treatment. Gene expression profiling is expected to enable us to diagnose tumors precisely and systematically. However, the classification task in this context is very challenging because of the curse of dimensionality and the small sample size problem. In this paper, we propose a novel method to solve these two problems. Our method is able to map gene expression data into a very low dimensional space and thus meets the recommended samples to features per class ratio. As a result, it can be used to classify new samples robustly with low and trustable (estimated) error rates. The method is based on linear discriminant analysis (LDA). However, the conventional LDA requires that the within-class scatter matrix S(w) be nonsingular. Unfortunately, Sw is always singular in the case of cancer classification due to the small sample size problem. To overcome this problem, we develop a generalized linear discriminant analysis (GLDA) that is a general, direct, and complete solution to optimize Fisher's criterion. GLDA is mathematically well-founded and coincides with the conventional LDA when S(w) is nonsingular. Different from the conventional LDA, GLDA does not assume the nonsingularity of S(w), and thus naturally solves the small sample size problem. To accommodate the high dimensionality of scatter matrices, a fast algorithm of GLDA is also developed. Our extensive experiments on seven public cancer datasets show that the method performs well. Especially on some difficult instances that have very small samples to genes per class ratios, our method achieves much higher accuracies than widely used classification methods such as support vector machines, random forests, etc.
Proceedings / IEEE Computational Systems Bioinformatics Conference, CSB. IEEE Computational Systems Bioinformatics Conference 02/2005;
-
Proceedings, The Twentieth National Conference on Artificial Intelligence and the Seventeenth Innovative Applications of Artificial Intelligence Conference, July 9-13, 2005, Pittsburgh, Pennsylvania, USA; 01/2005
