# Effective selection of informative SNPs and classification on the HapMap genotype data

- Nina Zhou
^{1}and - Lipo Wang
^{1}Email author

**8**:484

**DOI: **10.1186/1471-2105-8-484

© Zhou and Wang; licensee BioMed Central Ltd. 2007

**Received: **20 April 2007

**Accepted: **20 December 2007

**Published: **20 December 2007

## Abstract

### Background

Since the single nucleotide polymorphisms (SNPs) are genetic variations which determine the difference between any two unrelated individuals, the SNPs can be used to identify the correct source population of an individual. For efficient population identification with the HapMap genotype data, as few informative SNPs as possible are required from the original 4 million SNPs. Recently, Park *et al.* (2006) adopted the nearest shrunken centroid method to classify the three populations, i.e., Utah residents with ancestry from Northern and Western Europe (CEU), Yoruba in Ibadan, Nigeria in West Africa (YRI), and Han Chinese in Beijing together with Japanese in Tokyo (CHB+JPT), from which 100,736 SNPs were obtained and the top 82 SNPs could completely classify the three populations.

### Results

In this paper, we propose to first rank each feature (SNP) using a ranking measure, i.e., a modified t-test or F-statistics. Then from the ranking list, we form different feature subsets by sequentially choosing different numbers of features (e.g., 1, 2, 3, ..., 100.) with top ranking values, train and test them by a classifier, e.g., the support vector machine (SVM), thereby finding one subset which has the highest classification accuracy. Compared to the classification method of Park *et al.*, we obtain a better result, i.e., good classification of the 3 populations using on average 64 SNPs.

### Conclusion

Experimental results show that the both of the modified t-test and F-statistics method are very effective in ranking SNPs about their classification capabilities. Combined with the SVM classifier, a desirable feature subset (with the minimum size and most informativeness) can be quickly found in the greedy manner after ranking all SNPs. Our method is able to identify a very small number of important SNPs that can determine the populations of individuals.

## Background

When any one single nucleotide of *A*, *T*, *C* and *G* in the genome sequence is replace by one of any other 3 nucleotide, e.g., from AAATC CGG to AAATT CGG, we call this single base variation (C ⇒ T) as a single nucleotide polymorphism (SNP). It has the following three characteristics [1]: 1) very common in the human genome (a SNP occurs every 100 to 300 bases along the 3-billion-base human genome); 2)among the SNPs, two of every three SNPs are the variations from cytosine (C) to thymine (T); 3) very stable from generation to generation. Due to these characteristics, much research on SNPs has been developed, such as using SNPs to study the association of sequence variation [2–5] and to do population classification [6, 7].

In association studies [2–5], informative SNPs were usually selected based on certain correlation measures and therefore could represent other SNPs in the close proximity. For example, Bafna et al. [2] and Halldrsson et al. [3] proposed to select a subset of tag SNPs with the minimum size and highest informativeness value calculated from a self-defined informativeness measure, which evaluates how well a single SNP or a set of SNPs predict another single SNP or another set of SNPs within the neighborhoods. Eran et al. [4] proposed to select the informative SNPs with the maximum prediction accuracy, which is obtained from a prediction accuracy measure evaluating how well the value of an SNP is predicted by the values of only two closest tag SNPs. Phuong et al. [5] proposed the method of selecting informative SNPs by removing redundant features. Redundancy was measured by feature similarity between two features, i.e., the linkage disequilibrium (LD) measure *γ*^{2} [5].

In population studies, the selection of informative SNPs should be based on their population classification capability. Related research, such as selecting genetic markers with highest informativeness for inference of individual ancestry [8], selecting informative marker panels for population assignment [6] and detecting ethnically variant SNPs [7], has already been explored. Rosenberg et al. [8] proposed to use the informativeness for assignment (*I*_{
n
}) to measure the ability of each genetic loci or marker (feature) to infer individuals' ancestry, which was proved to be similar to the F-statistics measure [8]. In [6], Rosenberg et al. proposed the univariate, greedy, and maximum algorithms to select marker panels. The three algorithms were realized through a given performance function, e.g., the optimal rate of correct assignment (ORCA) [8], which measures the probability of correctly assigning an individual to the population from which the genotype of the individual has originated with the greatest possibility. The application of the algorithms on eight species was effective. Very recently, Park et al. developed a systematic approach based on nearest shrunken centroid (NSCM) method [9] to identify ethnically variant SNPs. According to [9], they calculated a shrunken value for each SNP of each class, and compared each SNP's shrunken value for different classes to determine the SNP's classification capability. The less the difference among the SNP's shrunken values for different classes, the less important the SNP for classifying the three different ethnic groups (classes) [10], i.e., CEU, YRI and JPT+CHB. 100,736 SNPs were obtained and the top 82 SNPs were able to completely classify the three populations.

In this paper, we propose to firstly rank SNPs according to a feature importance ranking measure, i.e., a modified t-test or F-statistics, where the higher the ranking value, the stronger the corresponding classification power. Then, from the ranking list, we sequentially choose different numbers of top ranked SNPs, e.g., 1, 2, 3, ..., 20 and so on, test them through a classifier, e.g., the support vector machine (SVM) [11, 12] and determine the SNP subset which has the highes classification accuracy. This process is repeated 30 times. Finally, we locate those important SNPs who always have top ranking values according to SNP subsets obtained from 30 simulations.

## Results and discussion

Combining all the features together from the 23 chromosomes, i.e., Chromosome 1, 2, ..., 22, X (the phased data of Chromosome Y is not available), we have nearly 4 million SNPs involved in the experiment. For most features (locus), their SNP types (feature values) are expressed as bi-allelic SNPs, i.e., consisting of two single alleles from 4 nucleotides *ATCG*. For example, if one SNP consists of the two allels *A* and *G* (see Fig. 1(b)), all the possible feature values for this locus will be *AA*, *AG* and *GG*, in which *AA* and *GG* are called homozygous, and *AG* is called hyterozygous. Since the phased haplotype data has two rows of haplotypes describing one individual, we transform the haplotype data into the genotype format (see Fig. 1(a)) for computational convenience. When transforming data from the haplotype format into the genotype format, we adopt two kinds of transformations considering different requirements of two algorithms (see Fig. 1(c)). For the modified t-test ranking measure, if simply transforming nominal values to normal numeric values and doing the calculation according to Equation (4), it will be possible to lose the meaning of different SNP types. We propose to use vectors to represent different SNP types and rank them by the modified t-test ranking measure (Equation (5)). For example (see Fig. 1(c)), according to the description of the modified t-test ranking measure, "11" (i.e,, *AA* in Fig. 1(c)) is represented by {0, 0, 1}, "00" (*GG*) is represented by {0, 1, 0}, and "10" (*AG*) is represented by {1, 0, 0}. As to the F-statistics ranking measure, since it involves the calculation of two single alleles for each bi-allelic SNPs, we will use 1 and 0 to represent the two different alleles, respectively. For example, given the same SNP reference type *A/G* as the one in the modified t-test ranking measure, we use 1 to represent *A* and 0 to represent *G*. Then, in each population we can calculate each allele's frequency and variation for each population, as well as those values for all the populations. Each SNP's F-statistics value is calculated from Equation (7). At the same time, we notice some special conditions. For example, if one locus with reference SNP type *A/G* only has the value *AA* for all the individuals, the frequency of the SNP allele *A* will be 100% and the frequency of allele *G* will be zero. Referring to Equation (7), either $\overline{p}$ or $\overline{q}$ in the denominator will be equal to zero. In fact, this feature has no classification capability for any populations. Therefore, we set the *F*_{
st
}value of that feature as zero. In summary, the greater the numerator and the smaller the denominator in Equation (7), the greater the value *F*_{
st
}and the more important the corresponding feature for classification.

We have 4 simulations to conduct, i.e., 4 different combinations of two rankings (F-statistics and modified t-test) and two classifications (on 3 populations and 4 populations, respectively). From the 210 samples, we randomly choose 40 samples from YRI and CEU, respectively, and 30 samples from JPT and CHB, respectively, as the training set. The 70 samples left are used as the testing set. Each simulation is repeated for 30 times.

We first rank the SNPs of 23 chromosomes, respectively. Then we choose each chromosome's top 100 SNPs, combine the 2300 features together, and rank them again. In this way, features involved in the experiment are greatly reduced and this also will not lead to loss of important information. On the contrary, it will improve the efficiency of the experiment.

Classification accuracy results obtained by the F-statistics measure for different feature subsets with different numbers of top ranked features (SNPs) in 30 simulations, on 3 and 4 populations, respectively

Feature Numbers | Mean accuracy ± std (minimal/maximal accuracy) (%) for 3 populations | Mean accuracy ± std (minimal/maximal accuracy) (%) for 4 populations |
---|---|---|

1 | 69.21 ± 1.60 (64.29/70) | 54.98 ± 1.60 (51.43/57.14) |

10 | 72.96 ± 7.82 (64.29/92.86) | 56.16 ± 2.36 (45.71/58.57) |

20 | 74.48 ± 7.82 (65.71/95.71) | 57.88 ± 4.26 (54.29/74.29) |

30 | 74.92 ± 8.79 (65.71/95.71) | 58.47 ± 5.18 (48.57/74.29) |

40 | 77.29 ± 10.55 (65.71/97.14) | 59.51 ± 5.08 (54.29/77.14) |

50 | 79.75 ± 11.96 (64.29/98.57) | 61.18 ± 7.24 (54.29/82.86) |

60 | 82.46 ± 11.41 (67.14/98.57) | 64.09 ± 7.10 (57.14/82.86) |

70 | 84.68 ± 11.15 (67.14/98.57) | 64.48 ± 7.73 (57.14/82.86) |

80 | 94.48 ± 7.03 (64.29/98.57) | 67.98 ± 8.86 (55.71/84.29) |

90 | 93.74 ± 5.98 (68.57/98.57) | 70.84 ± 9.13 (57.14/87.14) |

100 | 93.79 ± 3.44 (80/98.57) | 73.99 ± 7.09 (58.57/87.14) |

Classification accuracy results obtained by the modified t-test measure for different feature subsets with differen numbers of top ranked features (SNPs) in 30 simulations, on 3 and 4 populations, respectively

Feature Numbers | Mean accuracy ± std (minimal/maximal accuracy) (%) for 3 populations | Mean accuracy ± std (minimal/maximal accuracy) (%) for 4 populations |
---|---|---|

1 | 69.37 ± 1.43 (65.71/71.43) | 54.86 ± 1.54 (51.43/57.14) |

10 | 72.97 ± 7.14 (60.00/92.86) | 56.29 ± 6.03 (45.71/74.29) |

20 | 75.20 ± 7.82 (65.71/95.71) | 58.45 ± 7.15 (48.57/74.29) |

30 | 76.69 ± 9.23 (67.14/95.71) | 60.17 ± 9.34 (50.00/81.43) |

40 | 77.03 ± 8.65 (68.57/94.29) | 61.60 ± 7.77 (51.43/78.57) |

50 | 79.94 ± 9.36 (55.71/97.14) | 65.20 ± 8.21 (54.29/81.43) |

60 | 81.89 ± 11.03 (61.43/100) | 69.26 ± 9.21 (51.43/84.29) |

70 | 85.23 ± 10.92 (70.00/100) | 70.34 ± 9.38 (52.85/84.29) |

80 | 94.57 ± 9.75 (81.43/100) | 73.94 ± 7.73 (58.57/84.29) |

90 | 94.29 ± 3.73 (84.29/98.57) | 79.60 ± 4.53 (67.14/87.14) |

100 | 94.57 ± 3.06 (84.29/98.57) | 80.46 ± 4.57 (68.57/90.00) |

The maximum classification accuracy in each of 30 simulations together with the mean accuracy (standard deviation), and the relevant feature numbers leading to the maximal accuracy together with the mean number (standard deviation), for 3 populations and 4 populations, respectively

Feature Numbers | Maximum accuracy (%) | Mean accuracy ± std (%) | Relevant feature numbers | Average number of features ± std |
---|---|---|---|---|

f-statistics on 3 populations | 94.29 98.57 95.71 97.14 94.29 | 96.05 ± 1.58 (%) | 12 85 15 42 29 86 | 63.6 ± 25.8 |

94.29 95.71 95.71 95.71 97.14 | 37 56 78 90 71 46 | |||

97.14 95.71 97.14 95.71 98.57 | 79 79 49 8 75 74 | |||

92.86 97.14 97.14 97.14 92.86 | 74 100 83 50 81 | |||

97.14 95.71 95.71 95.71 97.14 | 67 38 82 81 93 84 | |||

95.71 98.57 95.71 97.14 92.86 | 53 | |||

f-statistics on 4 populations | 78.57 78.57 85.71 70.00 88.57 | 77.34 ± 6.57 (%) | 53 98 82 96 91 | 85.2 ± 15.1 |

78.57 80.00 82.86 70.00 80.00 | 100 93 81 99 90 | |||

65.71 78.57 82.86 68.57 81.43 | 59 99 88 55 73 81 | |||

80.00 70.00 78.57 81.43 74.29 | 56 99 100 100 74 | |||

72.86 84.26 74.29 84.29 88.57 | 74 98 94 88 72 81 | |||

68.57 75.71 64.29 75.71 70.00 | 99 98 90 | |||

Modified t-test on 3 populations | 95.71 100.00 95.71 98.57 | 97.09 ± 1.74 (%) | 27 84 19 90 29 95 | 64.0 ± 26.5 |

94.29 98.57 95.71 95.71 | 64 80 84 80 78 54 | |||

95.71 98.57 95.71 95.71 98.57 | 83 92 57 11 80 79 | |||

100.00 100.00 97.14 98.57 | 78 95 62 75 94 84 | |||

95.71 97.14 98.57 98.57 95.71 | 53 10 32 28 68 55 | |||

94.29 94.29 97.14 97.14 95.71 | ||||

98.57 97.14 98.57 | ||||

Modified t-test on 4 populations | 82.86 77.14 87.14 82.86 82.86 | 83.86 ± 3.16 (%) | 31 84 92 94 86 | 84.1 ± 16.3 |

84.29 88.57 80.00 81.43 82.86 | 100 84 99 83 87 | |||

82.86 84.29 87.14 84.29 85.71 | 96 61 83 93 99 95 | |||

81.43 82.86 84.29 84.29 75.71 | 80 81 88 99 99 75 | |||

81.43 84.29 81.43 84.29 90.00 | 95 82 95 51 83 73 | |||

84.29 85.71 85.71 85.71 90.00 | 99 55 |

Top ranked features whose appearance frequencies are greater than 83.33% (25/30) in 30 simulations, and their mean ranking values by the F-statistics ranking measure for 3 populations

Ranking No. on Mean Ranking Values | Name of SNPs | Chromosome | Mean ranking values in 30 simulations | Ranking No. on Appearance Frequency |
---|---|---|---|---|

1 | rs232045 | chr11 | 0.9573 | 7 |

2 | rs12786973 | chr11 | 0.9547 | 6 |

3 | rs7946015 | chr11 | 0.9544 | 2 |

4 | rs4756778 | chr11 | 0.9524 | 3 |

5 | rs7931276 | chr11 | 0.9521 | 9 |

6 | rs4823557 | chr11 | 0.9518 | 5 |

7 | rs10832001 | chr11 | 0.9506 | 4 |

8 | rs35397 | chr5 | 0.9491 | 8 |

9 | rs11604470 | chr11 | 0.9480 | 12 |

10 | rs10831841 | chr11 | 0.9478 | 11 |

11 | rs2296224 | chr1 | 0.9456 | 10 |

12 | rs12286898 | chr11 | 0.9387 | 13 |

13 | rs1869084 | chr11 | 0.9341 | 20 |

14 | rs4491181 | chr11 | 0.9307 | 26 |

15 | rs1604797 | chr11 | 0.9258 | 1 |

16 | rs7931276 | chr11 | 0.9161 | 14 |

17 | rs11826168 | chr11 | 0.9103 | 19 |

18 | rs477036 | chr11 | 0.9072 | 16 |

19 | rs7940199 | chr11 | 0.9032 | 22 |

20 | rs4429025 | chr11 | 0.8711 | 25 |

21 | rs6483747 | chr11 | 0.8435 | 17 |

22 | rs199138 | chr15 | 0.8417 | 18 |

Top ranked features whose appearance frequencies are greater than 83.33% (25/30) in 30 simulations, and their mean ranking values by the modified t-test ranking measure for 3 populations

Ranking No. on Mean Ranking Values | Name of SNPs | Chromosome | Mean ranking values in 30 simulations | Ranking No. on Appearance Frequency |
---|---|---|---|---|

1 | rs232045 | chr11 | 8.0956 | 7 |

2 | rs1869084 | chr11 | 8.0886 | 9 |

3 | rs4756778 | chr11 | 8.0079 | 6 |

4 | rs11218714 | chr11 | 8.0047 | 11 |

5 | rs10832001 | chr11 | 7.9810 | 3 |

6 | rs7946015 | chr11 | 7.8988 | 2 |

7 | rs11826168 | chr11 | 7.8517 | 4 |

8 | rs704737 | chr11 | 7.7786 | 18 |

9 | rs1083184 | chr11 | 7.7778 | 24 |

10 | rs16913196 | chr11 | 7.7774 | 13 |

11 | rs12786973 | chr11 | 7.7499 | 5 |

12 | rs12286898 | chr11 | 7.7421 | 12 |

13 | rs11604470 | chr11 | 7.7401 | 16 |

14 | rs35397 | chr5 | 7.7257 | 8 |

15 | rs7931276 | chr11 | 7.7060 | 14 |

16 | rs477036 | chr11 | 7.6644 | 17 |

17 | rs6483747 | chr11 | 7.6625 | 19 |

18 | rs7931276 | chr11 | 7.5996 | 15 |

19 | rs1604797 | chr11 | 7.3847 | 1 |

20 | rs10836565 | chr11 | 7.3053 | 10 |

21 | rs2296224 | chr1 | 7.1358 | 21 |

22 | rs4275650 | chr11 | 7.0043 | 23 |

23 | rs7924569 | chr11 | 6.9431 | 20 |

24 | rs2582905 | chr11 | 6.9264 | 22 |

All experiments are executed using Matlab 7.1 on a personal computer with Windows XP operating system and Pentium 4 CPU (3.4 GHZ) and 1 GHZ RAM. We perform statistics about the running time of the two ranking measures together with the training and testing time. The mean time using the F-statistics to rank all SNPs of 3 populations is 5342.9 seconds, while on average 5728.7 seconds for the modified t-test ranking measures. It may be because that calculating the median value *S*_{0} makes the modified t-test ranking measure take more time than the F-statistics measure. Both algorithms cost more time on 4 populations compared to 3 populations. The total training and testing time is 6915.1 seconds. In terms of classification accuracy, the modified t-test ranking measure is superior over the F-statistics measure. Besides, the modified t-test ranking measure is proposed to deal with vector features and provides a way for ranking nominal features.

Since features' ranking only indicates the relevance of each feature, those features with the same or close ranking values may have high correlation between each other, i.e., redundancy. Therefore, it is possible for us to further reduce the number of SNPs in our future work.

## Conclusion

In this paper, we propose to use two feature importance ranking measures, i.e., the modified t-test and F-statistics, to rank large amount of SNPs, and then use the greedy manner together with a classifier to determine a desirable feature subset, which has the minimum size but leads to the highest classification accuracy. The final results show that both ranking methods are efficient on determining the importance of the SNPs. Although the two ranking measures find nearly the same amount of SNPs, the modified t-test ranking measure tends to be better than the F-statistics measure in terms of the classification accuracy. Compared to the classification method of Park *et al.*[7], we obtain a better result, i.e., good classification of the 3 populations using fewer, i.e., on average 64, SNPs.

## Methods

In classification on large data sets, feature selection is necessary and shows many advantages such as saving computational time, reducing computational burden and improving efficiency. Feature ranking, as an usual step in many feature selection methods [16, 17], is adopted in our experiment to determine the features' classification power. In this paper, we will present two feature importance ranking measures: a modified t-test from [9, 18, 19] and F-statistics [20], and make an comparison about their ranking abilities so as to evaluate the modified t-test ranking measure.

### Modified T-test

*et al.*[9] developed the nearest shrunken centroid method, i.e., calculating a t-statistic value (Equations (1)) for each gene of each class. This t-statistic value measured the difference between the mean of one class and the mean of all the classes, and the difference is standardized by the within-class standard deviation.

*t*

_{ ic }indicates the t-statistics value for the

*i*-th feature of the

*c*-th class. ${\overline{x}}_{ic}$ indicates the

*i*-th feature's mean value in the

*c*-th class and ${\overline{x}}_{i}$ indicates the

*i*-th feature's mean value for all classes.

*x*

_{ ij }represents the

*i*-th feature of the

*j*-th sample.

*N*is the total number of all the samples for all the

*C*classes and

*n*

_{ c }is the number of samples for the

*c*-th class.

*S*

_{ i }is the within-class standard deviation and

*S*

_{0}is set to be the median value of

*S*

_{ i }for all the features. This t-statistic value of Tibshirani et al. [9] measured the deviation between each class and the mean of all classes and was used to constitute a classifier. The authors did not refer to using the t-statistic of each class to rank features for all the classes. In [19], Wang et al. extended the t-statistic algorithm to rank features for all the classes. That is, the t-score (t-statistic value) of feature

*i*is calculated as the greatest t-score for all classes:

*AA*,

*AT*and

*TT*), Equation (4) can not be used to deal with our problem. We proposed a modified t-test ranking method, in which different nominal values are represented by different vectors to realize the calculation. In the following, we generalized the t-score of each feature in 3 steps:

- 1.
Suppose the feature set is

*F*= (*f*_{1},...,*f*_{ i }, ...,*f*_{ g }), and feature*i*has*m*_{ i }different nominal values represented as ${f}_{i}=({x}_{i}^{(1)},{x}_{i}^{(2)},\mathrm{...},{x}_{i}^{({m}_{i})})$ - 2.
Transform each nominal feature value into a vector with the dimension

*m*_{ i }, i.e., ${x}_{i}^{(1)}\Rightarrow {X}_{i}^{(1)}=\{0,\mathrm{...},0,1\},{x}_{i}^{(2)}\Rightarrow {X}_{i}^{(2)}=\{0,\mathrm{...},1,0\},\mathrm{...},{x}_{i}^{({m}_{i})}\Rightarrow {X}_{i}^{({m}_{i})}=\{1,\mathrm{...},0,0\}$. - 3.Replace all the numerical features in Equations (1) and (2) with those vectors (see Equations (5) and (6)).${t}_{i}=max\left\{\frac{\left|{\overline{X}}_{ic}-{\overline{X}}_{i}\right|}{{M}_{c}{S}_{i}},c=1,2,\mathrm{...}C\right\}$(5)${S}_{i}^{2}=\frac{1}{N-C}{\displaystyle \sum _{c=1}^{C}{\displaystyle \sum _{j\in c}({X}_{ij}-{\overline{X}}_{ic}){({X}_{ij}-{\overline{X}}_{ic})}^{T}}}$(6)

The ranking rule is: the greater the t-scores, the more relevant the features.

### F-statistics

In our experiment, we will use another ranking measure, i.e., F-statistics, to make a comparison with the modified t-test. The version of F-statistics used in our experiment is based on the definition of [25], which was originally developed by [20] and used in population genetics to describe the level of heterozygosity in a population.

*C*sub-populations and each feature expressed as bi-allelic SNPs (i.e., consisting of any two different nucleotides from the four nucleotides

*ATCG*), the F-statistics (

*F*

_{ st }) is calculated as:

*p*and

*q*are corresponding to the two alleles' frequencies, respectively, in one population. $\overline{p}$ and $\overline{q}$ refer to the two alleles' mean frequencies for all the population classes.

*Var*

_{ p }represents the variance (See Equation 8) of one allele.

*p*

_{ c }designates the frequency of one allele for the

*c*-th population. And the mean frequency is easy to obtain from:

The ranking rule is same as the modified t-test, i.e., the larger the *F*_{
st
}value, the more significant the SNP for population classification.

### The Classifier

Although many classifiers, such as classical neural network, naive Bayes classifier and so on, can be applied in our classification, here we would like to choose the support vector machine (SVM) [11, 12] in our experiment because of its some attractive features, such as effectively avoiding overfitting and accomodating large feature spaces, fast speed and so on. It will be used not only in the final classification, but also in the feature selection to test different feature subsets and determine the one with the highest classification accuracy. During the classification process, we determine the kernel parameter *γ* and the penal parameter *ν* through the double cross-validation method.

## Declarations

### Acknowledgements

We thank Dr Maria Kowalczuk (the Assistant Editor), the BioMed Central Editorial Production Team and the anonymous reviewer who provided comments and suggestions that helped to significantly improve the paper. The experimental data was provided by the international HapMap Project website [10].

## Authors’ Affiliations

## References

- Duerinck KF[http://www.duerinck.com/snp.html]
- Bafna V, Halldorsson B, Schwartz R, Clark A, Istrail S: Haplotypes and Informative SNP selection: Don't block out information. In Proc of RECOMB 2003, 19–27.Google Scholar
- Halldrsson B, Bafna V, Lippert R, Schwartz R, de la Vega FM, Clark A, Istrail S: Optimal haplotype blockfree selection of tagging snps for genome-wide association studies. Genome research 2004, 14: 1633–1640. 10.1101/gr.2570004View ArticleGoogle Scholar
- Halperin E, Kimmel G, Shamir R: Tag SNP selection in genotype data for maximizing SNP prediction accuracy. Bioinformatics 2005, 21 Suppl 1: i195-i203. 10.1093/bioinformatics/bti1021View ArticlePubMedGoogle Scholar
- Phuong TM, Lin Z, Altman RB: Choosing SNPs using feature selection. Proc IEEE Comput Syst Bioinform Conf 2005, 301–309.Google Scholar
- Rosenberg NA: Algorithms for selecting informative marker panels for population assignment. Journal of computational biology 2005, 12: 1183–1201. 10.1089/cmb.2005.12.1183View ArticlePubMedGoogle Scholar
- Park J, Hwang S, Lee YS, Kim SC, Lee D: SNP@Ethnos: a database of ethnically variant single-nucleotide polymorphisms. Nucleic Acids Res 2007, 35(Database issue):D711-D715. 10.1093/nar/gkl962PubMed CentralView ArticlePubMedGoogle Scholar
- Rosenberg NA, Li LM, Ward R, Pritchard JK: Informativeness of Genetic Markers for Inference of Ancestry. Am J Hum Genet 2003, 73: 1402–1422. 10.1086/380416PubMed CentralView ArticlePubMedGoogle Scholar
- Tibshirani R, Hastie T, Narasimhan B, Chu G: Diagnosis ofmultiple cancer types by shrunken centroids of gene expression. Proc Natl Acad Sci USA 2002, 99: 6567–6572. 10.1073/pnas.082099299PubMed CentralView ArticlePubMedGoogle Scholar
- The International HapMap Consortium. The international Hapmap Project Nature 2003, 426: 789–796. [http://www.hapmap.org/genotypes] 10.1038/nature02168
- Vapnik V: Statistical learning theory. NewYork,: Wiley; 1998.Google Scholar
- Wang LP: Support Vector Machines: Theory and Applications. Berlin: Springer; 2005.Google Scholar
- Mandoiu I: Algorithms for SNP data collection and analysis.[http://www.engr.uconn.edu/~ion/FILES/ppt/uri_11_10_06.ppt]
- Stephens M, Smith NJ, Donnelly P: A new statistical method for haplotype reconstruction from population dat. American Journal of Human Genetics 2001, 68: 978–989. 10.1086/319501PubMed CentralView ArticlePubMedGoogle Scholar
- Gusev A, Mandoiu I, Pasaniuc B: Highly Scalable Genotype Phasing by Entropy Minimization. IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB) 2007.Google Scholar
- Guyon I, Elisseeff A: An Introduction to Variable and Feature Selection. Journal of Machine Learning Research 2003, 3: 1157–1182. 10.1162/153244303322753616Google Scholar
- Wang LP, Fu XJ: Data Mining with Computational Intelligence. Berlin: Springer-Verlag; 2005. ISBN 3–540–24522–7 ISBN 3-540-24522-7Google Scholar
- Devore J, Peck R: Statistics:the exploration and analysis of data. 3rd edition. CA: Duxbury Press; 1997.Google Scholar
- Wang L, Chu F, Xie W: Accurate cancer classification using expressions of very few genes. IEEE/ACM Trans Comput Biol Bioinform 2007, 4(1):40–53. 10.1109/TCBB.2007.1006View ArticlePubMedGoogle Scholar
- Wright S: The interpretation of population structure by F-statistics with special regard to systems of mating. Evolution 1965, 19: 395–420. 10.2307/2406450View ArticleGoogle Scholar
- Jaeger J, Sengupta R, Ruzzo WL: Improved Gene Selection For Classification Of Microarrays. Pac Symp Biocomput 2003, 53–64.Google Scholar
- Su Y, Murali TM, Pavlovic V, Schaffer M, Kasif S: RankGene: Identifcation of Diagnostic Genes Based on Expression Data. Bioinformatics 2003, 19: 1578–1579. 10.1093/bioinformatics/btg179View ArticlePubMedGoogle Scholar
- Wu B, Abbott T, Fishman D, McMurray W, Mor G, Stone K, Ward D, Williams K, Zhao H: Comparison of statistical methods for classifcation of ovarian cancer using mass spectrometry data. BioInformatics 2003, 19: 1636–1643. 10.1093/bioinformatics/btg210View ArticlePubMedGoogle Scholar
- Levner I: Feature selection and nearest centroid classification for protein mass spectrometry. BMC Bioinformatics 2005, 6: 68. 10.1186/1471-2105-6-68PubMed CentralView ArticlePubMedGoogle Scholar
- Trochim WM:The Research Methods Knowledge Base. 2nd edition. Atomic Dog Publishing; 2004. [http://www.socialresearchmethods.net/kb/]Google Scholar

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