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Am. J. Applied Sci., 9 (1): 127-131, 2012dimension of feature vectors and m<d is the number of Step 3: By using Eq. 1, compute classificationselected features. A feature fk is included in the subset s, accuracy αk using feature subset s ∪ fk on χ valif for this fk, the subset s gives the highest classification segment.accuracy (or the lowest misclassification error). Let χ Step 4: Repeat Steps 1-3 N times (we use N = 10) to={x1, x2,…xn} be the training sample set where each xi get an average classification accuracy α k (foris a d-dimensional vector. Let x i ∈ ℜ m be the ˆ k = 1, 2, …, d).corresponding vector having its features defined by Step 5: Allocate the feature to the subset s which givessubset s. Let Ω = {ωj; j = 1, 2 ,…c} be the finite set of highest α k , i.e., p = arg max α k and include fp in c classes and χ j be the set of m-dimensional training ˆ subset s; i.e., s ⇐ s∪ fp. If two or morevectors x i of class ωj. The Bayesian classification ˆ features are giving equal average classificationprocedure is described as follows. According to the accuracy then select fp which is individuallyBayes rule, the a posteriori probability P(ω j | x) can be ˆ giving the highest accuracy. Step 6: Exclude feature fp from the feature set f and goevaluated using the class conditional density function to Step 1 to find the next best feature until thep(x | ω j ) and a priori probability P(ωj). If we assume that ˆ average classification accuracy reaches thethe parametric distribution is normal then a posteriori maximum (i.e., max α k (q) ≥ max α k (q + 1)probability can be defined as Eq. 1: where α k (q) is the average classification 1 accuracy at q th iteratation).P(ω j | x) = ˆ exp (2π) m/2 ˆ | Σ j |1/ 2 (1) The above algorithm will give a subset of features. 1 ˆ ˆ ˆ+ ˆ ˆ T − 2 (x − µ j ) Σ j (x − µ j ) P(ω j ) However, if more than one subset of features is required then the procedure should be repeated on the remaining ˆwhere, µ j is the centroid and Σ j the covariance matrix ˆ features. Next, we describe materials and method.computed from χ j . Σ + is the pseudo-inverse of Σ j ˆ ˆ j ˆ MATERIALS AND METHODS ˆ(which is applied when Σ j is a singular matrix). If m < Publicly available DNA microarray gene ˆn then Σ j will be a non-singular matrix and therefore expression datasets are used from Kent Ridge Bio-conventional Σ −1 can be used in Eq. 1 instead of Σ + . ˆ j ˆ j medical repository (http://datam.i2r.a- star.edu.sg/datasets/krbd/). The program code is writtenThe training set χ can be partitioned into a smaller in Matlab on i7 dual-core Pentium processor in Linuxportion of training set χ tr and validation set χ val. The set environment.χ tr can be used to evaluate the parameters of equation 1(i.e., µ j and Σ j ) and the set χ val can be used to compute ˆ ˆ RESULTSclassification accuracy (or misclassification error) for In the experimentation 3 DNA microarray genethe feature vectors defined by the subset s. Theprocedure of finding feature subset is described in the expression datasets have been used. The description offollowing algorithm: the datasets is given as follows. Acute leukaemia dataset (Golub et al., 1999): ThisAlgorithm: dataset consists of DNA microarray gene expression data of human acute leukaemia for cancer classification.Step 0: Define feature set f = {f1, f2,…fd} and initialize Two types of acute leukaemia data are provided for s = {} as empty set. classification namely Acute Lymphoblastic LeukaemiaStep 1: Given the training feature vectors χ, partition it (ALL) and Acute Myeloid Leukaemia (AML). The randomly into two segments χtr and χval using dataset is subdivided into 38 training samples and 34 partitioning ratio r (we allocate approximate test samples. The training set consists of 38 bone 60% of samples to χtr and the remaining in the marrow samples (27 ALL and 11 AML) over 7129 other segment). probes. The test set consists of 34 samples with 20 ALLStep 2: Take feature subset s ∪ fk (for k =1, 2, …,d) at and 14 AML, prepared under different experimental a time and compute for this feature subset the conditions. All the samples have 7129 dimensions and training parameters µ j and Σ j on χ tr segment. ˆ ˆ all are numeric. 128
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Am. J. Applied Sci., 9 (1): 127-131, 2012 Lung dataset (Gordon et al., 2002): This dataset datasets are described in Table 1. Their correspondingcontains gene expression levels of Malignant classification accuracies on TRAIN data are also given.Mesothelioma (MPM) and adenocarcinoma (ADCA) of The biological significance of the identified genes isthe lung. There are 181 tissue samples (31 MPM and depicted in the last column of the table under p-value150 ADCA). The training set contains 32 samples, 16 statistics using Ingenuity Pathways Analysis (IPA,MPM and 16 ADCA. The rest of 149 samples are used http://www.ingenuity.com) tool. For acute leukemiafor testing. Each sample is described by 12533 genes. dataset the highest classification accuracy on training Breast cancer dataset (Van’t et al., 2002): This is a set is obtained at 2nd iteration which is 100%; for lung2 class problem with 78 training samples (34 relapse cancer dataset, 100% classification accuracy is obtainedand 44 non-relapses) and 19 test samples (12 relapse at the 1st iteration; and, for breast cancer dataset,and 7 non-relapses) of relapse and non-relapse. The highest classification accuracy 95% is obtained at thedimension of breast cancer dataset is 24481. 7th iteration. The proposed algorithm is compared with The proposed algorithm is used for feature several other existing techniques on DNA microarrayselection. For classification of test samples we use gene expression datasets. The performance (in terms ofBayesian classifier (using Eq. 1) and Linear classification accuracy) of various techniques isDiscriminant Analysis (LDA) technique using Nearest depicted in Table 2. It can be observed that theCentroid Classifier (NCC) with Euclidean distance proposed method is giving high classification accuracymeasure. The identified genes from all the three on very small number of selected features.Table 1 Genes identified on DNA microarray gene expression datasets TRAIN classificationDatasets Genes number/gene accession accuracy (%) P-valueAcute leukemia 4847 (X95735-at) 96.3 1.38e-4-3.20e-2 6055 (U37055-rna1-s-at) 100.0Lung cancer 2549 (32551-at) 100.0 6.90e-5-1.38e-2Breast cancer 10889 (AL080059) 75.3 6.61e-3-4.37e-2 4436 (NM-002829) 83.4 2295 (Connoting 34964-RC) 86.9 12455 (U90911) 89.4 14868 (D38521) 92.2 16795 (Connoting 54916-RC) 93.8 12817 (L41143) 95.0Table 2: A Comparison of classification accuracy on (a) acute leukemia (b) lung cancer and (c) breast cancer datasetsMethods Acute leukemia (Classification accuracy(Feature selection + classification) # Selected genes on TEST data) (%)Prediction strength+ SVMs (Furey et al., 2000) 25-1000 88- 94Discretization + decision rules (Tan and Gilbert, 2003) 1038 91RCBT (Cong et al., 2005) 10-40 91Neighbourhood analysis + weighted 50 85voting (Golub et al., 1999)CBF + decision trees (Wang et al., 2005) 1 91Information gain + Bayes classifier 2 91Information gain + LDA with NCC 2 88Chi-squared + Bayes classifier 2 91Chi-squared + LDA with NCC 2 88Proposed algorithm + Bayesian classifier 2 91Proposed algorithm + LDA with NCC 2 94B: Lung cancerDiscretization + decision trees (Tan and Gilbert, 2003) 5365 93Boosting (Li and Wong, 2003) unknown 81Bagging (Li and Wong, 2003) unknown 88RCBT (Cong et al., 2005) 10-40 98C4.5 (Li and Wong, 2003) 1 81Information gain + Bayes classifier 1 89Information gain + LDA with NCC 1 91Chi-squared + Bayes classifier 1 77Chi-squared + LDA with NCC 1 58Proposed algorithm + Bayesian classifier 1 89Proposed algorithm + LDA with NCC 1 98 129
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Am. J. Applied Sci., 9 (1): 127-131, 2012Table 2: ContinueC Breast cancerDCA (Thi et al., 2008) 19 74L1-SVM (Thi et al., 2008) 24045 64p-value of t-test + DLDA(Yan and Zheng, 2007) 50 59Golub + Golub (Yan and Zheng, 2007) 50 62SAM + DLDA (Yan and Zheng, 2007) 50 58Corr + Corr (Yan and Zheng, 2007) 50 62MPAS + Marginal (Yan and Zheng, 2007) 50 65MPAS + MPAS (Yan and Zheng, 2007) 50 69Information gain + Bayes classifier 7 37Information gain + LDA with NCC 7 63Chi-squared + Bayes classifier 7 58Chi-squared + LDA with NCC 7 58Proposed algorithm + Bayesian classifier 7 74Proposed algorithm + LDA with NCC 7 74 DISCUSSION Golub, T.R., D.K. Slonim, P. Tamayo, C. Huard and M. Gaasenbeek et al., 1999. Molecular classification A feature or gene selection algorithm using Bayes of cancer: Class discovery and class prediction byclassification approach has been presented. The gene expression monitoring. Science, 286: 531-pseudoinverse of covariance matrix is used in place of 537. DOI: 10.1126/science.286.5439.531inverse covariance matrix for the class-conditionalprobability density function (Eq. 1), to cater for any Gordon, G.J., R.V. Jensen, L.L. Hsiao, S.R. Gullanssingularities of the matrix (i.e., when the number of and J.E. Blumenstock et al., 2002. Translation ofselected genes > number of training samples). The gene microarray data into clinically relevant cancersubset is obtained in the forward selection manner. It can diagnostic tests using gene expression ratios inbe observed that on 3 DNA microarray gene expression lung cancer and mesothelioma. Cancer Res., 62:datasets, the proposed algorithm is exhibiting very 4963-4967. PMID: 12208747promising classification performance when compared Li, J. and L. Wong, 2003. Using rules to analyse bio-with several other feature selection techniques. medical data: A comparison between C4.5 and PCL. Adv. Web-Age Inform. Manage., 2762: 254- CONCLUSION 265. DOI: 10.1007/978-3-540-45160-0_25 A gene selection algorithm using Bayesian Sharma, A. and K.K. Paliwal, 2008. Cancerclassification approach has been presented. The classification by gradient LDA technique usingalgorithm has been experimented on several DNA microarray gene expression data. Data Knowl.microarray gene expression datasets and compared with Eng., 66: 338-347. DOI:the several other existing methods. It is observed that 10.1016/j.datak.2008.04.004the obtained genes exhibit high classification accuracy Sharma, A., C.H. Koh, S. Imoto and S. Miyano, 2011a.and also show biological significance. Strategy of finding optimal number of features on gene expression data. Elect. Lett., 47: 480-482. REFERENCES DOI: 10.1049/el.2011.0526Cong, G., K.L. Tan, A.K.H. Tung and X. Xu, 2005. Sharma, A., S. Imoto and S. Miyano, 2011b. A top-r Mining top-k covering rule groups for gene feature selection algorithm for microarray gene expression data. Proceedings of the ACM expression data. IEEE/ACM Trans. Comput. Biol. SIGMOD International Conference on Bioinform. 1-1. DOI: 10.1109/TCBB.2011.151 Management of Data, Jun. 13-17, Baltimore, MD, Tan, A.C. and D. Gilbert, 2003. Ensemble machine USA., pp: 670-681. DOI: learning on gene expression data for cancer 10.1145/1066157.1066234 classification. Applied Bioinform., 2: S75-83.Furey, T.S., N. Cristianini, N. Duffy, D.W. Bednarski and M. Schummer et al., 2000. Support vector PMID: 15130820 machine classification and validation of cancer Thi, H.A.L., V.V. Nguyen and S. Ouchani, 2008. Gene tissue samples using microarray expression data. selection for cancer classification using DCA. Adv. Bioinformatics, 16: 906-914. DOI: Data Min. Appli., 5139: 62-72. DOI: 10.1007/978- 10.1093/bioinformatics/16.10.906 3-540-88192-6_8 130
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Am. J. Applied Sci., 9 (1): 127-131, 2012Van’t, V., L.J. Dai, H. Van de, M.J. Vijver and Y.D. He Yan, X. and T. Zheng, 2007. Discriminant analysis et al., 2002. Gene expression profiling predicts using multigene expression profiles in clinical outcome of breast cancer. Lett. Nature. classification of breast cancer. Proceedings of the Nature, 415: 530-536. DOI: 10.1038/415530a International Conference on Bioinformatics andWang, Y., I.V. Tetko, M.A. Hall, E. Frank and A. Computational Biology, Jun. 25-28, CSREA Press, Facius et al., 2005. Gene selection from microarray Las Vegas Nevada, USA., pp: 643-649. data for cancer classification-a machine learning approach. Comput. Biol. Chem., 29: 37-46. DOI: 10.1016/j.compbiolchem.2004.11.001 131
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