A blocking strategy to improve gene selection for classification of gene expression data

Because of high dimensionality, machine learning algorithms typically rely on feature selection techniques in order to perform effective classification in microarray gene expression data sets. However, the large number of features compared to the number of samples makes the task of feature selection computationally hard and prone to errors. This paper interprets feature selection as a task of stochastic optimization, where the goal is to select among an exponential number of alternative gene subsets the one expected to return the highest generalization in classification. Blocking is an experimental design strategy which produces similar experimental conditions to compare alternative stochastic configurations in order to be confident that observed differences in accuracy are due to actual differences rather than to fluctuations and noise effects. We propose an original blocking strategy for improving feature selection which aggregates in a paired way the validation outcomes of several learning algorithms to assess a gene subset and compare it to others. This is a novelty with respect to conventional wrappers, which commonly adopt a sole learning algorithm to evaluate the relevance of a given set of variables. The rationale of the approach is that, by increasing the amount of experimental conditions under which we validate a feature subset, we can lessen the problems related to the scarcity of samples and consequently come up with a better selection. The paper shows that the blocking strategy significantly improves the performance of a conventional forward selection for a set of 16 publicly available cancer expression data sets. The experiments involve six different classifiers and show that improvements take place independent of the classification algorithm used after the selection step. Two further validations based on available biological annotation support the claim that blocking strategies in feature selection may improve the accuracy and the quality of the solution. The first validation is based on retrieving PubMEd abstracts associated to the selected genes and matching them to regular expressions describing the biological phenomenon underlying the expression data sets. The biological validation that follows is based on the use of the Bioconductor package GoStats in order to perform Gene Ontology statistical analysis.     

Linking gene expression data with patient survival times using partial least squares

There is an increasing need to link the large amount of genotypic data, gathered using microarrays for example, with various phenotypic data from patients. The classification problem in which gene expression data serve as predictors and a class label phenotype as the binary outcome variable has been examined extensively, but there has been less emphasis in dealing with other types of phenotypic data. In particular, patient survival times with censoring are often not used directly as a response variable due to the complications that arise from censoring. We show that the issues involving censored data can be circumvented by reformulating the problem as a standard Poisson regression problem. The procedure for solving the transformed problem is a combination of two approaches: partial least squares, a regression technique that is especially effective when there is severe collinearity due to a large number of predictors, and generalized linear regression, which extends standard linear regression to deal with various types of response variables. The linear combinations of the original variables identified by the method are highly correlated with the patient survival times and at the same time account for the variability in the covariates. The algorithm is fast, as it does not involve any matrix decompositions in the iterations. We apply our method to data sets from lung carcinoma and diffuse large B-cell lymphoma studies to verify its effectiveness.     

Dimension reduction methods for microarrays with application to censored survival data

MOTIVATION: Recent research has shown that gene expression profiles can potentially be used for predicting various clinical phenotypes, such as tumor class, drug response and survival time. While there has been extensive studies on tumor classification, there has been less emphasis on other phenotypic features, in particular, patient survival time or time to cancer recurrence, which are subject to right censoring. We consider in this paper an analysis of censored survival time based on microarray gene expression profiles. RESULTS: We propose a dimension reduction strategy, which combines principal components analysis and sliced inverse regression, to identify linear combinations of genes, that both account for the variability in the gene expression levels and preserve the phenotypic information. The extracted gene combinations are then employed as covariates in a predictive survival model formulation. We apply the proposed method to a large diffuse large-B-cell lymphoma dataset, which consists of 240 patients and 7399 genes, and build a Cox proportional hazards model based on the derived gene expression components. The proposed method is shown to provide a good predictive performance for patient survival, as demonstrated by both the significant survival difference between the predicted risk groups and the receiver operator characteristics analysis. AVAILABILITY: R programs are available upon request from the authors. SUPPLEMENTARY INFORMATION: http://dna.ucdavis.edu/~hli/bioinfo-surv-supp.pdf.     

Sliced inverse regression with regularizations

Summary .   In high-dimensional data analysis, sliced inverse regression (SIR) has proven to be an effective dimension reduction tool and has enjoyed wide applications. The usual SIR, however, cannot work with problems where the number of predictors, p , exceeds the sample size, n , and can suffer when there is high collinearity among the predictors. In addition, the reduced dimensional space consists of linear combinations of all the original predictors and no variable selection is achieved. In this article, we propose a regularized SIR approach based on the least-squares formulation of SIR. The L ₂ regularization is introduced, and an alternating least-squares algorithm is developed, to enable SIR to work with   n < p   and highly correlated predictors. The L ₁ regularization is further introduced to achieve simultaneous reduction estimation and predictor selection. Both simulations and the analysis of a microarray expression data set demonstrate the usefulness of the proposed method.     

Using uncorrelated discriminant analysis for tissue classification with gene expression data

The classification of tissue samples based on gene expression data is an important problem in medical diagnosis of diseases such as cancer. In gene expression data, the number of genes is usually very high (in the thousands) compared to the number of data samples (in the tens or low hundreds); that is, the data dimension is large compared to the number of data points (such data is said to be undersampled). To cope with performance and accuracy problems associated with high dimensionality, it is commonplace to apply a preprocessing step that transforms the data to a space of significantly lower dimension with limited loss of the information present in the original data. Linear discriminant analysis (LDA) is a well-known technique for dimension reduction and feature extraction, but it is not applicable for undersampled data due to singularity problems associated with the matrices in the underlying representation. This paper presents a dimension reduction and feature extraction scheme, called uncorrelated linear discriminant analysis (ULDA), for undersampled problems and illustrates its utility on gene expression data. ULDA employs the generalized singular value decomposition method to handle undersampled data and the features that it produces in the transformed space are uncorrelated, which makes it attractive for gene expression data. The properties of ULDA are established rigorously and extensive experimental results on gene expression data are presented to illustrate its effectiveness in classifying tissue samples. These results provide a comparative study of various state-of-the-art classification methods on well-known gene expression data sets     

Linear modes of gene expression determined by independent component analysis

MOTIVATION: The expression of genes is controlled by specific combinations of cellular variables. We applied Independent Component Analysis (ICA) to gene expression data, deriving a linear model based on hidden variables, which we term 'expression modes'. The expression of each gene is a linear function of the expression modes, where, according to the ICA model, the linear influences of different modes show a minimal statistical dependence, and their distributions deviate sharply from the normal distribution. RESULTS: Studying cell cycle-related gene expression in yeast, we found that the dominant expression modes could be related to distinct biological functions, such as phases of the cell cycle or the mating response. Analysis of human lymphocytes revealed modes that were related to characteristic differences between cell types. With both data sets, the linear influences of the dominant modes showed distributions with large tails, indicating the existence of specifically up- and downregulated target genes. The expression modes and their influences can be used to visualize the samples and genes in low-dimensional spaces. A projection to expression modes helps to highlight particular biological functions, to reduce noise, and to compress the data in a biologically sensible way.     

Ensemble learning of genetic networks from time-series expression data

MOTIVATION: Inferring genetic networks from time-series expression data has been a great deal of interest. In most cases, however, the number of genes exceeds that of data points which, in principle, makes it impossible to recover the underlying networks. To address the dimensionality problem, we apply the subset selection method to a linear system of difference equations. Previous approaches assign the single most likely combination of regulators to each target gene, which often causes over-fitting of the small number of data. RESULTS: Here, we propose a new algorithm, named LEARNe, which merges the predictions from all the combinations of regulators that have a certain level of likelihood. LEARNe provides more accurate and robust predictions than previous methods for the structure of genetic networks under the linear system model. We tested LEARNe for reconstructing the SOS regulatory network of Escherichia coli and the cell cycle regulatory network of yeast from real experimental data, where LEARNe also exhibited better performances than previous methods. AVAILABILITY: The MATLAB codes are available upon request from the authors.     

Interval-valued analysis for discriminative gene selection and tissue sample classification using microarray data

An important application of gene expression data is to classify samples in a variety of diagnostic fields. However, high dimensionality and a small number of noisy samples pose significant challenges to existing classification methods. Focused on the problems of overfitting and sensitivity to noise of the dataset in the classification of microarray data, we propose an interval-valued analysis method based on a rough set technique to select discriminative genes and to use these genes to classify tissue samples of microarray data. We first select a small subset of genes based on interval-valued rough set by considering the preference-ordered domains of the gene expression data, and then classify test samples into certain classes with a term of similar degree. Experiments show that the proposed method is able to reach high prediction accuracies with a small number of selected genes and its performance is robust to noise.     

Survival prediction of diffuse large-B-cell lymphoma based on both clinical and gene expression information

MOTIVATION: It is important to predict the outcome of patients with diffuse large-B-cell lymphoma after chemotherapy, since the survival rate after treatment of this common lymphoma disease is <50%. Both clinically based outcome predictors and the gene expression-based molecular factors have been proposed independently in disease prognosis. However combining the high-dimensional genomic data and the clinically relevant information to predict disease outcome is challenging. RESULTS: We describe an integrated clinicogenomic modeling approach that combines gene expression profiles and the clinically based International Prognostic Index (IPI) for personalized prediction in disease outcome. Dimension reduction methods are proposed to produce linear combinations of gene expressions, while taking into account clinical IPI information. The extracted summary measures capture all the regression information of the censored survival phenotype given both genomic and clinical data, and are employed as covariates in the subsequent survival model formulation. A case study of diffuse large-B-cell lymphoma data, as well as Monte Carlo simulations, both demonstrate that the proposed integrative modeling improves the prediction accuracy, delivering predictions more accurate than those achieved by using either clinical data or molecular predictors alone.     

Unravelling gene networks from noisy under-determined experimental perturbation data

Systems biology aims to study the properties of biological systems in terms of the properties of their molecular constituents. This occurs frequently by a process of mathematical modelling. The first step in this modelling process is to unravel the interaction structure of biological systems from experimental data. Previously, an algorithm for gene network inference from gene expression perturbation data was proposed. Here, the algorithm is extended by using regression with subset selection. The performance of the algorithm is extensively evaluated on a set of data produced with gene network models at different levels of simulated experimental noise. Regression with subset selection outperforms the previously stated matrix inverse approach in the presence of experimental noise. Furthermore, this regression approach enables us to deal with under-determination, that is, when not all genes are perturbed. The results on incomplete data sets show that the new method performs well at higher number of perturbations, even when noise levels are high. At lower number of perturbations, although still being able to recover the majority of the connections, less confidence can be placed in the recovered edges.     

Development of two-stage SVM-RFE gene selection strategy for microarray expression data analysis

Extracting a subset of informative genes from microarray expression data is a critical data preparation step in cancer classification and other biological function analyses. Though many algorithms have been developed, the Support Vector Machine - Recursive Feature Elimination (SVM-RFE) algorithm is one of the best gene feature selection algorithms. It assumes that a smaller "filter-out" factor in the SVM-RFE, which results in a smaller number of gene features eliminated in each recursion, should lead to extraction of a better gene subset. Because the SVM-RFE is highly sensitive to the "filter-out" factor, our simulations have shown that this assumption is not always correct and that the SVM-RFE is an unstable algorithm. To select a set of key gene features for reliable prediction of cancer types or subtypes and other applications, a new two-stage SVM-RFE algorithm has been developed. It is designed to effectively eliminate most of the irrelevant, redundant and noisy genes while keeping information loss small at the first stage. A fine selection for the final gene subset is then performed at the second stage. The two-stage SVM-RFE overcomes the instability problem of the SVM-RFE to achieve better algorithm utility. We have demonstrated that the two-stage SVM-RFE is significantly more accurate and more reliable than the SVM-RFE and three correlation-based methods based on our analysis of three publicly available microarray expression datasets. Furthermore, the two-stage SVM-RFE is computationally efficient because its time complexity is O(d*log(2)d}, where d is the size of the original gene set.     

Differential gene expression detection and sample classification using penalized linear regression models

Differential gene expression detection and sample classification using microarray data have received much research interest recently. Owing to the large number of genes p and small number of samples n (p > n), microarray data analysis poses big challenges for statistical analysis. An obvious problem owing to the 'large p small n' is over-fitting. Just by chance, we are likely to find some non-differentially expressed genes that can classify the samples very well. The idea of shrinkage is to regularize the model parameters to reduce the effects of noise and produce reliable inferences. Shrinkage has been successfully applied in the microarray data analysis. The SAM statistics proposed by Tusher et al. and the 'nearest shrunken centroid' proposed by Tibshirani et al. are ad hoc shrinkage methods. Both methods are simple, intuitive and prove to be useful in empirical studies. Recently Wu proposed the penalized t/F-statistics with shrinkage by formally using the (1) penalized linear regression models for two-class microarray data, showing good performance. In this paper we systematically discussed the use of penalized regression models for analyzing microarray data. We generalize the two-class penalized t/F-statistics proposed by Wu to multi-class microarray data. We formally derive the ad hoc shrunken centroid used by Tibshirani et al. using the (1) penalized regression models. And we show that the penalized linear regression models provide a rigorous and unified statistical framework for sample classification and differential gene expression detection.     

Feature Selection for high Dimensional DNA Microarray data using hybrid approaches

Feature selection from DNA microarray data is a major challenge due to high dimensionality in expression data. The number of samples in the microarray data set is much smaller compared to the number of genes. Hence the data is improper to be used as the training set of a classifier. Therefore it is important to select features prior to training the classifier. It should be noted that only a small subset of genes from the data set exhibits a strong correlation with the class. This is because finding the relevant genes from the data set is often non-trivial. Thus there is a need to develop robust yet reliable methods for gene finding in expression data. We describe the use of several hybrid feature selection approaches for gene finding in expression data. These approaches include filtering (filter out the best genes from the data set) and wrapper (best subset of genes from the data set) phases. The methods use information gain (IG) and Pearson Product Moment Correlation (PPMC) as the filtering parameters and biogeography based optimization (BBO) as the wrapper approach. K nearest neighbour algorithm (KNN) and back propagation neural network are used for evaluating the fitness of gene subsets during feature selection. Our analysis shows that an impressive performance is provided by the IG-BBO-KNN combination in different data sets with high accuracy (>90%) and low error rate.