Eigengene-based linear discriminant model for tumor classification using gene expression microarray data

MOTIVATION: The nearest shrunken centroids classifier has become a popular algorithm in tumor classification problems using gene expression microarray data. Feature selection is an embedded part of the method to select top-ranking genes based on a univariate distance statistic calculated for each gene individually. The univariate statistics summarize gene expression profiles outside of the gene co-regulation network context, leading to redundant information being included in the selection procedure. RESULTS: We propose an Eigengene-based Linear Discriminant Analysis (ELDA) to address gene selection in a multivariate framework. The algorithm uses a modified rotated Spectral Decomposition (SpD) technique to select 'hub' genes that associate with the most important eigenvectors. Using three benchmark cancer microarray datasets, we show that ELDA selects the most characteristic genes, leading to substantially smaller classifiers than the univariate feature selection based analogues. The resulting de-correlated expression profiles make the gene-wise independence assumption more realistic and applicable for the shrunken centroids classifier and other diagonal linear discriminant type of models. Our algorithm further incorporates a misclassification cost matrix, allowing differential penalization of one type of error over another. In the breast cancer data, we show false negative prognosis can be controlled via a cost-adjusted discriminant function. AVAILABILITY: R code for the ELDA algorithm is available from author upon request.     

A goal programming network for linear programming

Tank and Hopfield have shown that networks of analog neurons can be used to solve linear programming (LP) problems. We have re-examined their approach and found that their network model frequently computes solutions that are only suboptimal or that violate the LP problem's constraints. As their approach has proven unreliable, we have developed a new network model: the goal programming network. To this end, a network model was first developed for goal programming problems, a particular type of LP problems. From the manner the network operates on such problems, it was concluded that overconstrainedness, which is possibly present in an LP formulation, should be removed, and we have provided a simple procedure to accomplish this.     

Tumor classification using phylogenetic methods on expression data

Tumor classification is a well-studied problem in the field of bioinformatics. Developments in the field of DNA chip design have now made it possible to measure the expression levels of thousands of genes in sample tissue from healthy cell lines or tumors. A number of studies have examined the problems of tumor classification: class discovery, the problem of defining a number of classes of tumors using the data from a DNA chip, and class prediction, the problem of accurately classifying an unknown tumor, given expression data from the unknown tumor and from a learning set. The current work has applied phylogenetic methods to both problems. To solve the class discovery problem, we impose a metric on a set of tumors as a function of their gene expression levels, and impose a tree structure on this metric, using standard tree fitting methods borrowed from the field of phylogenetics. Phylogenetic methods provide a simple way of imposing a clear hierarchical relationship on the data, with branch lengths in the classification tree representing the degree of separation witnessed. We tested our method for class discovery on two data sets: a data set of 87 tissues, comprised mostly of small, round, blue-cell tumors (SRBCTs), and a data set of 22 breast tumors. We fit the 87 samples of the first set to a classification tree, which neatly separated into four major clusters corresponding exactly to the four groups of tumors, namely neuroblastomas, rhabdomyosarcomas, Burkitt's lymphomas, and the Ewing's family of tumors. The classification tree built using the breast cancer data separated tumors with BRCA1 mutations from those with BRCA2 mutations, with sporadic tumors separated from both groups and from each other. We also demonstrate the flexibility of the class discovery method with regard to standard resampling methodology such as jackknifing and noise perturbation. To solve the class prediction problem, we built a classification tree on the learning set, and then sought the optimal placement of each test sample within the classification tree. We tested this method on the SRBCT data set, and classified each tumor successfully.     

Kernel-imbedded Gaussian processes for disease classification using microarray gene expression data

Background  

Designing appropriate machine learning methods for identifying genes that have a significant discriminating power for disease outcomes has become more and more important for our understanding of diseases at genomic level. Although many machine learning methods have been developed and applied to the area of microarray gene expression data analysis, the majority of them are based on linear models, which however are not necessarily appropriate for the underlying connection between the target disease and its associated explanatory genes. Linear model based methods usually also bring in false positive significant features more easily. Furthermore, linear model based algorithms often involve calculating the inverse of a matrix that is possibly singular when the number of potentially important genes is relatively large. This leads to problems of numerical instability. To overcome these limitations, a few non-linear methods have recently been introduced to the area. Many of the existing non-linear methods have a couple of critical problems, the model selection problem and the model parameter tuning problem, that remain unsolved or even untouched. In general, a unified framework that allows model parameters of both linear and non-linear models to be easily tuned is always preferred in real-world applications. Kernel-induced learning methods form a class of approaches that show promising potentials to achieve this goal.     

Developing optimal prediction models for cancer classification using gene expression data

Microarrays can provide genome-wide expression patterns for various cancers, especially for tumor sub-types that may exhibit substantially different patient prognosis. Using such gene expression data, several approaches have been proposed to classify tumor sub-types accurately. These classification methods are not robust, and often dependent on a particular training sample for modelling, which raises issues in utilizing these methods to administer proper treatment for a future patient. We propose to construct an optimal, robust prediction model for classifying cancer sub-types using gene expression data. Our model is constructed in a step-wise fashion implementing cross-validated quadratic discriminant analysis. At each step, all identified models are validated by an independent sample of patients to develop a robust model for future data. We apply the proposed methods to two microarray data sets of cancer: the acute leukemia data by Golub et al. and the colon cancer data by Alon et al. We have found that the dimensionality of our optimal prediction models is relatively small for these cases and that our prediction models with one or two gene factors outperforms or has competing performance, especially for independent samples, to other methods based on 50 or more predictive gene factors. The methodology is implemented and developed by the procedures in R and Splus. The source code can be obtained at http://hesweb1.med.virginia.edu/bioinformatics.     

Effective dimension reduction methods for tumor classification using gene expression data

MOTIVATION: One particular application of microarray data, is to uncover the molecular variation among cancers. One feature of microarray studies is the fact that the number n of samples collected is relatively small compared to the number p of genes per sample which are usually in the thousands. In statistical terms this very large number of predictors compared to a small number of samples or observations makes the classification problem difficult. An efficient way to solve this problem is by using dimension reduction statistical techniques in conjunction with nonparametric discriminant procedures. RESULTS: We view the classification problem as a regression problem with few observations and many predictor variables. We use an adaptive dimension reduction method for generalized semi-parametric regression models that allows us to solve the 'curse of dimensionality problem' arising in the context of expression data. The predictive performance of the resulting classification rule is illustrated on two well know data sets in the microarray literature: the leukemia data that is known to contain classes that are easy 'separable' and the colon data set.     

Gene expression data classification using consensus independent component analysis

We propose a new method for tumor classification from gene expression data, which mainly contains three steps. Firstly, the original DNA microarray gene expression data are modeled by independent component analysis （ICA）. Secondly, the most discriminant eigenassays extracted by ICA are selected by the sequential floating forward selection technique. Finally, support vector machine is used to classify the modeling data. To show the validity of the proposed method, we applied it to classify three DNA microarray datasets involving various human normal and tumor tissue samples. The experimental results show that the method is efficient and feasible.     

A Bayesian network classification methodology for gene expression data.

We present new techniques for the application of a Bayesian network learning framework to the problem of classifying gene expression data. The focus on classification permits us to develop techniques that address in several ways the complexities of learning Bayesian nets. Our classification model reduces the Bayesian network learning problem to the problem of learning multiple subnetworks, each consisting of a class label node and its set of parent genes. We argue that this classification model is more appropriate for the gene expression domain than are other structurally similar Bayesian network classification models, such as Naive Bayes and Tree Augmented Naive Bayes (TAN), because our model is consistent with prior domain experience suggesting that a relatively small number of genes, taken in different combinations, is required to predict most clinical classes of interest. Within this framework, we consider two different approaches to identifying parent sets which are supported by the gene expression observations and any other currently available evidence. One approach employs a simple greedy algorithm to search the universe of all genes; the second approach develops and applies a gene selection algorithm whose results are incorporated as a prior to enable an exhaustive search for parent sets over a restricted universe of genes. Two other significant contributions are the construction of classifiers from multiple, competing Bayesian network hypotheses and algorithmic methods for normalizing and binning gene expression data in the absence of prior expert knowledge. Our classifiers are developed under a cross validation regimen and then validated on corresponding out-of-sample test sets. The classifiers attain a classification rate in excess of 90% on out-of-sample test sets for two publicly available datasets. We present an extensive compilation of results reported in the literature for other classification methods run against these same two datasets. Our results are comparable to, or better than, any we have found reported for these two sets, when a train-test protocol as stringent as ours is followed.     

A linear programming approach for estimating the structure of a sparse linear genetic network from transcript profiling data

Background

One important preprocessing step in the analysis of microarray data is background subtraction. In high-density oligonucleotide arrays this is recognized as a crucial step for the global performance of the data analysis from raw intensities to expression values.

Results

We propose here an algorithm for background estimation based on a model in which the cost function is quadratic in a set of fitting parameters such that minimization can be performed through linear algebra. The model incorporates two effects: 1) Correlated intensities between neighboring features in the chip and 2) sequence-dependent affinities for non-specific hybridization fitted by an extended nearest-neighbor model.

Conclusion

The algorithm has been tested on 360 GeneChips from publicly available data of recent expression experiments. The algorithm is fast and accurate. Strong correlations between the fitted values for different experiments as well as between the free-energy parameters and their counterparts in aqueous solution indicate that the model captures a significant part of the underlying physical chemistry.     

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.     

基于核局部线性嵌入的基因表达谱数据分类

针对局部线性嵌入算法（LocalLinearEmbedding,LLE）利用试凑法寻找近邻数耗时的缺陷性,提出一种增强的核局部线性嵌入算法（EnhancedKernelLocalLinearEmbedding,EKLLE）自动为样本分配邻域;该算法以高斯核函数为核心改进标准LLE距离度量准则,结合样本的类别信息,无需人工干预自动为样本设置不同的近邻数,克服了试凑法获得最优结果时需要大量时间;最后在各样本近邻数不相同的情况下对数据进行维数简约及待测样本分类。EKLLE算法有效地将高维基因表达谱数据映射到低维本质空间中,解决了传统LLE算法不能很好地处理合噪声或者稀疏数据的缺点。通过对比其他肿瘤样本分类实验,验证本文方法的实时性和精确性。     

CRCView: a web server for analyzing and visualizing microarray gene expression data using model-based clustering

CRCView is a user-friendly point-and-click web server for analyzing and visualizing microarray gene expression data using a Dirichlet process mixture model-based clustering algorithm. CRCView is designed to clustering genes based on their expression profiles. It allows flexible input data format, rich graphical illustration as well as integrated GO term based annotation/interpretation of clustering results. Availability: http://helab.bioinformatics.med.umich.edu/crcview/.     

Tumor classification by partial least squares using microarray gene expression data

MOTIVATION: One important application of gene expression microarray data is classification of samples into categories, such as the type of tumor. The use of microarrays allows simultaneous monitoring of thousands of genes expressions per sample. This ability to measure gene expression en masse has resulted in data with the number of variables p(genes) far exceeding the number of samples N. Standard statistical methodologies in classification and prediction do not work well or even at all when N < p. Modification of existing statistical methodologies or development of new methodologies is needed for the analysis of microarray data. RESULTS: We propose a novel analysis procedure for classifying (predicting) human tumor samples based on microarray gene expressions. This procedure involves dimension reduction using Partial Least Squares (PLS) and classification using Logistic Discrimination (LD) and Quadratic Discriminant Analysis (QDA). We compare PLS to the well known dimension reduction method of Principal Components Analysis (PCA). Under many circumstances PLS proves superior; we illustrate a condition when PCA particularly fails to predict well relative to PLS. The proposed methods were applied to five different microarray data sets involving various human tumor samples: (1) normal versus ovarian tumor; (2) Acute Myeloid Leukemia (AML) versus Acute Lymphoblastic Leukemia (ALL); (3) Diffuse Large B-cell Lymphoma (DLBCLL) versus B-cell Chronic Lymphocytic Leukemia (BCLL); (4) normal versus colon tumor; and (5) Non-Small-Cell-Lung-Carcinoma (NSCLC) versus renal samples. Stability of classification results and methods were further assessed by re-randomization studies.     

Assembling networks of microbial genomes using linear programming

Background  

Microbial genomes exhibit complex sets of genetic affinities due to lateral genetic transfer. Assessing the relative contributions of parent-to-offspring inheritance and gene sharing is a vital step in understanding the evolutionary origins and modern-day function of an organism, but recovering and showing these relationships is a challenging problem.     

Boosting for tumor classification with gene expression data

MOTIVATION: Microarray experiments generate large datasets with expression values for thousands of genes but not more than a few dozens of samples. Accurate supervised classification of tissue samples in such high-dimensional problems is difficult but often crucial for successful diagnosis and treatment. A promising way to meet this challenge is by using boosting in conjunction with decision trees. RESULTS: We demonstrate that the generic boosting algorithm needs some modification to become an accurate classifier in the context of gene expression data. In particular, we present a feature preselection method, a more robust boosting procedure and a new approach for multi-categorical problems. This allows for slight to drastic increase in performance and yields competitive results on several publicly available datasets. AVAILABILITY: Software for the modified boosting algorithms as well as for decision trees is available for free in R at http://stat.ethz.ch/~dettling/boosting.html.     

BagBoosting for tumor classification with gene expression data

MOTIVATION: Microarray experiments are expected to contribute significantly to the progress in cancer treatment by enabling a precise and early diagnosis. They create a need for class prediction tools, which can deal with a large number of highly correlated input variables, perform feature selection and provide class probability estimates that serve as a quantification of the predictive uncertainty. A very promising solution is to combine the two ensemble schemes bagging and boosting to a novel algorithm called BagBoosting. RESULTS: When bagging is used as a module in boosting, the resulting classifier consistently improves the predictive performance and the probability estimates of both bagging and boosting on real and simulated gene expression data. This quasi-guaranteed improvement can be obtained by simply making a bigger computing effort. The advantageous predictive potential is also confirmed by comparing BagBoosting to several established class prediction tools for microarray data. AVAILABILITY: Software for the modified boosting algorithms, for benchmark studies and for the simulation of microarray data are available as an R package under GNU public license at http://stat.ethz.ch/~dettling/bagboost.html.