On sparse Fisher discriminant method for microarray data analysis

Multi-Instance Dimensionality Reduction via Sparsity and Orthogonality

We study a multi-instance (MI) learning dimensionality-reduction algorithm through sparsity and orthogonality, which is especially useful for high-dimensional MI data sets. We develop a novel algorithm to handle both sparsity and orthogonality constraints that existing methods do not handle well simultaneously. Our main idea is to formulate an optimization problem where the sparse term appears in the objective function and the orthogonality term is formed as a constraint. The resulting optimization problem can be solved by using approximate augmented Lagrangian iterations as the outer loop and inertial proximal alternating linearized minimization (iPALM) iterations as the inner loop. The main advantage of this method is that both sparsity and orthogonality can be satisfied in the proposed algorithm. We show the global convergence of the proposed iterative algorithm. We also demonstrate that the proposed algorithm can achieve high sparsity and orthogonality requirements, which are very important for dimensionality reduction. Experimental results on both synthetic and real data sets show that the proposed algorithm can obtain learning performance comparable to that of other tested MI learning algorithms.

A novel feature extraction approach for microarray data based on multi-algorithm fusion

Feature extraction is one of the most important and effective method to reduce dimension in data mining, with emerging of high dimensional data such as microarray gene expression data. Feature extraction for gene selection, mainly serves two purposes. One is to identify certain disease-related genes. The other is to find a compact set of discriminative genes to build a pattern classifier with reduced complexity and improved generalization capabilities. Depending on the purpose of gene selection, two types of feature extraction algorithms including ranking-based feature extraction and set-based feature extraction are employed in microarray gene expression data analysis. In ranking-based feature extraction, features are evaluated on an individual basis, without considering inter-relationship between features in general, while set-based feature extraction evaluates features based on their role in a feature set by taking into account dependency between features. Just as learning methods, feature extraction has a problem in its generalization ability, which is robustness. However, the issue of robustness is often overlooked in feature extraction. In order to improve the accuracy and robustness of feature extraction for microarray data, a novel approach based on multi-algorithm fusion is proposed. By fusing different types of feature extraction algorithms to select the feature from the samples set, the proposed approach is able to improve feature extraction performance. The new approach is tested against gene expression dataset including Colon cancer data, CNS data, DLBCL data, and Leukemia data. The testing results show that the performance of this algorithm is better than existing solutions.

MALDI imaging MS reveals candidate lipid markers of polycystic kidney disease

Autosomal recessive polycystic kidney disease (ARPKD) is a severe, monogenetically inherited kidney and liver disease. PCK rats carrying the orthologous mutant gene serve as a model of human disease, and alterations in lipid profiles in PCK rats suggest that defined subsets of lipids may be useful as molecular disease markers. Whereas MALDI protein imaging mass spectrometry (IMS) has become a promising tool for disease classification, widely applicable workflows that link MALDI lipid imaging and identification as well as structural characterization of candidate disease-classifying marker lipids are lacking. Here, we combine selective MALDI imaging of sulfated kidney lipids and Fisher discriminant analysis (FDA) of imaging data sets for identification of candidate markers of progressive disease in PCK rats. Our study highlights strong increases in lower mass lipids as main classifiers of cystic disease. Structure determination by high-resolution mass spectrometry identifies these altered lipids as taurine-conjugated bile acids. These sulfated lipids are selectively elevated in the PCK rat model but not in models of related hepatorenal fibrocystic diseases, suggesting that they be molecular markers of the disease and that a combination of MALDI imaging with high-resolution MS methods and Fisher discriminant data analysis may be applicable for lipid marker discovery.

Variable selection in canonical discriminant analysis for family studies

In family studies, canonical discriminant analysis can be used to find linear combinations of phenotypes that exhibit high ratios of between-family to within-family variabilities. But with large numbers of phenotypes, canonical discriminant analysis may overfit. To estimate the predicted ratios associated with the coefficients obtained from canonical discriminant analysis, two methods are developed; one is based on bias correction and the other based on cross-validation. Because the cross-validation is computationally intensive, an approximation to the cross-validation is also developed. Furthermore, these methods can be applied to perform variable selection in canonical discriminant analysis. The proposed methods are illustrated with simulation studies and applications to two real examples.

Sparse linear discriminant analysis for simultaneous testing for the significance of a gene set/pathway and gene selection

MOTIVATION

Pathway and gene set-based approaches for the analysis of gene expression profiling experiments have become increasingly popular for addressing problems associated with individual gene analysis. Since most genes are not differently expressed, existing gene set tests, which consider all the genes within a gene set, are subject to considerable noise and power loss, a concern exacerbated in studies in which the degree of differential expression is moderate for truly differentially expressed genes. For a significantly differentially expressed pathway, it is also of substantial interest to select important genes that drive the differential expression of the pathway.

METHODS

We develop a unified framework to jointly test the significance of a pathway and to select a subset of genes that drive the significant pathway effect. To achieve dimension reduction and gene selection, we decompose each gene pathway into a single score by using a regularized form of linear discriminant analysis, called sparse linear discriminant analysis (sLDA). Testing for the significance of the pathway effect proceeds via permutation of the sLDA score. The sLDA-based test is compared with competing approaches with simulations and two applications: a study on the effect of metal fume exposure on immune response and a study of gene expression profiles among Type II Diabetes patients.

RESULTS

Our results show that sLDA-based testing provides a powerful approach to test for the significance of a differentially expressed pathway and gene selection.

AVAILABILITY

An implementation of the proposed sLDA-based pathway test in the R statistical computing environment is available at http://www.hsph.harvard.edu/~mwu/software/.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.