Canonical correlation analysis (CCA) is a well established technique for identifying linear relationships among two variable sets. Kernel CCA (KCCA) is the most notable nonlinear extension but it lacks interpretability and robustness against irrelevant features. The aim of this article is to introduce two nonlinear CCA extensions that rely on the recently proposed Hilbert-Schmidt independence criterion and the centered kernel target alignment. These extensions determine linear projections that provide maximally dependent projected data pairs. The paper demonstrates that the use of linear projections allows removing irrelevant features, whilst extracting combinations of strongly associated features. This is exemplified through a simulation and the analysis of recorded data that are available in the literature.

While clustering genes remains one of the most popular exploratory tools for expression data, it often results in a highly variable and biologically uninformative clusters. This paper explores a data fusion approach to clustering microarray data. Our method, which combined expression data and Gene Ontology (GO)-derived information, is applied on a real data set to perform genome-wide clustering. A set of novel tools is proposed to validate the clustering results and pick a fair value of infusion coefficient. These tools measure stability, biological relevance, and distance from the expression-only clustering solution. Our results indicate that a data-fusion clustering leads to more stable, biologically relevant clusters that are still representative of the experimental data.

MOTIVATION: We developed an EM-random forest (EMRF) for Haseman-Elston quantitative trait linkage analysis that accounts for marker ambiguity and weighs each sib-pair according to the posterior identical by descent (IBD) distribution. The usual random forest (RF) variable importance (VI) index used to rank markers for variable selection is not optimal when applied to linkage data because of correlation between markers. We define new VI indices that borrow information from linked markers using the correlation structure inherent in IBD linkage data. RESULTS: Using simulations, we find that the new VI indices in EMRF performed better than the original RF VI index and performed similarly or better than EM-Haseman-Elston regression LOD score for various genetic models. Moreover, tree size and markers subset size evaluated at each node are important considerations in RFs. AVAILABILITY: The source code for EMRF written in C is available at www.infornomics.utoronto.ca/downloads/EMRF.

In this paper we consider a general framework for clustering expression data that permits integration of various biological data sources through combination of corresponding dissimilarity measures. In the paper we briefly review currently published attempts to genomic data fusion and discuss a problem of validating results from clustering expression data. We apply our approach to a real microarray expression dataset which induces a correlation-based dissimilarity matrix, and use gene ontology - biological process annotations to derive GO-based dissimilarity matrix. The proposed procedure is verified using a simple knowledge-based validation measure based on protein-protein interaction database. Obtained results reveal that combining experimental data with comprehensive and reliable biological repository may improve performance of cluster analysis and yield biologically meaningful gene clusters

BACKGROUND: Expression array data are used to predict biological functions of uncharacterized genes by comparing their expression profiles to those of characterized genes. While biologically plausible, this is both statistically and computationally challenging. Typical approaches are computationally expensive and ignore correlations among expression profiles and functional categories. RESULTS: We propose a factor analysis model (FAM) for functional genomics and give a two-step algorithm, using genome-wide expression data for yeast and a subset of Gene-Ontology Biological Process functional annotations. We show that the predictive performance of our method is comparable to the current best approach while our total computation time was faster by a factor of 4000. We discuss the unique challenges in performance evaluation of algorithms used for genome-wide functions genomics. Finally, we discuss extensions to our method that can incorporate the inherent correlation structure of the functional categories to further improve predictive performance. CONCLUSION: Our factor analysis model is a computationally efficient technique for functional genomics and provides a clear and unified statistical framework with potential for incorporating important gene ontology information to improve predictions.

We propose a flexible, comprehensive approach for analysis of [15O]-water positron emission tomography (PET) brain images using a penalized version of linear discriminant analysis (PDA). We applied it to scans from 20 subjects (eight scans/subject) performing a finger movement task and analyzed: 1) two classes to obtain a covariance-normalized baseline-activation image, and 2) eight classes for the mean within subject temporal structure which contained baseline-activation and time-dependent changes in a two-dimensional canonical subspace. We imposed spatial smoothness on the resulting image(s) by expanding it in five tensor-product B-spline (TPS) bases of varying smoothness, and further regularized with a ridge-type penalty on the noise covariance matrix. The discrimination approach of PDA provides a probabilistic framework within which prediction error (PE) estimates are derived. We used these to optimize over TPS bases and a ridge hyperparameter (expressed as equivalent degrees of freedom, EDF). We obtained unbiased, low variance PE estimates using modern resampling tools (.632+ Bootstrap and cross validation), and compared PDA of 1) TPS-projected, mean-normalized and unnormalized scans and 2) mean-normalized scans with and without additional presmoothing. By examining the tradeoffs between PE and EDF, as a function of basis selection and image smoothing we demonstrate the utility of PDA, the PE framework, and the relationship between singular value decomposition and smooth TPS bases in the analysis of functional neuroimages.