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Motivation: Inner holes, artifacts and blank spots are common in microarray images, but current image analysis methods do not pay them enough attention. We propose a new robust model-based method for processing microarray images so as to estimate foreground and background intensities. The method starts with a very simple but effective automatic gridding method, and then proceeds in two steps. The first step applies model-based clustering to the distribution of pixel intensities, using the Bayesian Information Criterion (BIC) to choose the number of groups up to a maximum of three. The second step is spatial, finding the large spatially connected components in each cluster of pixels. The method thus combines the strengths of the histogram-based and spatial approaches. It deals effectively with inner holes in spots and with artifacts. It also provides a formal inferential basis for deciding when the spot is blank, namely when the BIC favors one group over two or three., Results: We apply our methods for gridding and segmentation to cDNA microarray images from an HIV infection experiment. In these experiments, our method had better stability across replicates than a fixed-circle segmentation method or the seeded region growing method in the SPOT software, without introducing noticeable bias when estimating the intensities of differentially expressed genes., Availability: spotSegmentation, an R language package implementing both the gridding and segmentation methods is available through the Bioconductor project (http://www.bioconductor.org). The segmentation method requires the contributed R package MCLUST for model-based clustering (http://cran.us.r-project.org)., Contact: fraley@stat.washington.edu.

The rapid increase in Ihe size of data sets makes clustering all the more important to capture and summarize the information, at the same time making clustering more difficult to accomplish. If model-based clustering is applied directly to a large data set, it can be too slow for practical application. A simple and common approach is to first cluster a random sample of moderate size, and then use the clustering model found in this way to classify the remainder of the objects. We show that, in its simplest form, this method may lead to unstable results. Our experiments suggest that a stable method with better performance can be obtained with two straightforward modifications to the simple sampling method: several tentative models are identified from the sample instead of just one, and several HM sleps are used rather than just one E step to classify the full data set. We find that there are significant gains from increasing the size of the sample up to about 2,000, but not from further increases. These conclusions are based on the application of several alternative strategies to the segmentation of three different multispectral images, and to several simulated data sets. [ABSTRACT FROM AUTHOR]

Agglomerative hierarchical clustering methods based on Gaussian probability models have recently shown promise in a variety of applications. In this approach, a maximum-likelihood pair of clusters is chosen for merging at each stage. Unlike classical methods, model-based methods reduce to a recurrence relation only in the simplest case, which corresponds to the classical sum of squares method. We show how the structure of the Gaussian model can be exploited to yield efficient algorithms for agglomerative hierarchical clustering. [ABSTRACT FROM AUTHOR]

This paper, concerns further developments in primal projective methods based on the potential function of De Ghellinck and Vial. Their method is unique in that feasibility and optimality are approached simultaneously from an interior starting point, without the addition of an artificial variable to handle feasibility, and without penalty or barrier terms. This behavior is obtained by incorporating the infeasibilities within the potential function. The primal algorithm requires an initial optimal objective estimate, and results are given demonstrating sensitivity to its value. We show that, by choosing a different initial search direction, feasibility and optimality can be treated in separate phases. Results are given, indicating that the two-phase method is often superior to the original single-phase method. We also describe a variant that selects the search direction on the basis of potential reduction, and a technique that shows the use of estimates that ape net necessarily lower bounds for the optimal objective value. [ABSTRACT FROM AUTHOR]