MOTIVATION: Set-based variance component tests have been identified as a way to increase power in association studies by aggregating weak individual effects. However, the choice of test statistic has been largely ignored even though it may play an important role in obtaining optimal power. We compared a standard statistical test-a score test-with a recently developed likelihood ratio (LR) test. Further, when correction for hidden structure is needed, or gene-gene interactions are sought, state-of-the art algorithms for both the score and LR tests can be computationally impractical. Thus we develop new computationally efficient methods. RESULTS: After reviewing theoretical differences in performance between the score and LR tests, we find empirically on real data that the LR test generally has more power. In particular, on 15 of 17 real datasets, the LR test yielded at least as many associations as the score test-up to 23 more associations-whereas the score test yielded at most one more association than the LR test in the two remaining datasets. On synthetic data, we find that the LR test yielded up to 12% more associations, consistent with our results on real data, but also observe a regime of extremely small signal where the score test yielded up to 25% more associations than the LR test, consistent with theory. Finally, our computational speedups now enable (i) efficient LR testing when the background kernel is full rank, and (ii) efficient score testing when the background kernel changes with each test, as for gene-gene interaction tests. The latter yielded a factor of 2000 speedup on a cohort of size 13 500. AVAILABILITY: Software available at http://research.microsoft.com/en-us/um/redmond/projects/MSCompBio/Fastlmm/. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

The comparison of ordinary partitions of a set of objects is well established in the clustering literature, which comprehends several studies on the analysis of the properties of similarity measures for comparing partitions. However, similarity measures for clusterings are not readily applicable to biclusterings, since each bicluster is a tuple of two sets (of rows and columns), whereas a cluster is only a single set (of rows). Some biclustering similarity measures have been defined as minor contributions in papers which primarily report on proposals and evaluation of biclustering algorithms or comparative analyses of biclustering algorithms. The consequence is that some desirable properties of such measures have been overlooked in the literature. We review 14 biclustering similarity measures. We define eight desirable properties of a biclustering measure, discuss their importance, and prove which properties each of the reviewed measures has. We show examples drawn and inspired from important studies in which several biclustering measures convey misleading evaluations due to the absence of one or more of the discussed properties. We also advocate the use of a more general comparison approach that is based on the idea of transforming the original problem of comparing biclusterings into an equivalent problem of comparing clustering partitions with overlapping clusters.

The features describing a data set may often be arranged in meaningful subsets, each of which corresponds to a different aspect of the data. An unsupervised algorithm (SCAD) that performs fuzzy clustering and aspects weighting simultaneously was recently proposed. However, there are several situations where the data set is represented by proximity matrices only (relational data), which renders several clustering approaches, including SCAD, inappropriate. To handle this kind of data, the relational clustering algorithm CARD, based on the SCAD algorithm, has been recently developed. However, CARD may fail and halt given certain conditions. To fix this problem, its steps are modified and then reordered to also reduce the number of parameters required. The improved CARD is assessed over hundreds of real and artificial data sets.

This paper is concerned with the computational efficiency of clustering algorithms when the data set to be clustered is described by a proximity matrix only (relational data) and the number of clusters must be automatically estimated from such data. Two relational versions of an evolutionary algorithm for clustering are derived and compared against two systematic (repetitive) approaches that can also be used to automatically estimate the number of clusters in relational data. Exhaustive experiments involving six artificial and two real data sets are reported and analyzed.