Spectral clustering strategies for heterogeneous disease expression data.

Clustering of gene expression data simplifies subsequent data analyses and forms the basis of numerous approaches for biomarker identification, prediction of clinical outcome, and personalized therapeutic strategies. The most popular clustering methods such as K-means and hierarchical clustering are intuitive and easy to use, but they require arbitrary choices on their various parameters (number of clusters for K-means, and a threshold to cut the tree for hierarchical clustering). Human disease gene expression data are in general more difficult to cluster efficiently due to background (genotype) heterogeneity, disease stage and progression differences and disease subtyping; all of which cause gene expression datasets to be more heterogeneous. Spectral clustering has been recently introduced in many fields as a promising alternative to standard clustering methods. The idea is that pairwise comparisons can help reveal global features through the eigen techniques. In this paper, we developed a new recursive K-means spectral clustering method (ReKS) for disease gene expression data. We benchmarked ReKS on three large-scale cancer datasets and we compared it to different clustering methods with respect to execution time, background models and external biological knowledge. We found ReKS to be superior to the hierarchical methods and equally good to K-means, but much faster than them and without the requirement for a priori knowledge of K. Overall, ReKS offers an attractive alternative for efficient clustering of human disease data.

Proximity to the US-Mexico border: a key to explaining geographic variation in US methamphetamine, cocaine and heroin purity.

AIMS: Although illicit drug purity is a widely discussed health risk, research explaining its geographic variation within a country is rare. This study examines whether proximity to the US-Mexico border, the United States' primary drug import portal, is associated with geographic variation in US methamphetamine, heroin and cocaine purity. DESIGN: Distances (proximity) between the US-Mexico border and locations of methamphetamine, cocaine and heroin seizures/acquisitions (n = 239,070) recorded in STRIDE (System to Retrieve Information from Drug Evidence) were calculated for the period of 1990-2004. The association of drug purity with these distances and other variables, including time and seizure/acquisition size, was examined using hierarchical multivariate linear modeling (HMLM). SETTING: Coterminous United States. FINDINGS: Methamphetamine, cocaine and heroin purity generally decreased with distance from the US-Mexico border. Heroin purity, however, after initially declining with distance, turned upwards-a U-shaped association. During 2000-04, methamphetamine purity also had a U-shaped association with distance. For each of the three drugs, temporal changes in the purity of small acquisitions (<10 g) were typically more dynamic in areas closer to the US-Mexico border. CONCLUSIONS: Geographic variance in methamphetamine, cocaine and heroin purity throughout the coterminous United States was associated with US-Mexico border proximity. The U-shaped associations between border-distance and purity for heroin and methamphetamine may be due to imports of those drugs via the eastern United States and southeast Canada, respectively. That said, areas closer to the US-Mexico border generally had relatively high illicit drug purity, as well as more dynamic change in the purity of small ('retail level') drug amounts.