A New Dimension Reduction Method: Factor Discriminant K-means

Reduced K-means (RKM) and Factorial K-means (FKM) are two data reduction techniques incorporating principal component analysis and K-means into a unified methodology to obtain a reduced set of components for variables and an optimal partition for objects. RKM finds clusters in a reduced space by maximizing the between-clusters deviance without imposing any condition on the within-clusters deviance, so that clusters are isolated but they might be heterogeneous. On the other hand, FKM identifies clusters in a reduced space by minimizing the within-clusters deviance without imposing any condition on the between-clusters deviance. Thus, clusters are homogeneous, but they might not be isolated. The two techniques give different results because the total deviance in the reduced space for the two methodologies is not constant; hence the minimization of the within-clusters deviance is not equivalent to the maximization of the between-clusters deviance. In this paper a modification of the two techniques is introduced to avoid the afore mentioned weaknesses. It is shown that the two modified methods give the same results, thus merging RKM and FKM into a new methodology. It is called Factor Discriminant K-means (FDKM), because it combines Linear Discriminant Analysis and K-means. The paper examines several theoretical properties of FDKM and its performances with a simulation study. An application on real-world data is presented to show the features of FDKM.     

The transmembrane protein meckelin (MKS3) is mutated in Meckel-Gruber syndrome and the wpk rat

Meckel-Gruber syndrome is a severe autosomal, recessively inherited disorder characterized by bilateral renal cystic dysplasia, developmental defects of the central nervous system (most commonly occipital encephalocele), hepatic ductal dysplasia and cysts and polydactyly. MKS is genetically heterogeneous, with three loci mapped: MKS1, 17q21-24 (ref. 4); MKS2, 11q13 (ref. 5) and MKS3 (ref. 6). We have refined MKS3 mapping to a 12.67-Mb interval (8q21.13-q22.1) that is syntenic to the Wpk locus in rat, which is a model with polycystic kidney disease, agenesis of the corpus callosum and hydrocephalus. Positional cloning of the Wpk gene suggested a MKS3 candidate gene, TMEM67, for which we identified pathogenic mutations for five MKS3-linked consanguineous families. MKS3 is a previously uncharacterized, evolutionarily conserved gene that is expressed at moderate levels in fetal brain, liver and kidney but has widespread, low levels of expression. It encodes a 995-amino acid seven-transmembrane receptor protein of unknown function that we have called meckelin.     

Deficiency in catechol-O-methyltransferase and 2-methoxyoestradiol is associated with pre-eclampsia

Despite intense investigation, mechanisms that facilitate the emergence of the pre-eclampsia phenotype in women are still unknown. Placental hypoxia, hypertension, proteinuria and oedema are the principal clinical features of this disease. It is speculated that hypoxia-driven disruption of the angiogenic balance involving vascular endothelial growth factor (VEGF)/placenta-derived growth factor (PLGF) and soluble Fms-like tyrosine kinase-1 (sFLT-1, the soluble form of VEGF receptor 1) might contribute to some of the maternal symptoms of pre-eclampsia. However, pre-eclampsia does not develop in all women with high sFLT-1 or low PLGF levels, and it also occurs in some women with low sFLT-1 and high PLGF levels. Moreover, recent experiments strongly suggest that several soluble factors affecting the vasculature are probably elevated because of placental hypoxia in the pre-eclamptic women, indicating that upstream molecular defect(s) may contribute to pre-eclampsia. Here we show that pregnant mice deficient in catechol-O-methyltransferase (COMT) show a pre-eclampsia-like phenotype resulting from an absence of 2-methoxyoestradiol (2-ME), a natural metabolite of oestradiol that is elevated during the third trimester of normal human pregnancy. 2-ME ameliorates all pre-eclampsia-like features without toxicity in the Comt(-/-) pregnant mice and suppresses placental hypoxia, hypoxia-inducible factor-1alpha expression and sFLT-1 elevation. The levels of COMT and 2-ME are significantly lower in women with severe pre-eclampsia. Our studies identify a genetic mouse model for pre-eclampsia and suggest that 2-ME may have utility as a plasma and urine diagnostic marker for this disease, and may also serve as a therapeutic supplement to prevent or treat this disorder.