Faster k-Medoids Clustering: Improving the PAM, CLARA, and CLARANS Algorithms

Clustering non-Euclidean data is difficult, and one of the most used algorithms besides hierarchical clustering is the popular algorithm Partitioning Around Medoids (PAM), also simply referred to as k-medoids. In Euclidean geometry the mean-as used in k-means-is a good estimator for the cluster center, but this does not hold for arbitrary dissimilarities. PAM uses the medoid instead, the object with the smallest dissimilarity to all others in the cluster. This notion of centrality can be used with any (dis-)similarity, and thus is of high relevance to many domains such as biology that require the use of Jaccard, Gower, or more complex distances. A key issue with PAM is its high run time cost. We propose modifications to the PAM algorithm to achieve an O(k)-fold speedup in the second SWAP phase of the algorithm, but will still find the same results as the original PAM algorithm. If we slightly relax the choice of swaps performed (at comparable quality), we can further accelerate the algorithm by performing up to k swaps in each iteration. With the substantially faster SWAP, we can now also explore alternative strategies for choosing the initial medoids. We also show how the CLARA and CLARANS algorithms benefit from these modifications. It can easily be combined with earlier approaches to use PAM and CLARA on big data (some of which use PAM as a subroutine, hence can immediately benefit from these improvements), where the performance with high k becomes increasingly important. In experiments on real data with k=100, we observed a 200-fold speedup compared to the original PAM SWAP algorithm, making PAM applicable to larger data sets as long as we can afford to compute a distance matrix, and in particular to higher k (at k=2, the new SWAP was only 1.5 times faster, as the speedup is expected to increase with k)

Association of neurexin 3 polymorphisms with smoking behavior.

The Neurexin 3 gene (NRXN3) has been associated with dependence on various addictive substances, as well as with the degree of smoking in schizophrenic patients and impulsivity among tobacco abusers. To further evaluate the role of NRXN3 in nicotine addiction, we analyzed single nucleotide polymorphisms (SNPs) and a copy number variant (CNV) within the NRXN3 genomic region. An initial study was carried out on 157 smokers and 595 controls, all of Spanish Caucasian origin. Nicotine dependence was assessed using the Fagerstrom index and the number of cigarettes smoked per day. The 45 NRXN3 SNPs genotyped included all the SNPs previously associated with disease, and a previously described deletion within NRXN3. This analysis was replicated in 276 additional independent smokers and 568 controls. Case-control association analyses were performed at the allele, genotype and haplotype levels. Allelic and genotypic association tests showed that three NRXN3 SNPs were associated with a lower risk of being a smoker. The haplotype analysis showed that one block of 16 Kb, consisting of two of the significant SNPs (rs221473 and rs221497), was also associated with lower risk of being a smoker in both the discovery and the replication cohorts, reaching a higher level of significance when the whole sample was considered [odds ratio = 0.57 (0.42-0.77), permuted P = 0.0075]. By contrast, the NRXN3 CNV was not associated with smoking behavior. Taken together, our results confirm a role for NRXN3 in susceptibility to smoking behavior, and strongly implicate this gene in genetic vulnerability to addictive behaviors

X-chromosome tiling path array detection of copy number variants in patients with chromosome X-linked mental retardation

Contiene 3 ficheros adicionales con información suplementaria.-- et al.[Background] Aproximately 5–10% of cases of mental retardation in males are due to copy number variations (CNV) on the X chromosome. Novel technologies, such as array comparative genomic hybridization (aCGH), may help to uncover cryptic rearrangements in X-linked mental retardation (XLMR) patients. We have constructed an X-chromosome tiling path array using bacterial artificial chromosomes (BACs) and validated it using samples with cytogenetically defined copy number changes. We have studied 54 patients with idiopathic mental retardation and 20 controls subjects.[Results] Known genomic aberrations were reliably detected on the array and eight novel submicroscopic imbalances, likely causative for the mental retardation (MR) phenotype, were detected. Putatively pathogenic rearrangements included three deletions and five duplications (ranging between 82 kb to one Mb), all but two affecting genes previously known to be responsible for XLMR. Additionally, we describe different CNV regions with significant different frequencies in XLMR and control subjects (44% vs. 20%).[Conclusion] This tiling path array of the human X chromosome has proven successful for the detection and characterization of known rearrangements and novel CNVs in XLMR patients.The authors thank the "Genoma España" and Genome Canada joint R+D+I projects in human health, plants and aquiculture; the former "Departament d'Universitats i Societat de la Informació" (DURSI) and the "Departament de Salut", from the Catalan Autonomous Government (2005SGR00008 - Generalitat de Catalunya); the Instituto de Salud Carlos III (PI041126, CIBER-ESP), the EU's Sixth Framework Programme [FP6-2005-LIFESCIHEALTH-7; ANEUPLOIDY No. 037627] and Fundación Areces (U-2006-FARECES-O).Peer reviewe

Fat Mass and Obesity-Associated Gene (FTO) in Eating Disorders: Evidence for Association of the rs9939609 Obesity Risk Allele with Bulimia nervosa and Anorexia nervosa

Objective: The common single nucleotide polymorphism (SNP) rs9939609 in the fat mass and obesity-associated gene (FTO) is associated with obesity. As genetic variants associated with weight regulation might also be implicated in the etiology of eating disorders, we evaluated whether SNP rs9939609 is associated with bulimia nervosa (BN) and anorexia nervosa (AN). Methods: Association of rs9939609 with BN and AN was assessed in 689 patients with AN, 477 patients with BN, 984 healthy non-population-based controls, and 3,951 population-based controls (KORA-S4). Based on the familial and premorbid occurrence of obesity in patients with BN, we hypothesized an association of the obesity risk A-allele with BN. Results: In accordance with our hypothesis, we observed evidence for association of the rs9939609 A-allele with BN when compared to the non-population-based controls (unadjusted odds ratio (OR) = 1.142, one-sided 95% confidence interval (CI) 1.001-infinity; one-sided p = 0.049) and a trend in the population-based controls (OR = 1.124, one-sided 95% CI 0.932-infinity; one-sided p = 0.056). Interestingly, compared to both control groups, we further detected a nominal association of the rs9939609 A-allele to AN (OR = 1.181, 95% CI 1.027-1.359, two-sided p = 0.020 or OR = 1.673, 95% CI 1.101-2.541, two-sided p = 0.015,). Conclusion: Our data suggest that the obesity-predisposing FTO allele might be relevant in both AN and BN. Copyright (C) 2012 S. Karger GmbH, Freibur

MRPS18CP2 alleles and DEFA3 absence as putative chromosome 8p23.1 modifiers of hearing loss due to mtDNA mutation A1555G in the 12S rRNA gene

<p>Abstract</p> <p>Background</p> <p>Mitochondrial DNA (mtDNA) mutations account for at least 5% of cases of postlingual, nonsyndromic hearing impairment. Among them, mutation A1555G is frequently found associated with aminoglycoside-induced and/or nonsyndromic hearing loss in families presenting with extremely variable clinical phenotypes. Biochemical and genetic data have suggested that nuclear background is the main factor involved in modulating the phenotypic expression of mutation A1555G. However, although a major nuclear modifying locus was located on chromosome 8p23.1 and regardless intensive screening of the region, the gene involved has not been identified.</p> <p>Methods</p> <p>With the aim to gain insights into the factors that determine the phenotypic expression of A1555G mutation, we have analysed in detail different genetic and genomic elements on 8p23.1 region (<it>DEFA3 </it>gene absence, <it>CLDN23 </it>gene and <it>MRPS18CP2 </it>pseudogene) in a group of 213 A1555G carriers.</p> <p>Results</p> <p>Family based association studies identified a positive association for a polymorphism on <it>MRPS18CP2 </it>and an overrepresentation of <it>DEFA3 </it>gene absence in the deaf group of A1555G carriers.</p> <p>Conclusion</p> <p>Although none of the factors analysed seem to have a major contribution to the phenotype, our findings provide further evidences of the involvement of 8p23.1 region as a modifying locus for A1555G 12S rRNA gene mutation.</p

Suicide attempts in bulimia nervosa: Personality and psychopathological correlates

Background: Little evidence exists about suicidal acts in eating disorders and its relation with personality. We explored the prevalence of lifetime suicide attempts (SA) in women with bulimia nervosa (BN), and compared eating disorder symptoms, general psychopathology, impulsivity and personality between individuals who had and had not attempted suicide. We also determined the variables that better correlate with of SA. Method: Five hundred sixty-six BN outpatients (417 BN purging, 47 BN non-purging and 102 subthreshold BN) participated in the study. Results: Lifetime prevalence of suicide attempts was 26.9%. BN subtype was not associated with lifetime SA (p = 0.36). Suicide attempters exhibited higher rates on eating symptomatology, general psychopathology, impulsive behaviors, more frequent history of childhood obesity and parental alcohol abuse (p < 0.004). Suicide attempters exhibited higher scores on harm avoidance and lower on self-directedness, reward dependence and cooperativeness (p < 0.002). The most strongly correlated variables with SA were: lower education, minimum BMI, previous eating disorder treatment, low self-directedness, and familial history of alcohol abuse (p < 0.006). Conclusion: Our results support the notion that internalizing personality traits combined with impulsivity may increase the probability of suicidal behaviors in these patients. Future research may increase our understanding of the role of suicidality to work towards rational prevention of suicidal attempts