Determining the Number of Clusters Using the Weighted Gap Statistic

Yan, Mingjin; Ye, Keying

doi:10.1111/j.1541-0420.2007.00784.x

Cited by 136 publications

(109 citation statements)

References 9 publications

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“…The optimal number of clusters (i.e., seasons) was determined using the difference of difference-weighted (DD-weighted) gap method (Yan and Ye 2007), which is based on the gap statistic (Tibshirani et al 2001). The gap statistic is defined as:…”

Section: Data Collectionmentioning

confidence: 99%

The temporal niche and seasonal differences in predation risk to translocated and resident woodland caribou (Rangifertaranduscaribou)

2017

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https://mc06.manuscriptcentral.com/cjz-pubs translocated caribou tended to occupy low-elevation habitats extensively used by cougars, resulting in predation of eight translocated caribou, six of which were by cougars. We concluded that the translocated caribou did not adopt the predator avoidance strategies of resident caribou, rendering them more vulnerable to cougars. We make recommendations for future herd augmentations.

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Section: Data Collectionmentioning

confidence: 99%

The temporal niche and seasonal differences in predation risk to translocated and resident woodland caribou (Rangifertaranduscaribou)

2017

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“…To identify subgroups of ALL cases defined by methylation signatures, we performed unsupervised hierarchical clustering of high variance (SD >1 across the cohort; n = 4,037 probe sets), followed by determination of association between cluster membership and cytogenetic subtype by calculation of the gap statistic (24,25) and Rand index (26). This procedure identified 8 robust clusters of leukemic samples using both indices.…”

Section: Dna Methylation Profiles In B-all Are Associated With Genetimentioning

confidence: 99%

“…Initial analysis was performed on probe sets with across-patient SD >1 (n = 4,037) in order to filter out uninformative probe sets. Gap statistic analysis (24,25) was used in order to identify the optimal cutoff of the tree, and the adjusted Rand index (26) was used to compare the extent of concurrence between the clustering results and the underlying cytogenetic subtypes. To further determine the stability of these clustering results, the hierarchical clustering was repeated at different SD cutoffs, and the gap statistic and Rand index was determined for each.…”

Section: Figurementioning

confidence: 99%

“…Gap statistic analysis (24,25) was used in order to identify the optimal cutoff of hierarchical clustering trees, and the adjusted Rand index (26) was used to examine correlation between the clustering results and the underlying cytogenetic subtypes. Limma (27) with FDR correction (typically 10%) and ANOVA with FDR and Dunnett's post-hoc test were used for supervised analysis of methylation signatures.…”

Section: Figurementioning

confidence: 99%

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Integrated genetic and epigenetic analysis of childhood acute lymphoblastic leukemia

Figueroa¹,

Chen²,

Andersson³

et al. 2013

J. Clin. Invest.

125

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Acute lymphoblastic leukemia (ALL) is the commonest childhood malignancy and is characterized by recurring structural genetic alterations. Previous studies of DNA methylation suggest epigenetic alterations may also be important, but an integrated genome-wide analysis of genetic and epigenetic alterations in ALL has not been performed. We analyzed 137 B-lineage and 30 T-lineage childhood ALL cases using microarray analysis of DNA copy number alterations and gene expression, and genome-wide cytosine methylation profiling using the HpaII tiny fragment enrichment by ligation-mediated PCR (HELP) assay. We found that the different genetic subtypes of ALL are characterized by distinct DNA methylation signatures that exhibit significant correlation with gene expression profiles. We also identified an epigenetic signature common to all cases, with correlation to gene expression in 65% of these genes, suggesting that a core set of epigenetically deregulated genes is central to the initiation or maintenance of lymphoid transformation. Finally, we identified aberrant methylation in multiple genes also targeted by recurring DNA copy number alterations in ALL, suggesting that these genes are inactivated far more frequently than suggested by structural genomic analyses alone. Together, these results demonstrate subtype-and disease-specific alterations in cytosine methylation in ALL that influence transcriptional activity, and are likely to exert a key role in leukemogenesis. IntroductionAcute lymphoblastic leukemia (ALL) is the commonest childhood malignancy (1); despite impressive advances in the success of therapy for ALL, it remains the leading cause of cancer-related death in young people. A detailed understanding of the genetic and epigenetic events contributing to leukemogenesis and treatment responsiveness is important in order to identify potential new avenues for therapy in this condition.Pediatric ALL is characterized by a range of recurring numeric and structural chromosomal alterations. These include B-precursor ALL (B-ALL) with (a) high hyperdiploidy (>50 chromosomes), (b) hypodiploidy (<44 chromosomes), (c) t(12;21)(p13;q22) encoding ETV6-RUNX1 (also known as TEL-AML1), (d) t(1;19)(q23;p13.3) encoding TCF3-PBX1 (also known as E2A-PBX1), (e) t(9;22)(q34;q11) encoding BCR-ABL1, (f) cytokine receptor-like factor 2 (CRLF2) rearrangement (CRLF2r), and (g) MLL rearrangement at 11q23 (MLLr); MYC rearrangement in mature B cell leukemia/lymphoma; and TLX1 (also known as HOX11), TLX3 (also known as HOX11L2), LYL1, TAL1, and MLL rearrangement in T-lineage ALL (T-ALL) (2). These alterations are important events in leukemogenesis and are associated with responsiveness to therapy, treatment outcome, and distinct gene expression profiles (3). However, several of these translocations may be acquired years before development of overt leukemia (4), and mouse models have shown that these alterations are frequently insufficient to cause leukemia, which suggests that cooperating genetic events are required. Furthermore, recurring chr...

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“…Determining the number of clusters in a data set is a fundamental problem in cluster analysis [9], [38], [39], [40], [41], [42], [43], [44], [45]. Although this problem is still largely unresolved, numerous methods have been suggested for it.…”

Section: Some Related Methods For Cluster Number Detectionmentioning

confidence: 99%

Detecting the Number of Clusters in n-Way Probabilistic Clustering

Cichocki

Xie

et al. 2010

IEEE Trans. Pattern Anal. Mach. Intell.

164

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Abstract-Recently, there has been a growing interest in multiway probabilistic clustering. Some efficient algorithms have been developed for this problem. However, not much attention has been paid on how to detect the number of clusters for the general n-way clustering (n ! 2). To fill this gap, this problem is investigated based on n-way algebraic theory in this paper. A simple, yet efficient, detection method is proposed by eigenvalue decomposition (EVD), which is easy to implement. We justify this method. In addition, its effectiveness is demonstrated by the experiments on both simulated and real-world data sets.

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Determining the Number of Clusters Using the Weighted Gap Statistic

Cited by 136 publications

References 9 publications

The temporal niche and seasonal differences in predation risk to translocated and resident woodland caribou (Rangifertaranduscaribou)

The temporal niche and seasonal differences in predation risk to translocated and resident woodland caribou (Rangifertaranduscaribou)

Integrated genetic and epigenetic analysis of childhood acute lymphoblastic leukemia

Detecting the Number of Clusters in n-Way Probabilistic Clustering

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