Use of cluster separation indices and the influence of outliers: application of two new separation indices, the modified silhouette index and the overlap coefficient to simulated data and mouse urine metabolomic profiles

Dixon, Sarah J.; Heinrich, Nina; Holmboe, Maria E.; Schaefer, Michele L.; Reed, Randall R.; Trevejo, José; Brereton, Richard G.

doi:10.1002/cem.1189

Cited by 23 publications

(12 citation statements)

References 24 publications

(27 reference statements)

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“…Simply, a visual inspection of the clustering pattern or class separation in a scores plot is not typically sufficient to infer statistical relevance. Methods using cluster overlap metrics [99], statistical distances [98], and hierarchical clustering [100, 101] have been successfully used to quantify separations in scores plots. Also, class membership may be inferred from 95% confidence ellipses calculated from scores [101].…”

Section: Methods Selectionmentioning

confidence: 99%

Multivariate Analysis in Metabolomics

Worley

Powers

2012

CMB

680

610

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Metabolomics aims to provide a global snapshot of all small-molecule metabolites in cells and biological fluids, free of observational biases inherent to more focused studies of metabolism. However, the staggeringly high information content of such global analyses introduces a challenge of its own; efficiently forming biologically relevant conclusions from any given metabolomics dataset indeed requires specialized forms of data analysis. One approach to finding meaning in metabolomics datasets involves multivariate analysis (MVA) methods such as principal component analysis (PCA) and partial least squares projection to latent structures (PLS), where spectral features contributing most to variation or separation are identified for further analysis. However, as with any mathematical treatment, these methods are not a panacea; this review discusses the use of multivariate analysis for metabolomics, as well as common pitfalls and misconceptions.

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Section: Methods Selectionmentioning

confidence: 99%

Multivariate Analysis in Metabolomics

Worley

Powers

2012

CMB

680

610

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“…The Davies-Bouldin index leaves the power of the norms for the distance between the class centres ( m 1 À m 2 k k p ) and the dispersion (here S w ) as parameters, and can therefore be seen as a generalization of the Fisher criterion. The original use of the Davies-Bouldin index was for the problem of finding an optimal subdivision of data points into classes when true class membership is unknown, which is also known as the clustering problem [14,15]. Davies and Bouldin define five properties that should hold for a cluster similarity measure.…”

Section: Relation To the Fisher Criterionmentioning

confidence: 99%

On the separation of classes: can the Fisher criterion be improved upon when classes have unequal variance–covariance structure?

Åberg

Jacobsson

2010

Journal of Chemometrics

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A value of class separation can be used as a criterion to optimize data-analytical protocols for multivariate classification problems. The Fisher criterion assumes equal variance-covariance structure, an assumption which is often violated in real datasets. The practical consequences of using the Fisher criterion compared to exploiting the variance-covariance differences has not been studied previously. Here, we show that about 50 samples are required to benefit from using the unequal variance-covariance structures for estimating class separation in two dimensions and more samples are required in higher dimensions. The results show that the Fisher criterion is robust and accurate for selection between pretreatments compared to a newly derived criterion called the Cooke criterion.

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“…The biological datasets used in the analysis have been described in more detail elsewhere (Dixon et al 2009) and a summary of sample numbers used in this paper is presented in Table 3. For the diet study (dataset 8), urine was sampled from 10 mice on a high fat diet and 9 controls at 10-12 weeks of age.…”

Section: Datasets and Sample Collectionmentioning

confidence: 99%

Monte-Carlo methods for determining optimal number of significant variables. Application to mouse urinary profiles

et al. 2009

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Three methods for variable selection are described, namely the t-statistic, Partial Least Squares Discriminant Analysis (PLS-DA) weights and regression coefficients, with the aim of determining which variables are the most significant markers for discriminating between two groups: a variable's level of significance is related to its magnitude. Monte-Carlo methods are employed to determine empirical significance of variables, by permuting randomly the class membership 5000 times to obtain null distributions, and comparing the observed statistic for each variable with the null distribution. Seven simulations consisting of 200 samples, divided equally between two classes, and 300 variables, are constructed; in one dataset there are no induced correlations between variables, in two datasets correlations are induced but there is no induced separation between the classes, and in four datasets, separation is induced by selecting 20 of the variables to be discriminators. In addition two metabolomic datasets were analysed consisting of the GCMS of urinary extracts from mice both to determine the effect of stress and to determine the effect of diet on the urinary chemosignal. It is shown that the t-statistic combined with Monte-Carlo permutations provides similar results to PLS weights. PLS regression coefficients find the least number of markers but, for the simulations, the lowest False Positives rates.

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Use of cluster separation indices and the influence of outliers: application of two new separation indices, the modified silhouette index and the overlap coefficient to simulated data and mouse urine metabolomic profiles

Cited by 23 publications

References 24 publications

Multivariate Analysis in Metabolomics

Multivariate Analysis in Metabolomics

On the separation of classes: can the Fisher criterion be improved upon when classes have unequal variance–covariance structure?

Monte-Carlo methods for determining optimal number of significant variables. Application to mouse urinary profiles

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