Agglomerative joint clustering of metabolic data with spike at zero: A Bayesian perspective

Abstract

In many biological applications, for example high-dimensional metabolic data, the measurements consist of several continuous measurements of subjects or tissues over multiple attributes or metabolites. Measurement values are put in a matrix with subjects in rows and attributes in columns. The analysis of such data requires grouping subjects and attributes to provide a primitive guide toward data modeling. A common approach is to group subjects and attributes separately, and construct a two-dimensional dendrogram tree, once on rows and then on columns. This simple approach provides a grouping visualization through two separate trees, which is difficult to interpret jointly. When a joint grouping of rows and columns is of interest, it is more natural to partition the data matrix directly. Our suggestion is to build a dendrogram on the matrix directly, thus generalizing the two-dimensional dendrogram tree to a three-dimensional forest. The contribution of this research to the statistical analysis of metabolic data is threefold. First, a novel spike-and-slab model in various hierarchies is proposed to identify discriminant rows and columns. Second, an agglomerative approach is suggested to organize joint clusters. Third, a new visualization tool is invented to demonstrate the collection of joint clusters. The new method is motivated over gas chromatography mass spectrometry (GCMS) metabolic data, but can be applied to other continuous measurements with spike at zero property.

The Spike-and-Slab Lasso Generalized Linear Models for Prediction and Associated Genes Detection

“…The spike-and-slab prior is the fundamental basis for most Bayesian variable selection approaches, and has proved remarkably successful McCulloch 1993, 1997;Chipman 1996;Chipman et al 2001;Ročková and George 2014, and unpublished results). Recently, Bayesian spike-and-slab priors have been applied to predictive modeling and variable selection in largescale genomic studies (Yi et al 2003;Ishwaran and Rao 2005;de los Campos et al 2010;Zhou et al 2013;Lu et al 2015;Shankar et al 2015;Shelton et al 2015;Partovi Nia and Ghannad-Rezaie 2016). However, most previous spikeand-slab variable selection approaches use the mixture normal priors on coefficients and employ Markov Chain Monte Carlo (MCMC) algorithms (e.g., stochastic search variable selection) to fit the model.…”

Group spike-and-slab lasso generalized linear models for disease prediction and associated genes detection by incorporating pathway information

“…The mixture spike-and-slab prior improves the accuracy of coefficient estimation and prognostic prediction by adaptively inducing different amounts of shrinkage for different predictors and thus achieving nice effect of removing irrelevant predictors while supporting the larger coefficients. Similar to other Bayesian approaches, most spike-and-slab variable selection approaches proposed previously use the mixture normal priors on coefficients and employ Markov Chain Monte Carlo (MCMC) algorithms to fit the model (Lu et al, 2015;Partovi Nia and Ghannad-Rezaie, 2016;Shankar et al, 2015;Shelton et al, 2015). However, these MCMC methods are computationally intensive for analyzing large-scale and high-dimensional genetic data.…”

“…The spike-and-slab prior is the fundamental basis for most Bayesian variable selection approaches and has proved remarkably successful (Chipman, 1996;Chipman et al, 2001;McCulloch, 1993, 1997;George, 2014, 2016a). The mixture priors have been applied to predictive modeling and variable selection in large-scale genomic studies (de los Campos et al, 2010;Ishwaran and Rao, 2005;Lu et al, 2015;Partovi Nia and Ghannad-Rezaie, 2016;Shankar et al, 2015;Shelton et al, 2015;Yi et al, 2003;Zhou et al, 2013). We have recently incorporated this prior with GLMs and Cox models, and developed the spike-and-slab lasso GLMs and Cox models for prediction and gene detection, respectively (Tang et al, 2017a,b).…”

Editorial: Special issue on models for continuous data with a spike at zero

“…The paper by Partovi Nia and Hannad‐Rezaie () discusses a biological application entailing clustering in high‐dimensional metabolic data. In particular, they focus on joint grouping of rows and columns, that is when one is looking for clusters of individuals (units, objects, etc.)…”