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Rigid geometry solves "curse of dimensionality" effects in clustering methods: An application to omics data.

ABSTRACT: The quality of samples preserved long term at ultralow temperatures has not been adequately studied. To improve our understanding, we need a strategy to analyze protein degradation and metabolism at subfreezing temperatures. To do this, we obtained liquid chromatography-mass spectrometry (LC/MS) data of calculated protein signal intensities in HEK-293 cells. Our first attempt at directly clustering the values failed, most likely due to the so-called "curse of dimensionality". The clusters were not reproducible, and the outputs differed with different methods. By utilizing rigid geometry with a prime ideal I-adic (p-adic) metric, however, we rearranged the sample clusters into a meaningful and reproducible order, and the results were the same with each of the different clustering methods tested. Furthermore, we have also succeeded in application of this method to expression array data in similar situations. Thus, we eliminated the "curse of dimensionality" from the data set, at least in clustering methods. It is possible that our approach determines a characteristic value of systems that follow a Boltzmann distribution.

SUBMITTER: Adachi S

PROVIDER: S-EPMC5470695 | biostudies-literature | 2017

REPOSITORIES: biostudies-literature

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Rigid geometry solves "curse of dimensionality" effects in clustering methods: An application to omics data.

Adachi Shun S

PloS one 20170614 6

The quality of samples preserved long term at ultralow temperatures has not been adequately studied. To improve our understanding, we need a strategy to analyze protein degradation and metabolism at subfreezing temperatures. To do this, we obtained liquid chromatography-mass spectrometry (LC/MS) data of calculated protein signal intensities in HEK-293 cells. Our first attempt at directly clustering the values failed, most likely due to the so-called "curse of dimensionality". The clusters were n ...[more]

PMID: 28614363

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Project description:Omics data integration is becoming necessary to investigate the still unknown genomic mechanisms of complex diseases. During the integration process, many challenges arise such as data heterogeneity, the smaller number of individuals in comparison to the number of parameters, multicollinearity, and interpretation and validation of results due to their complexity and lack of knowledge about biological mechanisms. To overcome some of these issues, innovative statistical approaches are being developed. In this work, we applied penalized regression methods (LASSO and ENET) to explore relationships between common genetic variants, DNA methylation and gene expression measured in bladder tumor samples and have proposed a permutation-based method to concomitantly assess significance and correct by multiple testing with the MaxT algorithm. The overall analysis flow consisted of three steps: (1) SNPs/CpGs were selected per each gene probe within 1Mb window upstream and downstream the gene; (2) LASSO and ENET were applied to assess the association between each expression probe and the selected SNPs/CpGs in three multivariable models (SNP, CPG, and Global models, the latter integrating SNPs and CPGs); and (3) the significance of each model was assessed using the permutation-based MaxT method. We identified 48 genes whom expression levels were associated with both SNPs and GPGs. Importantly, we replicated results for 36 (75%) of them in an independent data set (TCGA). We checked the performance of the proposed method with a simulation study and further supported our results with a biological interpretation based on an enrichment analysis. The approach we propose allows reducing computational time and is flexibly and easy to implement when analyzing several omics data. Our results highlight the importance of integrating omics data by applying appropriate statistical strategies to discover new insights into the complexity of disease genetic mechanisms. Gene expression data were obtained from 44 tumor samples using the Affymetrix DNA Microarray Human Gene 1.0 ST Array with 32,321 probes.

Dataset Information

Rigid geometry solves "curse of dimensionality" effects in clustering methods: An application to omics data.

Publications

Rigid geometry solves "curse of dimensionality" effects in clustering methods: An application to omics data.

Similar Datasets

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