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Theoretical properties of distance distributions and novel metrics for nearest-neighbor feature selection.

ABSTRACT: The performance of nearest-neighbor feature selection and prediction methods depends on the metric for computing neighborhoods and the distribution properties of the underlying data. Recent work to improve nearest-neighbor feature selection algorithms has focused on new neighborhood estimation methods and distance metrics. However, little attention has been given to the distributional properties of pairwise distances as a function of the metric or data type. Thus, we derive general analytical expressions for the mean and variance of pairwise distances for Lq metrics for normal and uniform random data with p attributes and m instances. The distribution moment formulas and detailed derivations provide a resource for understanding the distance properties for metrics and data types commonly used with nearest-neighbor methods, and the derivations provide the starting point for the following novel results. We use extreme value theory to derive the mean and variance for metrics that are normalized by the range of each attribute (difference of max and min). We derive analytical formulas for a new metric for genetic variants, which are categorical variables that occur in genome-wide association studies (GWAS). The genetic distance distributions account for minor allele frequency and the transition/transversion ratio. We introduce a new metric for resting-state functional MRI data (rs-fMRI) and derive its distance distribution properties. This metric is applicable to correlation-based predictors derived from time-series data. The analytical means and variances are in strong agreement with simulation results. We also use simulations to explore the sensitivity of the expected means and variances in the presence of correlation and interactions in the data. These analytical results and new metrics can be used to inform the optimization of nearest neighbor methods for a broad range of studies, including gene expression, GWAS, and fMRI data.

SUBMITTER: Dawkins BA

PROVIDER: S-EPMC7870093 | biostudies-literature | 2021

REPOSITORIES: biostudies-literature

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Theoretical properties of distance distributions and novel metrics for nearest-neighbor feature selection.

Dawkins Bryan A BA Le Trang T TT McKinney Brett A BA

PloS one 20210208 2

The performance of nearest-neighbor feature selection and prediction methods depends on the metric for computing neighborhoods and the distribution properties of the underlying data. Recent work to improve nearest-neighbor feature selection algorithms has focused on new neighborhood estimation methods and distance metrics. However, little attention has been given to the distributional properties of pairwise distances as a function of the metric or data type. Thus, we derive general analytical ex ...[more]

PMID: 33556091

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Project description:Relief-F is a nonparametric, nearest-neighbor machine learning method that has been successfully used to identify relevant variables that may interact in complex multivariate models to explain phenotypic variation. While several tools have been developed for assessing differential expression in sequence-based transcriptomics, the detection of statistical interactions between transcripts has received less attention in the area of RNA-seq analysis. We describe a new extension and assessment of Relief-F for feature selection in RNA-seq data. The ReliefSeq implementation adapts the number of nearest neighbors (k) for each gene to optimize the Relief-F test statistics (importance scores) for finding both main effects and interactions. We compare this gene-wise adaptive-k (gwak) Relief-F method with standard RNA-seq feature selection tools, such as DESeq and edgeR, and with the popular machine learning method Random Forests. We demonstrate performance on a panel of simulated data that have a range of distributional properties reflected in real mRNA-seq data including multiple transcripts with varying sizes of main effects and interaction effects. For simulated main effects, gwak-Relief-F feature selection performs comparably to standard tools DESeq and edgeR for ranking relevant transcripts. For gene-gene interactions, gwak-Relief-F outperforms all comparison methods at ranking relevant genes in all but the highest fold change/highest signal situations where it performs similarly. The gwak-Relief-F algorithm outperforms Random Forests for detecting relevant genes in all simulation experiments. In addition, Relief-F is comparable to the other methods based on computational time. We also apply ReliefSeq to an RNA-Seq study of smallpox vaccine to identify gene expression changes between vaccinia virus-stimulated and unstimulated samples. ReliefSeq is an attractive tool for inclusion in the suite of tools used for analysis of mRNA-Seq data; it has power to detect both main effects and interaction effects. Software Availability: http://insilico.utulsa.edu/ReliefSeq.php.

Dataset Information

Theoretical properties of distance distributions and novel metrics for nearest-neighbor feature selection.

Publications

Theoretical properties of distance distributions and novel metrics for nearest-neighbor feature selection.

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