Nonmetric ANOVA: a generic framework for analysis of variance on dissimilarity measures
Malyutina, A.; Tang, J.; Amiryousefi, A.
Show abstract
Classic Analysis of Variance (ANOVA; cA) tests the explanatory power of a partitioning on a set of objects. Nonparametric ANOVA (npA) extends to a case where instead of the object values themselves, their mutual distances are available. While considerably widening the applicability of the cA, the npA does not provide a statistical framework for the cases where the mutual dissimilarity measurements between objects are nonmetric. Based on the central limit theorem (CLT), we introduce nonmetric ANOVA (nmA) as an extension of the cA and npA models where metric properties (identity, symmetry, and subadditivity) are relaxed. Our model allows any dissimilarity measures to be defined between objects where a distinctiveness of a specific partitioning imposed on those are of interest. This derivation accommodates an ANOVA-like framework of judgment, indicative of significant dispersion of the partitioned outputs in nonmetric space. We present a statistic which under the null hypothesis of no differences between the mean of the imposed partitioning, follows an exact F-distribution allowing to obtain the consequential p-value. Three biological examples are provided and the performance of our method in relation to the cA and npA is discussed. Significance StatementThe Nonmetric Analysis of Variance (nmANOVA) conveys a framework that allows a compatible type of ANOVA for the cases where the proper metric measurements between objects are either lost, unknown or however inaccessible. While classic ANOVA is based on the measurements of the data from a base datum, the nmANOVA is formulated on the dissimilarity outputs (not necessarily metric) defined between all objects. As the main goal of ANOVA in providing a statistical test for assessing the significance of a considered partitioning on the data, the nmANOVA is yielding a paralleled scheme of inference with 1) accommodating the outcomes dissimilarities into within and between groups statistics, 2) assessing their respective divergence with a parametric distribution, and 3) providing a resultant p-value indicative of evidences fore rejecting the null hypothesis.
Matching journals
The top 4 journals account for 50% of the predicted probability mass.
Similar papers in this journal
- Model guided trait-specific co-expression network estimation as a new perspective for identifying molecular interactions and pathways 95%
- Mcadet: a feature selection method for fine-resolution single-cell RNA-seq data based on multiple correspondence analysis and community detection 95%
- Using random forests to uncover the predictive power of distance-varying cell interactions in tumor microenvironments 94%
Similar papers in this journal
- Practical Identifiability in the Frame of Nonlinear Mixed Effects Models: the Example of the in vitro Erythropoiesis 95%
- Gene regulation network inference using k-nearest neighbor-based mutual information estimation- Revisiting an old DREAM 95%
- TIME-CoExpress: Temporal Trajectory Modeling of Dynamic Gene Co-expression Patterns Using Single-Cell Transcriptomics Data 94%
Similar papers in this journal
Similar papers in this journal
- Novel AI-powered computational method using tensor decomposition for identification of common optimal bin sizes when integrating multiple Hi-C datasets 95%
- Tensor decomposition- and principal component analysis-based unsupervised feature extraction to select more reasonable differentially expressed genes: Optimization of standard deviation versus state-of-art methods 95%
- Interpretable deep recommender system model for prediction of kinase inhibitor efficacy across cancer cell lines 94%
"Similar papers" are the closest papers from that journal in the model's embedding space. They show what the match is built on, but the ranking comes mostly from a classifier over the whole training set, not from these examples alone.