Tensor analysis of animal behavior by matricization and feature selection

Contemporary neurobehavior research often collects multi-dimensional tensor (MDT) data containing time-series measurements for multiple features from multiple animals subjected to various perturbations. Proper analysis of the MDT data can reveal neural circuitries driving the behavior. However, many MDT analyses, such as tensor decomposition, may not yield results that are easy to interpret or directly compatible with standard multivariate analysis designed for 2-dimensional tensor (2DT) structures. To address this issue, the MDT data are transformed into 2DT by dimensionality reduction techniques, including matricization methods such as Index Construction and Feature Concatenation. Nonetheless, matricization may exclude key information or introduce spurious noise to multivariate analysis, so its impact on multivariate analysis remains elusive. Here, we demonstrated different matricization approaches and feature selection methods. We evaluated their impacts on multivariate analysis performance using an MDT dataset of zebrafish visual-motor response collected from wildtypes and visually-impaired mutants. We matricized the MDT dataset using various Index Construction and Feature Concatenation methods, then identified informative 2DT features using the filter and embedded methods. To evaluate these feature-selection methods, we applied several classifiers to distinguish zebrafish of different genotypes and assessed their performances with cross-validation and holdout validation. We found that most classifiers performed the best using 2DT features matricized by Feature Concatenation and selected by the embedded method or union operation. The results also revealed unique behavioral differences between the wildtypes and mutants, but not identified by multivariate analysis or MDT analysis. Our results demonstrate the utility of analyzing MDT behavioral data by matricization and feature selection.