Tensor analysis of animal behavior by matricization and feature selection

Contemporary neurobehavior research often collects multi-dimensional tensor (MDT) data, consisting of time-series measurements for multiple features from multiple animals subjected to various perturbations. Proper analysis of the MDT data can facilitate the dissection of the underlying neural circuitry driving the behavior. However, many common approaches for MDT analysis, such as tensor decomposition, often yield results that are difficult to interpret and not directly compatible with standard multivariate analysis (MVA), which is designed for simpler, lower-dimensional data structures. To address this issue, dimensionality reduction techniques, including matricization methods such as Index Construction and Feature Concatenation, are applied to transform all or a subset of the features in the MDT into a lower-dimensional tensor, commonly a 2-dimensional tensor (2DT), that is compatible with MVA. However, the matricization methods may exclude information from the MDT features or create too many 2DT features that introduce spurious noise to the downstream analyses. Their impacts on the downstream MVA performance remain elusive. In this study, we systematically evaluated different approaches for matricization and feature selection and their impacts on MVA performance using an MDT dataset of zebrafish visual- motor response collected from wild-types (WTs) 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 approaches, we conducted a classification task distinguishing WT and visually-impaired zebrafish by multiple classifiers. We then assessed classification performance with cross-validation and holdout validation. We found that most classifiers performed the best when using all 2DT features matricized by Feature Concatenation and selected by the embedded method. The results also revealed unique behavioral differences between the WTs and visually-impaired mutants that were not identified by standard MVA or MDT analysis. Our results demonstrate the utility of analyzing MDT behavioral data by matricization and feature selection.