Discovery of Linked Neural and Behavioral Subspaces with External Dynamic Components Analysis

Neural recordings are often high-dimensional while latent dynamics related to behavior are low-dimensional. Similarly, ethological behaviors are described by large numbers of dynamic features and it is important to know both the dimensionality and composition of the neurally relevant behavioral subspace. However, methods for data-driven identification of behavioral subspaces relevant for neural recordings is nascent. Here, we introduce external Dynamics Components Analysis (eDCA), a linear dimensionality reduction method that finds subspaces of past neural data that have maximal mutual information with subspaces of future behavior data. We validate eDCA on synthetically generated data and show that it identifies ‘causal’ neural subspaces relevant for behavioral subspaces and accurately recovers the relative importance of neural variables relevant for generating behavioral variables. Next, we apply eDCA to data from Macaque arm reaching on a 2D grid with simultaneously recorded neurons from primary motor cortex. We show eDCA neural subspaces decode behavior comparable to state-of-the-art methods (e.g., PSID). When both neural and behavioral data are corrupted by additional variables, we find that eDCA discards the superfluous dimensions. Decoding results additionally indicate that the relevant neural and behavioral subspaces are ~7 and 3 dimensional, respectively. Finally, we apply eDCA to high-dimensional speech data with simultaneously recorded ECoG from speech sensorimotor cortex. From the speech sound spectrograms, eDCA identifies neural subspaces relevant for the less acoustically salient (compared to vowels), but articulatorily important consonant sounds. Together, these results demonstrate that eDCA directly learns subspaces of neural dynamics that are `causally' relevant for subspaces of behavioral dynamics. Thus, by compressing both neural and behavioral data, eDCA removes the burden of manual feature selection in complex, ethological behavior and aids in identifying the dimensionality of the relevant neural and behavioral data.