Experimental advances in neuroscience enable the acquisition of increasingly large-scale, high-dimensional and high-resolution neuronal and behavioral datasets, yet addressing the full spatiotemporal complexity of these datasets poses significant challenges for data analysis and modeling. I present a new geometric analysis framework, and demonstrate its application to the analysis of calcium imaging from the primary motor cortex in a learning mammal. To extract neuronal regions of interest, we develop Local Selective Spectral Clustering, a new method for identifying high-dimensional overlapping clusters while disregarding noisy clutter. We demonstrate the capability of this method to extract hundreds of detailed neurons with demixed and denoised time-traces. Next, we propose to represent and analyze the extracted time-traces as a rank-3 tensor of neurons, time-frames and trials. We introduce a data-driven method for tensor analysis and organization, which infers the coupled multi-scale structure of the data. In analyzing neuronal activity from the motor cortex we identify in an unsupervised manner: functional subsets of neurons, activity patterns associated with particular behaviors, and long-term temporal trends.