Recent advances in experimental methods in neuroscience enable the acquisition of large-scale, high-dimensional and high-resolution datasets. These complex and rich datasets call for the development of advanced data analysis tools, as commonly used techniques do not suffice to capture the spatiotemporal network complexity. In this talk I will present new data-driven methods based on global and local spectral embeddings for the processing and organization of high-dimensional datasets, and demonstrate their application to the analysis of neuronal measurements. We develop a new greedy adaptive spectral clustering method capable of handling overlapping clusters and disregarding clutter. Applied to in-vivo calcium imaging of neurons and apical dendrites, we extract hundreds of neuronal structures with detailed morphology, and demixed and denoised time-traces. Next we introduce a nonlinear, data-driven and model-free approach for the analysis of a spatiotemporal dynamical system, represented as a rank-3 tensor. Applying our methodology to neuronal measurements, we identify, solely from observations and in a purely unsupervised data-driven manner, functional subsets of neurons, activity patterns associated with particular behaviors and pathological dysfunction caused by external intervention