Figure 6. Principal component-based analysis identifies cell assembly neurons and the time course of their activation.

(A) Binned spiking activity of a network composed of 25 neurons simulated for 8000 bins (200 bins shown). Neurons are modeled as Poissonian processes with random mean rate between 1 and 5 spikes/bin, uniformly distributed across the neurons. In addition, each neuron is set to fire at 6× its mean rate at 0.5% of the bins randomly chosen (referred to as activation bins). In order to simulate cell assemblies, we set all activation bins to be independent, except for two groups of neurons which have simultaneous activation bins. (B) Autocorrelation matrix (ACM). (C) Theoretical eigenvalues distribution for independent neuronal activity (top), and the eigenvalues histogram computed from the simulated network (bottom). Note that 2 eigenvalues fall above the theoretical upper limit predicted for random activity, which correspond to the two cell assemblies present in the network. Notice further that three other eigenvalues fall below the lower limit; the number of eigenvalues outside the theoretical limits is therefore 5, which corresponds to the number of neurons participating in cell assemblies. (D) ACM eigenvectors associated with the two eigenvalues above the theoretical limit for random activity. These vectors are referred to as principal components (PCs). (E) Neuronal representations in the subspace spanned by the PCs (referred to as the Assembly Space). Since the PCs are the vectors which best describe strong correlated activity, neurons with larger projections on the Assembly Space are the neurons involved in cell assemblies (the label of these neurons are also shown). (F) Interaction Matrix; the entries of this matrix are measures of correlated activity of cell assembly neurons in the Assembly Space. Higher values denote neuron pairs pertaining to the same cell assembly, whereas lower values denote neurons whose activity is orthogonal. (G) From the Interaction Matrix, a simple clustering algorithm (described in Supplementary Information files) identifies the neurons of each cell assembly. (H) Same binned spiking activity as in A but rearranged in order to show cell assembly neurons on top, as labeled. (I,J) Assembly Vectors are defined as mean vectors in the Assembly Space (I); these vectors are used to compute projector operators (J). (K) The projector operators are then applied to the binned spiking activity, revealing the time course of the activation strength of each cell assembly. Note that these results corroborate the activations seen by visual inspection of H. Since the cell assemblies were non-overlapping in this example, the identity of cell assembly neurons can be directly inferred by a simple analysis of the PCs (represented by the dashed line from D to H). However, such straight inference cannot be performed in cases where one or more neurons pertain to two or more assemblies (see Figure 7).