A novel distance measure for the unsupervised clustering of temporal patterns in high-dimensional neuronal ensembles
Temporally ordered multi-neuron patterns likely encode information in the brain. We introduce an unsupervised method, SPOTDisClust (Spike Pattern Optimal Transport Dissimilarity Clustering), for their detection from high-dimensional neural ensembles. SPOTDisClust measures similarity between two ensemble spike patterns by determining the minimum transport cost of transforming their corresponding normalized cross-correlation matrices into each other (SPOTDis). Then, it performs density-based clustering based on the resulting inter-pattern dissimilarity matrix. SPOTDisClust does not require binning and can detect complex patterns (beyond sequential activation) even when high levels of out-of-pattern \"noise\" spiking are present. Our method handles efficiently the additional information from increasingly large neuronal ensembles and can detect a number of patterns that far exceeds the number of recorded neurons. In an application to neural ensemble data from macaque monkey V1 cortex, SPOTDisClust can identify different moving stimulus directions on the sole basis of temporal spiking patterns.\n\nAuthor summaryThe brain encodes information by ensembles of neurons, and recent technological developments allow researchers to simultaneously record from over thousands of neurons. Neurons exhibit spontaneous activity patterns, which are constrained by experience and development, limiting the portion of state space that is effectively visited. Patterns of spontaneous activity may contribute to shaping the synaptic connectivity matrix and contribute to memory consolidation, and synaptic plasticity formation depends crucially on the temporal spiking order among neurons. Hence, the unsupervised detection of spike sequences is a sine qua non for understanding how spontaneous activity contributes to memory formation. Yet, sequence detection presents major methodological challenges like the sparsity and stochasticity of neuronal output, and its high dimensionality. We propose a dissimilarity measure between neuronal patterns based on optimal transport theory, determining their similarity from the pairwise cross-correlation matrix, which can be taken as a proxy of the \"trace\" that is left on the synaptic matrix. We then perform unsupervised clustering and visualization of patterns using density clustering on the dissimilarity matrix and low-dimensional embedding techniques. This method does not require binning of spike times, is robust to noise, jitter and rate fluctuations, and can detect more patterns than the number of neurons.