On neural spike sorting with mixture models

Abstract

While the nature of physics is to understand matter, the nature of neuroscience is perhaps to understand brain. With the advent of neural data collecting hardware, from single electrode tip to electrode array, there is a need to analyze these huge amount of neural data. The analysis of these data will require new developments in the inferential and statistical tools. This thesis attempts to develop a new set of statistical mixture models and methods and apply them to the neural data analysis.

The problem we are trying to solve is called neural spike sorting in literature. There are three basic objectives of spike sorting. The first is to estimate the number of neurons which contribute to the recorded neural data. The second is to identify the spikes, i.e. the little curves in the recorded neural data, with the neurons. The third is to find the characteristic spike shape of each neuron. Spike sorting can not be formulated in standard terms of multivariate clustering. Because a spike can originate from simultaneous activity of multiple neurons, and is called an overlapped spike. These overlapped spikes do not belong to any of the available clusters. Therefore new model can be developed.

This thesis attempts to sort spikes either when there are no overlapped spikes or when there are, while providing a new set of statistical mixture models and methods. To estimate the number of neurons, we extend the current statistical mixture models to allow a contamination class of mixture components, and extend the current statistical mixture methods to estimate the number of mixture components, i.e. the number of neurons. To estimate the characteristic shape and identify the spikes with the neurons, we extend the current statistical mixture models and methods to allow a sparse set of mixture components which model the overlapped spikes. Lastly we also develop a multivariate extension of Lewicki (1994) to sort spikes from multiple electrode tips.