An Approximate EM Approach to Sorting Overlapping Spikes
In the past neuroscience has focused on explaining the function of single neurons, but now more and more interest is directed towards the local interactions between neurons. This leads to greater demands on spike sorting algorithms to cope with strongly correlated neurons which predominantly produce overlapping spikes. |
While existing spike sorting algorithms work in two stages: the first to identify spike times and the second to cluster the found spike shapes, we propose an algorithm based on the expectation-maximisation (EM) algorithm which iterates between finding spike times given an estimate of spike shapes and estimating spike shapes given the current spike times. Overlapping spikes are automatically resolved in this framework and contribute to the learning process.
Because the computations involved in the original formulation of the algorithm are prohibitive, we further propose three approximations. Two of them have severe problems with local optima. Although the third overcomes these, this is payed for by a deviation from the original problem setting which proposed correction leads to bad convergence behaviour. Additionally we discuss possible improvements of the third approximation.
We define performance in terms of recall and precision. The algorithm is tested and compared to other algorithms on a test data set which has been previously published and very closely resembles real data. On average our algorithm correctly finds a bit less than 2 out of 3 spikes with considerable variation to the better and lower mainly depending on the spike shapes, the number of cells in the data and the noise level. The performance of one of the tested clustering algorithms is often better, although not much. Even a simple matched filter approach often performs as well as our more complicated algorithm. On the other hand, clustering and matched filter exhibit a large drop in performance when only overlapping spikes are considered while the performance of our algorithm stays equal.
In conclusion we find that our algorithm works not as good as wished, but automatically handles overlapping spikes as expected.