Basic to multi-neuron study is the ability to resolve the spike waveforms
associated with the multiple individual neurons, which often are present on single or multiple electrodes. For reviews of spike sorting techniques, see Wheeler and Heetderks, 1982, Schmidt, 1984, Lewicki, 1998, Wheeler, 1999.
For many data acquisition systems, spike detection is done on-line, and the software can read in and use the already-detected spike waveforms. For continuously-recorded data files, the software can perform spike detection by using a threshold-crossing algorithm.
When spike waveforms are present, the software helps to separate the waveforms collected from single or multiple electrodes into distinct waveform groups or classes that are associated with individual neurons. Each class of waveforms is called a unit or a cluster.
The software currently provides the following spike-sorting algorithms, grouped into categories:
All sorting methods work in so-called “feature space” except for the Waveform Crossing, Template, Boxes, Lines and Bands sorting methods. Instead of using the entire raw waveform, sorting methods that work in feature space characterize the essence of the waveform by using a few calculated features. The feature space
can be defined by selecting from among several features for each axis. The features available for assignment to the axes in feature space include:
• Projections onto principal components (PCA)
• Waveform heights at chosen times (“slices”)
• Peak height, valley height, peak-valley difference, widths
• For stereotrode and tetrode data, per-electrode and ratio-between-electrodes features
Thus the waveform can be represented by the point (x,y) in a 2D feature space, or (x,y,z) in a 3D feature space, where the x, y and z axes can be chosen from the available features.
In the 3D view of the feature space points, it is possible to navigate the eyepoint through the 3D space to get a better idea of what the data set looks like and to find a vantage point where clusters are best separated. After the desired perspective in 3D space is achieved, the sorting methods can be applied.
For a detailed description of the features, see Section 6.4, “Features Available for Sorting” on page 342.
Manual sorting methods
Manual spike sorting methods allow full control of the sorting process, and it is possible to indicate manually which waveforms should be assigned to each unit.
With the Waveform Crossing method, the units are manually selected by using the actual waveforms. Crossing a bundle of waveforms with the mouse pointer can specify the unit.
Using the Contours method, a cluster is specified by drawing an arbitrary shape in feature space (usually around a visible cluster). The software assigns all waveforms inside the arbitrary shape to that cluster. When the Contours method is applied from the 3D view, it operates in a 2D projection of the 3D feature space that is a standard perspective projection based on the chosen viewpoint. That is, the 3D feature space is first transformed to a 2D feature space (“screen space”) by using a standard perspective projection, then the Contour sorting algorithm runs in screen space. The other sorting algorithms can also be run in either 2D or 3D feature space.
The Boxes sorting method requires placing two boxes on the Waveforms view to define each unit. Each box thus specifies a region in time-voltage space. Any waveforms that intersect with both boxes for a unit are sorted into that unit. The boxes can be resized and moved to any position on the Waveforms view.
The Lines sorting method is similar to the Waveform Crossing method, except a unit can be defined as several lines segments that the waveforms must intersect.
2 System Overview
The Bands sorting method is similar to the Template method (see Semi-automatic sorting methods, below) except that instead of using a single tolerance value for the entire unit, the tolerance can be tailored to be different for different portions of the waveform. This use of variable tolerances effectively defines a variable-width ‘corridor’ through which waveforms for a particular unit must pass. You define the initial unit template by crossing waveforms; then you can adjust the tolerances and the template itself by dragging on-screen handles.
Note: The Lines and Bands sorting methods function the same way in the Offline Sorter software as in the OmniPlex System.
Semi-automatic sorting methods
The Semi-automatic sorting methods generally require specifying cluster centers (and therefore implicitly indicate the number of clusters), and then the algorithm assigns waveforms to the clusters.
The Template method requires picking an existing waveform to serve as the template for a unit. The software then adds other waveforms to the unit based on their similarity (in the least-squares difference sense) to the template unit, with a user-defined tolerance.
The K-Means method is a well-known iterative algorithm that assigns each waveform to one of the user-specified cluster centers, based on Euclidean
distance in feature space. Then it recomputes the cluster centers, and it repeats the process until no more waveforms change units.
The Standard E-M method is a variation of the Expectation Maximization algorithm. The Expectation Maximization algorithms in general fit a mixture of Gaussians to the point densities in feature space by varying the normal
distribution parameters (means, covariances) to maximize a likelihood function.
This algorithm uses the user-specified center points to start the search.
The Semi-automatic sorting methods are also capable of using an existing set of sorted units as a starting point, in what is referred to as “Continue” sorting. The algorithms can run using the centroids or template waveforms of existing clusters as the starting points, instead of manually specifying them.
Automatic sorting methods
The Automatic sorting methods are capable of automatically finding the optimal number of clusters, and of assigning waveforms to the clusters. Thus they require no user intervention to arrive at the initial clustering of the data, and they can operate on completely unsorted data.
The Valley Seeking automatic method uses a Valley Seeking algorithm that it applies to inter-point distances to automatically determine the number of clusters and the cluster memberships.
The T-Distribution E-M (T-Dist E-M) method is another variation of the
Expectation Maximization algorithm that fits a mixture of T-Distributions instead
of Gaussians to the point densities in feature space. This algorithm is also capable of adjusting the number of clusters as it runs (by removing unfavorable clusters) to arrive at the optimum number of clusters.
The Scanning methods are a family of automatic sorting methods that attempt to find an optimal clustering by stepping a sorting parameter (a value that controls how the sorting is performed) through a range of values. One of the Sorting Quality Statistics described in Section 6.6, “Sorting Quality Statistics” on page 357, is chosen as the metric that defines what ‘optimal’ means. For
example, Valley Seeking automatic sorting method has a sorting parameter called the Parzen Multiplier that affects how the clustering proceeds. The Valley
Seeking Scan sorting method will step the value of the Parzen Multiplier through a user-defined range of values and calculate the Sorting Quality Statistics for each step. The step that produces the best value of the chosen Sorting Quality Statistic is taken as the final sorting.
Working with sorted data—inspecting, adjusting and re-sorting
The software provides many mechanisms for inspecting and manually adjusting the sorting results; it is possible to add or remove waveforms from clusters or invalidate them completely. The waveforms can be re-sorted by using any of the clustering methods. After the units have been defined, the contours, templates and principal components can be saved to a TPL file and they can be used to sort waveforms in other data files.
For more information on the sorting algorithms, see Section 6.5, “Details of the Sorting Algorithms” on page 349.
References
Lewicki, M.S., A review of methods for spike sorting: the detection and classification of neural action potentials, Network: Comput. Neural Syst., 9, R53-R78, 1998.
Schmidt, E.M., Computer separation of multi-unit neuroelectric data: a review, J.
Neurosci. Meth., 12, 95-111, 1984.
Wheeler, B.C., Automatic Discrimination of Single Units, Methods for Neural Ensemble Recordings, ed. by M. Nicolelis, CRC Press, Boca Raton, 61-77, 1999.
Wheeler, B.C., and Heetderks, W.J., A comparison of techniques for
classification of multiple neural signals, IEEE Trans. Biomed. Eng., 29, 752-759, 1982.