Figure 1:

Schematic demonstrating the effect of kernel selection on the measure of similarity for two-dimensional neural features. Since kernel similarity between two points depends on only their coordinate-wise differences, we let p₁ = (0, 0) be a point at the origin and consider the kernel-determined similarity between p₁ and a second point p₂ = (x, y). For each plot, the color at (x, y) represents the measure of similarity according to the selected kernel ${\tilde{K}}_{\tilde{\theta }}\left(p_1,p_2\right).$ Traveling along the red line illustrates the effect of increasing the difference in measurements for a single neuron. For the RBF kernel (A), moving along the arrow results in the kernel becoming arbitrarily small. By contrast, the MK kernel (B) never falls below half of the value at the origin as it moves along the arrow. For 40 dimensions, the MK kernel would never fall below 39/40 of its maximal value. Hence, when the RBF kernel is used for closed-loop decoding, nonstationarities from a single neural feature would result in no similarity between the current neural feature and any of the training data. By contrast, the MK kernel will remain relatively unaffected by even a drastic change in a single neuron and continue to effectively use the information from the remaining neurons.