Figure 2.

Procedures for analyzing high-dimensional neural data in a biologically informative way. (A) Illustration of dimensionality in multichannel recordings. Time-varying data are collected simultaneously from populations of neurons. These are typically spiking rates over some time window. The rates exist in a space that has the same dimensionality as the number of channels recorded. However, neuronal responses are typically not unique or independent, so it is likely that pairs of neurons have correlated firing rates (here, channels 1 and 7). This allows for dimensionality techniques (here, principal components analysis) to capture most of the variability in a reduced number of dimensions. (B) Population response trajectories to different stimulus conditions can be traced through this reduced space over time. (C) Firing rates of neurons, left, often relate to more than one experimental variable (here, stimulus and behavior, gray bars). The high-dimensional responses of many neurons may be reduced with supervision so that they are also de-mixed, and the independent stimulus and behavior selective responses are clear. (D) One-way representations change between brain areas is that they allow different variables to become more easily, or linearly, separable. In this example, one stimulus attribute is separable in Area X (color), while both shape and color are separable in Area Y, depending on the decision line (dashed).