Neural responses in higher cortical areas often display a baffling complexity. In animals performing behavioral tasks, single neurons will typically encode several parameters simultaneously, such as stimuli, rewards, decisions, etc. When dealing with this large heterogeneity of responses, cells are conventionally classified into separate response categories using various statistical tools. However, this classical approach usually fails to account for the distributed nature of representations in higher cortical areas. Alternatively, principal component analysis (PCA) or related techniques can be employed to reduce the complexity of a data set while retaining the distributional aspect of the population activity. These methods, however, fail to explicitly extract the task parameters from the neural responses. Here we suggest a coordinate transformation that seeks to ameliorate these problems by combining the advantages of both methods. Our basic insight is that variance in neural firing rates can have different origins (such as changes in a stimulus, a reward, or the passage of time), and that, instead of lumping them together, as PCA does, we need to treat these sources separately. We present a method that seeks an orthogonal coordinate transformation such that the variance captured from different sources falls into orthogonal subspaces and is maximized within these subspaces. Using simulated examples, we show how this approach can be used to demix heterogeneous neural responses. Our method may help to lift the fog of response heterogeneity in higher cortical areas.
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