Demixed principal component analysis of population activity in higher cortical areas reveals independent representation of task parameters

Neurons in higher cortical areas, such as the prefrontal cortex, are known to be tuned to a variety of sensory and motor variables. The resulting diversity of neural tuning often obscures the represented information. Here we introduce a novel dimensionality reduction technique, demixed principal component analysis (dPCA), which automatically discovers and highlights the essential features in complex population activities. We reanalyze population data from the prefrontal areas of rats and monkeys performing a variety of working memory and decision-making tasks. In each case, dPCA summarizes the relevant features of the population response in a single figure. The population activity is decomposed into a few demixed components that capture most of the variance in the data and that highlight dynamic tuning of the population to various task parameters, such as stimuli, decisions, rewards, etc. Moreover, dPCA reveals strong, condition-independent components of the population activity that remain unnoticed with conventional approaches. Introduction In many state of the art experiments, a subject, such as a rat or a monkey, performs a behavioral task while the activity of tens to hundreds of neurons in the animal’s brain is monitored using electrophysiological or imaging techniques. The common goal of these studies is to relate the external task parameters, such as stimuli, rewards, or the animal’s actions, to the internal neural activity, and to then draw conclusions about brain function. This approach has typically relied on the analysis of single neuron recordings. However, as soon as hundreds of neurons are taken into account, the complexity of the recorded data poses a fundamental challenge in itself. This problem has been particularly severe in higher-order areas such as the prefrontal cortex, where neural responses display a baffling heterogeneity, even if animals are carrying out rather simple tasks (Brody et al., 2003; Machens, 2010; Mante et al., 2013; Cunningham and Yu, 2014). Traditionally, this heterogeneity has often been ignored. In neurophysiological studies, it is common practice to pre-select cells based on particular criteria, such as responsiveness to the same stimulus, and to then average the firing rates of the pre-selected cells. This practice eliminates much of the richness 1 ar X iv :1 41 0. 60 31 v1 [ qbi o. N C ] 2 2 O ct 2 01 4 of single-cell activities, similar to imaging techniques with low spatial resolution, such as MEG, EEG, or fMRI. While population averages can identify the information that higher-order areas process, they ignore how exactly that information is represented on the neuronal level (Wohrer et al., 2013). Indeed, most neurons in higher cortical areas will typically encode several task parameters simultaneously, and therefore display what has been termed “mixed selectivity” (Rigotti et al., 2013). Instead of looking at single neurons and selecting from or averaging over a population of neurons, neural population recordings can be analyzed using dimensionality reduction methods (for a review, see Cunningham and Yu, 2014). In recent years, several such methods have been developed that are specifically targeted to electrophysiological data, taking into account the binary nature of spike trains (Yu et al., 2009; Pfau et al., 2013), or the dynamical properties of the population response (Buesing et al., 2012; Churchland et al., 2012). However, these approaches reduce the dimensionality of the data without taking task parameters, i.e., sensory and motor variables controlled or monitored by the experimenter, into account. Consequently, mixed selectivity remains in the data even after the dimensionality reduction step, impeding interpretation of the results. A few recent studies have sought to solve these problems by developing methods that reduce the dimensionality of the data in a way that is informed by the task parameters (Machens, 2010; Machens et al., 2010; Brendel et al., 2011; Mante et al., 2013). One possibility is to adopt a parametric approach, i.e. to assume a specific (e.g. linear) dependency of the firing rates on the task parameters, and then use regression to construct variables that demix the task components (Mante et al., 2013). While this method can help to sort out the mixed selectivities, it still runs the risk of missing important structures in the data if the neural activities do not conform to the dependency assumptions (e.g. because of nonlinearities). Here, we follow an alternative route by developing an unbiased dimensionality reduction technique that fulfills two constraints. It aims to find a decomposition of the data into latent components that (a) are easily interpretable with respect to the experimentally controlled and monitored task parameters; and (b) preserve the original data as much as possible, ensuring that no valuable information is thrown away. Our method, which we term demixed principal component analysis (dPCA), improves our earlier methodological work (Machens, 2010; Machens et al., 2010; Brendel et al., 2011) by eliminating unnecessary orthogonality constraints on the decomposition. In contrast to several recently suggested algorithms for decomposing firing rates of individual neurons into demixed parts (Pagan and Rust, 2014; Park et al., 2014), our focus is on dimensionality reduction. There is no a priori guarantee that neural population activities can be linearly demixed into latent variables that reflect individual task parameters. Nevertheless, we applied dPCA to spike train recordings from monkey prefrontal cortex (PFC) (Romo et al., 1999; Qi et al., 2011) and from rat orbitofrontal cortex (OFC) (Feierstein et al., 2006; Kepecs et al., 2008), and obtained remarkably successful demixing. In each case, dPCA automatically summarizes all the important, previously described features of the population activity in a single figure. Importantly, our method provides an easy visual comparison of complex population data across different tasks and brain areas, which allows us to highlight both similarities and differences in the neural activities. Demixed PCA also reveals several hitherto largely ignored features of population data: (1) most of the activity in these datasets is not related to any of the controlled task parameters, but depends only on time (“condition-independent activity”); (2) all measured task parameters can be extracted with essentially orthogonal linear readouts; and (3) taskrelevant information is shifted around in the neural population space, moving from one component to another during the course of the trial. Results Demixed Principal Component Analysis (dPCA) We illustrate our method with a toy example (Figure 1). Consider a standard experimental paradigm in which a subject is first presented with a stimulus and then reports a binary decision. The firing rates of two simulated neurons are shown in Figure 1A. The first neuron’s firing rate changes with time, with stimulus (at the beginning of the trial), and with the animal’s decision (at the end of the trial). The second neuron’s firing rate also changes with time, but only depends on the subject’s decision (not on the stimulus). As time progresses within a trial, the joint activity of the two neurons traces out a trajectory