Demixed principal component analysis of neural population data
- Champalimaud Centre for the Unknown, Portugal
- École Normale Supérieure, France
- Centre for Integrative Neuroscience, University of Tübingen, Germany
- Wake Forest University School of Medicine, United States
- Cold Spring Harbor Laboratory, United States
- Universidad Nacional Autónoma de México, Mexico
- El Colegio Nacional, Mexico
- Harvard University, United States
Figures
Figure 1
Existing approaches to population analysis, illustrated with recordings from monkey PFC during a somatosensory working memory task (Romo et al., 1999).
(a) Cartoon of the paradigm, adapted from Romo and Salinas (2003). Legend shows 12 experimental conditions. (b) Average per-condition firing rates (PSTHs) for four exemplary neurons out of . …
Figure 2
Linear dimensionality reduction.
(a) Linear discriminant analysis maps the firing rates of individual neurons onto a latent component that allows us to decode a task parameter of interest. Shades of grey inside each neuron show the …
Figure 3
Demixed PCA applied to recordings from monkey PFC during a somatosensory working memory task (Romo et al., 1999).
(a) Cartoon of the paradigm, adapted from Romo and Salinas (2003). (b) Demixed principal components. Top row: first three condition-independent components; second row: first three stimulus …
Figure 4
Demixed PCA applied to recordings from monkey PFC during a visuospatial working memory task (Qi et al., 2011).
Same format as Figure 3. (a) Cartoon of the paradigm, adapted from Romo and Salinas (2003). (b) Demixed principal components. In each subplot there are ten lines corresponding to ten conditions (see …
Figure 5
Demixed PCA applied to recordings from rat OFC during an olfactory discrimination task (Feierstein et al., 2006).
Same format as Figure 3. (a) Cartoon of the paradigm, adapted from Wang et al. (2013). (b) Each subplot shows one demixed principal component. In each subplot there are four lines corresponding to …
Figure 6
Demixed PCA applied to recordings from rat OFC during an olfactory categorization task (Kepecs et al., 2008).
Same format as Figure 3 (a) Cartoon of the paradigm, adapted from Wang et al. (2013). (b) Each subplot shows one demixed principal component. In each subplot there are ten lines corresponding to ten …
Figure 7
Encoder weights for the leading dPCA components across the neural population.
(a) Distributions of encoder weights for the 15 leading dPCA components across the neural population, in each of the four datasets. Each subplot shows 15 probability density curves, one curve per …
Figure 8
Marginalization procedure.
PSTHs of three exemplary neurons from the somatosensory working memory task decomposed into marginalizations.
Figure 9
Balanced and unbalanced data.
(a) In this toy example there are two task parameters (factors), with two possible values each. Parameter A (left) is represented by the size of the dot, parameter B (middle) is represented by the …
Figure 10
Re-stretching (time warping) procedure.
We defined several alignment events (such as odour poke in, odour poke out, etc.) and for each trial found the times of these events. After aligning all trials on (left) we computed median …
Figure 11
Cross-validation errors depending on the regularization parameter .
Each subplot corresponds to one dataset and shows mean (solid lines) and min/max (boundaries of shaded regions) of the relative cross-validation errors for ten repetitions. Different colors refer to …
Figure 12
Cross-validated time-dependent classification accuracies of linear classifiers (black lines) given by the first three stimulus/decision/interaction dPCs (columns) in each dataset (rows).
Shaded gray regions show distribution of classification accuracies expected by chance as estimated by 100 iterations of shuffling procedure.
Figure 13
Toy example illustrating the pseudo-inverse intuition.
(a) Firing rate trajectories of two neurons for three different stimuli. (b) Same data with dPCA decoding and encoding axes. The encoding axes are approximately equivalent to the axes of the …
Figure 14
Some demixed components as given by three different demixing methods (rows) in various datasets and marginalizations (columns).
Empty subplots mean that the corresponding method did not find any components. All projections were -scored to make them of the same scale. Barplots on the right show fractions of variance in each …
Figure 15
Fourier-like artifacts in PCA.
(Left) In this toy example, single neuron responses are generated from the same underlying Gaussian but are randomly shifted in time. (Right) First three PCA components of the population data. While …
Videos
Video 1
Stimulus representation in the somatosensory working memory task
Two leading stimulus dPCs in the somatosensory working memory task (components #5 and #10 as horizontal and vertical axis correspondingly). Each frame of this movie corresponds to one time point . …
Video 2
Illustration of the dPCA algorithm.
Illustration of the dPCA algorithm using the somatosensory working memory task.
Tables
Table 1
Demixed PCA in comparison with existing methods. Columns: 'Signif.' refers to the method of counting significantly tuned cells, as shown in Figure 1c–e. TDR refers to the 'targeted dimensionality …
| Signif. | TDR | LDA | PCA | FA | GPFA | jPCA | LDS | dPCA | |
|---|---|---|---|---|---|---|---|---|---|
| Takes task parameters into account & provides summary statistics of population tuning | ✓ | ✓ | ✓ | ✓ | |||||
| Allows to reconstruct neural firing (captures variance) | ✓ | ✓ | ✓ | ✓ | ✓ | ||||
| Based on dynamical model | ✓ | ✓ | |||||||
| Based on probabilistic model | ✓ | ✓ | ✓ | ||||||
| Takes spike trains as input | ✓ | ✓ |
