Biomedical Engineering Reference
In-Depth Information
properties across our ensemble by performing PCA on the peri-
stimulus peristimulus time histograms of our recorded neurons
in dmPFC and motor cortex. Common forms of variance might
correspond to functional groups of neurons within our ensemble.
Finally, the 'scores' of each principal component on particular
neurons can be computed by matrix multiplying the components
by the original data. By restricting components based on variance,
dramatic dimension reduction can occur; for instance, in random
data, where one component explains
90% of variance, one can
go from the original data of 490 values (10 bins X 49 simulated
neurons) to 49 values (1 component X 49 neurons), a 90% reduc-
tion. The speed and performance of classification and clustering
algorithms are improved by such dimension reduction.
We performed principal component analysis on neural data
from prefrontal and motor cortices during delayed-response
performance. When plotting the variance from each component,
we noted that only 3-4 components were large, or greater than a
straight line drawn from the smaller components (
Fig. 7.3A
).
The components isolated represented behavioral modula-
tions. For instance, component 1 (inverted for clarity) had a large
modulation related to responding, component 2 was related to
holding the lever down, component 3 was modulated during
pressing and releasing the lever, and component 4 was modulated
in anticipation of the stimulus (
Fig. 7.3B
). The sign of a given
PC carries information about the relative increases or decreases
of firing rates by specific subsets of neurons. However, here we
were not interested in this point. Instead, we focused on the issue
of whether neurons had similar patterns of activity (i.e., similar
changes in firing rates around the behavioral events). Therefore,
in this example, we discarded the sign of the components.
To determine if there are functional classes within our data
set, we examined the projection of PCA scores onto the neurons
we recorded. For instance, neuron 1 in motor cortex has a large
score for PC4 only (
Fig. 7.3C
) and therefore is likely involved in
motor anticipation. To determine which scores were statistically
significant, components were extracted from time-shuffled data. A
principal component score of
>
0. 05.
Therefore, we interpret scores above this value as significant. We
found that 11 neurons had significant projections of component
1 (6 in motor cortex, 5 in dmPFC), 8 neurons had significant
projections of component 2 (3 in motor cortex, 5 in dmPFC)
and 2 neurons had significant projections of component 3 and 4
(
Fig. 7.3C
).
PCA is a user-friendly and data-driven tool for exploration
of multivariate data. However, there are several potential pitfalls
regarding its use. First, the data set must be clean of artifacts
(e.g., solenoids) and inconsistent spike sorting across channels can
limit the interpretation of PCA. Second, the amount of variance
|
9. 8
|
corresponded to a p
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