Information Technology Reference
In-Depth Information
800
first principal component
second principal component
600
400
200
0
-200
-400
-600
-800
0
0.05
0.1
0.15
0.2
0.25
time (s)
Fig. 1.4: First two principal component functions (i.e., eigenfunctions) in the space
of intensity functions. They are computed by substituting the coefficients of the first
two eigenvectors of the Gram matrix in Equation (1.42).
30
25
20
20
15
10
10
5
0
0
-10
−5
−10
-20
−15
-30
−20
-80
-60
-40
-20
0
20
40
60
80
−80
−60
−40
−20
0
20
40
60
80
PC1
PC1
(a) Projection of the spike trains
in the training set.
(b) Projection of the spike trains
in the testing set.
Fig. 1.5: Projection of spike trains onto the first two principal components. The
different point marks differentiate between spike trains corresponding to each one
of the classes.
is the main responsible for the dispersion between classes of the projected spike
trains. This happens because the direction of maximum variance is the one that
passes through both clusters of points in the RKHS due to the small dispersion
within class. The second principal component seems to be responsible for disper-
sion due to the jitter noise introduced in the spike trains and suggests that other
principal components play a similar role.
