Information Technology Reference
In-Depth Information
To illustrate the ways in which unsupervised machine learning methods can be
applied to uncover neural correlates of musical perception or emotions induced by
listening to music, a set of case studies is described below.
5.5.1.1 Case Study 1: PCA for Uncovering EEG Dynamics During Music
Appreciation
In work by Lin et al. ( 2009 ), PCA was used to help uncover neural correlates of
emotions during a music listening task. EEG was recorded from 26 participants
who listened to 16 different musical segments, selected to induce particular emo-
tional responses. Power spectral densities (a frequency-domain feature) were then
estimated from 1-s non-overlapping windows over 30 s of EEG recorded during
each of the musical clips. This was done for each of the traditional EEG frequency
bands (delta: 1
3 Hz, theta: 4
7 Hz, alpha: 8
13 Hz, beta: 14
30 Hz, and gamma:
-
-
-
-
31
50 Hz), forming an initial feature set containing 2,400 features per subject
(5 frequency bands
-
nal
feature set was then produced by taking the spectral differences between left and
right hemisphere channel pairs for all channels from the International 10/20 system
(e.g. Fp1-Fp2 etc.). 1 The
×
30 time windows
×
16 musical clips) per channel. The
final feature set is denoted as X where each element
X i ; k
denotes a feature k extracted from the EEG recorded while the participant listened
to a piece of music i .
PCA attempts to identify an orthogonal transformation that translates a set of
potentially correlated variables into a set of linearly uncorrelated variables. These
new variables are referred to as the principal components (PCs) (Smith 2002 ).
PCA operates by
first subtracting the mean from the data to centre it. Thus, in
our case study, Lin and coll ea gues took their original feature set X and derived a
new, zero-mean, feature set X by subtracting the mean from X.
The covariance matrix of the featur e set
X
is then used to measure the strength of
the relationships between all rows of
X
. This is de
ned as the matrix
C
where each
element
C i ; j denotes the covarian ce between rows
i
and
j
(corresponding to musical
pieces
i
and
j
) in the feature set
X
.
P k ¼ 1 ð X i ; k X i ;: Þð X j ; k X j ;: Þ
ð n 1 Þ
C i ; j ¼
ð 5 : 1 Þ
w here
X j ; k denote the k th features from different musical pieces i and j , and
X i ;: denotes the mean over a feature vector for an individual piece of music i .
Eigen decomposition is then applied to analyse the structure of this covariance
matrix. The covariance matrix is decomposed into a matrix of eigenvectors and a
vector of eigenvalues. This may be de
X i ; k and
ned as
Cu ¼ k u ;
ð 5 : 2 Þ
1
Please refer to Chap. 2 for an introduction to EEG electrode placement systems.
 
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