Information Technology Reference
In-Depth Information
where
u
denotes an eigenvector of the covariance matrix
C
and
denotes the
λ
corresponding eigenvalue.
The eigenvalues identi
ed for
C
may be ranked in increasing value with the
corresponding eigenvectors containing projections of the feature set onto principal
components, which are placed in the order of decreasing variance. Thus, the
eigenvector corresponding to the largest eigenvalue contains a projection of the
feature set
X
which has the greatest variance over the selection of musical pieces
played. This eigenvector may then be used to classify musical pieces with high
accuracy with respect to their emotional valence while using a subset of the data.
Lin et al. (
2009
) select a set of the
first few eigenvectors calculated from the
EEG such that they contain more than 80 % of the variance of the feature set. These
eigenvectors are then used as features in a classi
cation stage, which is reported to
produce classi
cation accuracies of up to 85 %.
A similar approach can also be seen in (Ogawa et al.
2005
) in which PCA and
canonical discriminant analysis (CDA) are each used to identify features that may
be extracted from the EEG. These methods are applied to EEG to attempt to
identify metrics for the identi
cation of pieces of music for use in music therapy.
5.5.1.2 Case Study 2: ICA to Identify Neural Correlates of Music
ICA is used by Cong et al. (
2013
) to identify feature sets which are able to identify
neural correlates of perception of long pieces of naturalistic music. EEG was
recorded from 14 participants, while they listened to an 8.5-min-long piece of music
(modern tango by Astor Piazzolla), via 64 electrodes.
ICA is based upon the assumption that the recorded neurological data are
derived from recording a mixture of statistically independent sources. This may be
explained by an analogy of a cocktail party. In a party, you may be able to hear
several people talking at the same time. Speci
cally, although the sounds produced
by each speaker may be independent of one another, the sound you hear contains a
linear mixture of each of the speakers. Thus, in order to attend to what one speci
c
speaker is saying, you must attempt to separate this linear mixture of sounds into
their original sources.
ICA attempts to solve this problem by identifying a linear transformation from
the recorded multichannel EEG data
x
to a set of independent neural sources
s
.It
does so by imposing the assumption that the neural sources are statistically inde-
pendent of one another and identifying a transformation matrix which, when
applied to the EEG, results in maximally independent estimated sources. This may
be de
ned as
s
¼
A
1
x
;
ð
5
:
3
Þ
where
A
−
1
denotes the transformation matrix, to translate the EEG into the esti-
mated sources s and may be inverted to reconstruct the recorded EEG from the
estimated sources,
