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G. D. Johnson and D. J. Krusienski
as the FFT provides an efficient computation of the Fourier Transform for digital
signals, the discrete wavelet transform (DWT) provides an efficient computation of
the wavelet transform using specific scale and shift factors that minimize redundancy
in the time-frequency representation.
For a given spectral analysis approach, the resulting spectral amplitudes are typically evaluated in the and/or frequency bands. These frequency bins are commonly
used to train a classification or regression model, such as Fischer’s Linear Discriminant or Support Vector Machine [18]. A classification model is more appropriate for providing discrete selections, while a regression model is more appropriate
for achieving continuous, graded control [31]. Another consideration is whether to
implement linear or non-linear models. In general, it has been found that linear models can have several advantages over non-linear models for BCI applications [25].
Linear models are less prone to over-fitting with limited training data, and can offer
added simplicity for computation, user training, and data interpretation.
Labeled events from a calibration session can be used to a train classification/regression model. The resulting classification will be performed on every sliding window, producing a continuous output if the update rate is sufficiently short. A
block diagram of the preprocessing and feature extraction for sensorimotor rhythms
is shown in Fig. 9.2. A similar approach can also be used to detect transient imagery
events [21].
9.2.2 Common Spatial Patterns
A widely-used alternative to the traditional spectrum analysis approaches described
in the previous section is the method of common spatial patterns (CSP) [26, 30]. CSP
generates spatial filters that simultaneously minimize the variance for one class and
maximize the variance for the other class, thus resulting in a simple classification
based on the projected signal variances. An illustration of the CSP feature space for
a 2-class scenario with 2 features is shown in Fig. 9.7. First, the signals are bandpass
filtered in the range of interest. The CSP decomposition of a feature matrix is given
as:
Y W X,
(9.5)
where X is an N feature × T observance matrix, W is an L × N matrix (L ≤ N) whose
L rows represent the individual components of the decomposition, and Y is an L × T
matrix subspace of X . For a two-class classification problem, W can be determined
to decompose the feature matrix such that the resulting projections corresponding
to the extreme eigenvalues of the transformed covariance matrices have maximal
variance for one class and minimal variance for the other class. First, for the two
classes (1 and 2), the class-labeled observations are sorted by the respective class
and the class-specific covariance matrices are determined:
G. D. Johnson and D. J. Krusienski
as the FFT provides an efficient computation of the Fourier Transform for digital
signals, the discrete wavelet transform (DWT) provides an efficient computation of
the wavelet transform using specific scale and shift factors that minimize redundancy
in the time-frequency representation.
For a given spectral analysis approach, the resulting spectral amplitudes are typically evaluated in the and/or frequency bands. These frequency bins are commonly
used to train a classification or regression model, such as Fischer’s Linear Discriminant or Support Vector Machine [18]. A classification model is more appropriate for providing discrete selections, while a regression model is more appropriate
for achieving continuous, graded control [31]. Another consideration is whether to
implement linear or non-linear models. In general, it has been found that linear models can have several advantages over non-linear models for BCI applications [25].
Linear models are less prone to over-fitting with limited training data, and can offer
added simplicity for computation, user training, and data interpretation.
Labeled events from a calibration session can be used to a train classification/regression model. The resulting classification will be performed on every sliding window, producing a continuous output if the update rate is sufficiently short. A
block diagram of the preprocessing and feature extraction for sensorimotor rhythms
is shown in Fig. 9.2. A similar approach can also be used to detect transient imagery
events [21].
9.2.2 Common Spatial Patterns
A widely-used alternative to the traditional spectrum analysis approaches described
in the previous section is the method of common spatial patterns (CSP) [26, 30]. CSP
generates spatial filters that simultaneously minimize the variance for one class and
maximize the variance for the other class, thus resulting in a simple classification
based on the projected signal variances. An illustration of the CSP feature space for
a 2-class scenario with 2 features is shown in Fig. 9.7. First, the signals are bandpass
filtered in the range of interest. The CSP decomposition of a feature matrix is given
as:
Y W X,
(9.5)
where X is an N feature × T observance matrix, W is an L × N matrix (L ≤ N) whose
L rows represent the individual components of the decomposition, and Y is an L × T
matrix subspace of X . For a two-class classification problem, W can be determined
to decompose the feature matrix such that the resulting projections corresponding
to the extreme eigenvalues of the transformed covariance matrices have maximal
variance for one class and minimal variance for the other class. First, for the two
classes (1 and 2), the class-labeled observations are sorted by the respective class
and the class-specific covariance matrices are determined: