Mathematics in Independent Component Analysis

Chapter 20. Signal Processing 86(3):603-623, 2006 275
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Fig. 4. Mixing matrices recovered for the synthetic s-EMG using different methods;
(a) ICA using joint approximate diagonalization of eigenmatrices (JADE), (b, c)
nonnegative matrix factorization with different preprocessing (NMF, NMF∗), (d, e)
Sparse NMF (sNMF, sNMF∗) with the same two preprocessing methods as NMF,
and (f) sparse component analysis (SCA).
3.1 Artificial signals
In the first example, we compare performance in the well-known setting of
artificially created toy-signals.
3.1.1 Single s-EMG
For visualization, we will first analyze a single artificial s-EMG recording, and
only later present batch-runs over multiple separate realizations to test for
statistical robustness. As data set, we use toy signals as in section 3.1 but
with only three source components for easier visualization. The ICA-result
is produced using JADE after PCA to 3 components. Please note that here
and in the following we perform dimension reduction because in the small
sensor volumes in question not many MUs are present. This is confirmed by
considering the eigenvalue structure of the covariance matrix: taking the mean
over 10 real s-EMG data sets — further discussed in section 3.2 — the ratio
of third to first largest eigenvalue is only 0.11, and the ratio of the fourth to
the first only 0.04. Taking sums, in the mean we loose only 5.7% of raw data
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