Independent component analysis (ICA) is a recently developed, useful extension of standard principal component analysis (PCA). The ICA model is utilized mainly in blind separation of unknown source signals from their linear mixtures. In this application only the source signals which correspond to the coefficients of the ICA expansion are of interest. In this paper, we propose neural structures related to multilayer feedforward networks for performing complete ICA. The basic ICA network consists of whitening, separation, and basis vector estimation layers. It can be used for both blind source separation and estimation of the basis vectors of ICA. We consider learning algorithms for each layer, and modify our previous nonlinear PCA type algorithms so that their separation capabilities are greatly improved. The proposed class of networks yields good results in test examples with both artificial and real-world data.
Conventionally, mismatch negativity (MMN) is analyzed through the calculation of the difference waves. This helps to eliminate some exogenous event-related potential (ERP) components. However, this reduces the signal-to-noise ratio (SNR). This study aims to test whether or not the optimal digital filtering performs better than the difference waves procedure in quantitative ERP analyses in an uninterrupted sound paradigm. The participants were 102 children aged 8-16 years. The MMN was elicited in a passive oddball paradigm presenting an uninterrupted sound consisting of two alternating tones (600 and 800 Hz) of the same duration (100 msec) with infrequent shortenings of one of the 600 Hz tones (50 or 30 msec). In the grand average, both the 50 and 30 msec tones showed a clear MMN-like activity. Each 100 msec tone elicited some rhythmic activity with relatively consistent ERP waveforms. The difference waves calculated from the offset of the deviant stimuli (time correction due to shortening of the deviant stimuli) failed to separate the MMN from this activity, and produced spurious ERPs at early latencies. The optimal digital filtering freed the MMN from this rhythmic activity, improved the SNR, and thus stabilized the quantitative amplitude and latency analyses of the MMN. The frequency range for optimal extraction of the MMN in this paradigm was 2-8.5 Hz.
Eigenvector-based methods such as multiple signal classification (MUSIC) are currently popular in sinusoidal frequency estimation due to their high resolution. A problem with these methods is the often high cost of estimating the eigenvectors of the autocorrelation matrix spanning the signal (or noise) subspace. In this work, we propose an efficient Fourier transform-based method avoiding eigenvector computation for approximating the signal subspace. The resulting signal subspace estimate can be used directly to define a MUSIC-type frequency estimator or as a very good initial guess in context with adaptive or iterative eigenvector computation schemes. At low signal-to-noise ratios, the approximation yields better results than exact MUSIC. It is also more robust than MUSIC against overestimating the number of sinusoids. Some variations of the basic method are briefly discussed.
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