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We consider asymptotic behavior of partial sums and sample covariances for linear processes whose innovations are dependent. Central limit theorems and invariance principles are established under fairly mild conditions. Our results go beyond earlier ones by allowing a quite wide class of innovations which includes many important nonlinear time series(More)
Recently, several manifold learning algorithms have been proposed, such as ISOMAP (Tenenbaum et al., 2000), Locally Linear Embedding (Roweis & Saul, 2000), Laplacian Eigenmap (Belkin & Niyogi, 2001), Locality Preserving Projection (LPP) (He & Niyogi, 2003), etc. All of them aim at discovering the meaningful low dimensional structure of the data space.(More)
D id you know your brain continuously emits electric waves, even while you sleep? Based on a sample of wave measurements, physicians specializing in sleep medicine can use statistical tools to classify your sleep pattern as normal or problematic. Brain-computer interfaces (BCIs) now being developed can classify a disabled person' s thinking based on wave(More)
Sleep staging is the pattern recognition task of classifying sleep recordings into sleep stages. This task is one of the most important steps in sleep analysis. It is crucial for the diagnosis and treatment of various sleep disorders, and also relates closely to brain-machine interfaces. We report an automatic, online sleep stager using electroencephalogram(More)
The P300 brain-computer interface (BCI) using electroencephalogram (EEG) signals can allow amyotrophic lateral sclerosis (ALS) patients to instruct computers to perform tasks. To strengthen the P300 response and increase classification accuracy, we proposed an experimental design where characters are intensified according to orthogonal Latin square pairs.(More)
Canonical correlation analysis has been widely used in the literature to identify the underlying structure of a multivariate linear time series. Most of the studies assume that the innovations to the multivariate system are Gaussian. On the other hand, there are many applications in which the normality assumption is either questionable or clearly(More)