Multiscale Analysis of Random Processes (Cancelled)
2021/2/23-2021/6/16 Every Tuesday, 10:10-12:00(第3、4節), every Wednesday, 09:10-10:00(第2節)
R.440, Astronomy-Mathematics Building, National Taiwan University
Speaker:
Gi-Ren Liu 劉聚仁(National Cheng Kung University)
Organizer:
Gi-Ren Liu 劉聚仁(National Cheng Kung University)
Chun-Hsiung Hsia 夏俊雄(National Taiwan University)
Background
The background of this course is calculus, basic complex analysis, and probability.
After completed course, the students are expected to be able to:
• understand how to quantify the pattern of signals,
• evaluate the impact of deformation on the extracted features, and
• characterize random processes by the scattering transform.
Outline
This course will introduce the wavelet-based scattering transform. In 2012, Stephane Mallat proposed this transformation, which is computed through a cascade of wavelet transforms and modulus nonlinearities. Its structure enables us to retrieve the lost information caused by the pooling operator and provides us with an interpretable feature extraction method. We plan to study its invariance properties, including the translation invariance and the deformation stability. Next, we will introduce some stochastic processes, including the Poisson processes, the fractional Brownian motions, and the stochastic self-similar processes. The scattering transform of these stochastic processes have different statistical properties, which provide us a measurement of the appearance of multiscale activities among random processes. Finally, we will introduce its application in the sleep stage classification. The progress of this course is listed as follows.
The 1st week: Effects of time warping on the Fourier coefficients
The 2nd week: Relationship between the Fourier transform and the wavelet transform The 3rd week: Structure of the scattering transform (ST)
The 4th week: Translation invariance of ST The 5-6th week: Deformation stability of ST The 7th week: Poisson processes
The 8th week: Statistical property of the second-order ST of the Poisson processes The 9th week: Fractional Brownian motions (FBM)
The 10th week: Statistical property of the second-order ST of the FBMs The 11th week: Stochastic self-similar processes (SSP)
The 12th week: Statistical property of the second-order ST of the SSPs
The 13th week: Application of the ST on the feature extraction of physiological signals The 14th week: Dimension reduction methods (Diffusion maps)
The 15th week: Automatic sleep scoring system based on the ST and the diffusion maps The 16th week: Discussion