Time Frequency analysis �and Dimension reduction �on Sleep data�

2021 URP Group 6 midterm report

學員：蘇彥維（陽明交大應數系）

指導教授：劉聚仁教授（成大數學系）

郝嘉誠（陽明交大電機系）

曾以諾（成大數學系）

邱能泰（陽明交大醫學系）

2021 URP program

指導教授：劉聚仁教授（成大數學系）

其他參與人員：許元春教授（陽明交大應數系）、黃于真醫師（長庚胸腔科）、Hau-Tieng Wu(Duke University) 、江旻修(成大數學所)、周彥洵(成大數學所)

進行方式：

1. 線上教學：每週四晚上7- 9點
2. 實體教學：三次

上課內容

1. Time Frequency analysis: Short-Time Fourier Transform, Wavelet Transform, Scattering Transform.
2. Dimension Reduction Technique: Diffusion Maps
3. Supplements: Singular Value Decomposition, PCA, CCA, Optimal Shrinkage.
4. Hands-on lesson: Medical Data Processing .

助教：徐志維（陽明交大應數所）、陳柏穎（清華數學所）

1. An Overview
2. Feature extraction

Scattering transform

• Dimension reduction technique
1. Prerequisite: Singular Value Decomposition
2. Diffusion Maps
• Medical Applications
• Future Works
• References

Contents

An Overview

When we sleep, our body restores muscles, conserves energy, and releases hormones, and the brain stores new information and removes toxic substances. Insufficient sleep is related to the reduction of physical performance and consequences of cognitive dysfunction.

https://newsroom.ucla.edu/releases/ucla-scientists-discover-why-we-need-sleep

An Overview

Correct cognition of sleeping is helpful for diagnosis of varies disease(Sleep apnea(睡眠呼吸終止症), Narcolepsy(猝睡症), etc.). With the aid of modern physical monitors, scientist defined ” Sleep Stages ” by visually inspecting the recorded medical signals.

The work we do is to develop a supervised-learning algorithm to separate the sleep stages.

It is the first step to move on to the clinical sleep stage diagnosis.

Sleep Stages

Awake

Sleep

Awake

REM

NREM

Awake

REM

S1

S2

S3

S4

Awake

REM

N1

N2

N3

R&K

AASM

R&K : Rechtschaffen and Kales

AASM : American Academy of Sleep Medicine

Polysomnography, PSG (多項睡眠生理檢查)

Overview of methodology

EEG(Brain Wave)

Wavelet transform and its extension�(Scattering transform)

Short Time Fourier Transform based Syncrosqueeze transform

Diffusion Maps, PCA, CCA

Support Vector Machine �Classifier

Evaluation

EEG(Brain Wave)

Wavelet transform and its extension�(Scattering transform)

Short Time Fourier Transform based Syncrosqueeze transform

Diffusion Maps, PCA, CCA

Support Vector Machine �Classifier

Evaluation

PPG(脈搏)

EOG(眼波)

Flow(呼吸)

Our current Progress

Feature Extraction

Dimension Reduction

Direction 1

Direction 2

Feature extraction

Feature extraction on Frequency domain

Short Time Fourier Transform – Unstable to time warping

Time averaging removes fine-scale information; However, it lose too much information.

Scattering transform – layer structure

We define the zeroth-order coefficients of the scattering transform by

The first-order coefficients of the scattering transform is defined by:

The second-order coefficients of the scattering transform is defined by:

The m-th order coefficients of the scattering transform is defined by:

Scattering transform – layer structure

Prerequisites :

Singular Value Decomposition

Notation

列

行

Singular Value Decomposition

Singular Value Decomposition

figure source: stackexchange

Geometric perspective: Best fit projection

Eckart–Young–Mirsky Theorem

Eckart–Young–Mirsky Theorem

QED

Eckart–Young–Mirsky Theorem

(Triangular inequality)

(EYM for induced 2 norm)

QED

Eckart–Young–Mirsky Theorem : Proof

QED

Application

• Dimension reduction
• Image compression
• Eigenface

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3456x5184 double

Dimension Reduction Method:

Diffusion Maps

Problems

A Graph Based Model

A Graph Based Model

A Graph Based Model

Diffusion Distance

Diffusion Distance

Diffusion Distance

Diffusion Distance

Medical applications

TIDIS

The database we applied is authorized by Taiwan Integrate Database for Intelligent Sleep (TIDIS).

TIDIS collect and organize the database from six cooperated sleep centers. We are allowed to obtain and use the database from certain four.

Summarize the database

Here, we summary of the information of the patients in our work. The sampling rate column indicates the rate of each channel used by the sleep center. Notice that there are two sampling rates for center B-2 since the machine takes two different settings. Therefore, it is necessary to resample those subjects into 200 sampling rate.

Process

DM for dimension reduction

Epoch

Awake

REM

N1

N2

N3

30-second epochs are the basic time periods on which data analysis and interpretation is performed.

Each 30-second epoch was annotated as one of the sleep stages.

DM of scattering coefficients of EEG signal

Future works

Improve the algorithm

1. Try various dimension reduction techniques.
2. Implement on the medical institutions and collect the feedback from experts.
3. Define the prediction quality index.

​

Portable device

1. Increase the calculated speed of the algorithm.

​

Reference

1. Bandeira, A. S., Singer, A. &, Strohmer, T. Mathematics of Data Science , Book in Preparation.
2. Panchenko, D. Introduction to Probability Theory, 2019
3. Blum, A., Hopcroft, J., & Kannan, R. Foundations of Data Science. Cambridge University Press, 2020.
4. Stephane, Mallat. A Wavelet Tour of Signal Processing: The Sparse Way, Third edition, Academic Press, 2009
5. Afonso S. Bandeira , Nikita Zhivotovskiy, Lecture Notes for Mathematics of Machine Learning. ETH Zurich, 2021.
6. Berry RB, Brooks R, Gamaldo CE, Harding SM, Lloyd RM, Marcus CL and Vaughn BV for the American Academy of Sleep Medicine. The AASM Manual for the Scoring of Sleep and Associated Events: Rules, Terminology and Technical Specifications, Version 2.6
7. Douglas Kirsch, MD(2021) Stages and architecture of normal sleep. Susan M Harding, MD(Ed.), UpToDate

Thank you for your listening

Preprocessing on EEG, EOG feature extraction (我覺得這頁被問到再講?)

EEG signal

Channels and process flow in the algorithm

We use five channels in the algorithm. They are C3O2, O2A1, left EOG, right EOG, and chin-EMG. The following figure is the process flow of frequency features extraction.