- Role
Computational Methods for Data Analysis
(SLN 10207, MWF 8:30-9:20, Lowe 216)- Instruction
Professor J. Nathan Kutz
- kutz (at) amath.washington.edu
- 206-685-3029, Guggenheim Hall 414b
- Office Hours: Tue & Thu 8:30-9:30am and W 3-5pm in Gug 414B (EDGE: 206-685-3029)
- -
- Teaching Assistant: Xing Fu
- xingf (at) u.washington.edu
- Office Hours: Thursday 2:30-4 and Friday 3-5 in Gug 406 , phone: (206) 685-8069
- Lectures and Homework
Video Lectures: EDGE (online) , On Campus Students
- Course Notes: 582notes.pdf
- Discussion Board: Catalyst
- Check grades: GRADES
- Homework Dropbox: DROPBOX
- Homework: HW 1 (Due 1/14), HW 2 (Testdata.mat) (Due 1/21), HW 3 (music1.wav, music2.wav) (Due 2/7), HW 4 (derek1, derek2, derek3, derek4) (Due 2/17), HW 5 (cam1_1.mat, cam1_2.mat, cam1_3.mat, cam1_4.mat), (cam2_1.mat, cam2_2.mat, cam2_3.mat, cam2_4.mat), (cam3_1.mat, cam3_2.mat, cam3_3.mat, cam3_4.mat) (Due 2/25)
- MATLAB: Student Edition (recommended if you do not have access)
- Check grades: GRADES
- Prerequisites
Solid background in ODEs and familiarity with PDEs and MATLAB, or permission.
- Course Description
-
Exploratory and objective data analysis methods applied to the physical, engineering, and biological sciences. Brief review of statistical methods and their computational implementation for studying time series analysis, spectral analysis, filtering methods, principal component analysis, orthogonal mode decomposition, and image processing and compression.
- Objectives
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How to recognize and solve numerically practical problems which may arise in your research. We will solve some serious problems using the full power of MATLAB's built in functions and routines. This class is geared for those who need to get the basics in scientific computing methods for data analysis. Many of today's major research methods for exploring data analysis will be covered: signal processing, frequency filtering, time-frencency analysis, wavelets, principal component analysis, proper orthogonal decomposition, empirical mode decomposition etc. Applications will range from image processing to characterizing atmospheric dynamics.
- Lecture Notes:
582notes.pdf
- Reference Texts:
- Reference Texts:
- 1. D. L. Hartmann,
ATM 552 Objective Analysis.
(freely available)
- 2. L. N. Trefethen, Finite Difference and Spectral Methods. (freely available).
- 3. L. N. Trefethen, Spectral Methods in MATLAB. SIAM.
- 4. L. N. Trefethen and D. Bau, Numerical Linear Algebra. SIAM.
- 5. I. Daubechies, Ten Lectures on Wavelets SIAM (1992).
Syllabus
- (1) Review of Statistics: (1 week)
We will begin with a brief review of statistical methods. The principles of statistics will be largely applied in a computational context for extracting meaningful information from data.
- (a) mean, variance, moments
- (b) probability distributions
- (c) significance testing, hypothesis testing
- (b) probability distributions
- (2)
Spectral and Time-Frequency Analysis: (4 weeks)
We will introduce the ideas of signal processing, filtering, time-frequency representations including wavelet expansions. Our application will be largely to problems in image processing, denoising and noise reduction.
- (a)
digital signal processing
- (b) noise reduction and filtering
- (c) image processing and face recognition
- (d) time-frequency methods and wavelets
- (b) noise reduction and filtering
- (3) Objective Analysis Techniques: (5 weeks)
These methods are practical attempts to reduce the dimensionality of the data as well as infer statistically meaningful trends in what otherwise appears to be noisy data.
- (a) Principal Component Analysis (PCA)
- (b) Proper Orthogonal Decomposition (POD)
- (c) Emperical Mode Decomposition (EMD)
- (d) Singular Value Decomposition (SVD)
- (b) Proper Orthogonal Decomposition (POD)
Grading
Your course grade will be determined entirely from your homework. There will be no exams. Each of the homework sets will be part of your final grade. For the first 6 weeks of the quarter, you will receive weekly homework that you will turn in (hand written or typed up... EDGE students can email directly their electronic file or scanned in solutions.) This is worth 60% of your grade. Additionally, there will be a final report which will be part of a computational notebook generated by the student (worth 40%). This homework should be written as if it were an article/tutorial being prepared for submission. I expect a high level of professionalism on these reports. The following is the expected format for homework submission:- Title/author/abstract Title, author/address lines, and short (100 words or less) abstract. (It is not to be a separate title page!)
- Sec. I. Introduction and Overview
- Sec. II. Theoretical Background
- Sec. III. Algorithm Implementation and Development
- Sec. IV. Computational Results
- Sec. V. Summary and Conclusions
- Appendix A MATLAB functions used and brief implementation explanation
- Appendix B MATLAB codes
- Appendix C (optional) Any algebraically intense calculations (long and drawn out calculations have no business in Sec. II!)
I will grade based upon how completely you solved the homework as well as neatness and little things like: did you label your graphs and include figure captions. I expect the final project to have a brief overview of the chapters along with conluding remarks. Further, the professionalism of the final document will be evaluated.A few things should be kept in mind when generating your reports:
- 1. Use a professional grade word processor (Latex or MSword, for example)
- 2. For equations: Latex already does a nice job, but in Word, use Microsoft Equation Editor 3.0
- 3. Label your graphs. Include brief figure captions. Reference the figure in the text with a more detailed account of the figure.
- 4. Figures should be set flush with the top or bottom of a page.
- 5. Label all equations.
- 6. Provide references where appropriate.
- 7. All coding should be shuffled to Appendix A and B. Reference it when necessary.
- 8. Always remember: this report is being written for YOU! So be clear and concise.
- 9. Spellcheck.
- 2. L. N. Trefethen, Finite Difference and Spectral Methods. (freely available).
