On March 23rd, Computational Methods for Data Analysis will be closing for this session.

All quizzes and homework assignments need to be completed and finalized by March 23rd at 11:59pm PST. Currently enrolled students can continue to access the course via a “Course Archive” button on the Coursera landing page for the course.

We look forward to continuing to provide you additional courses from the University of Washington and Dr. Nathan Kutz in the future.

Thanks you for your participation in this course.

The University of Washington

Mon 16 Mar 2015 8:02 AM CET

This is the final week of the course! Dimensionality reduction for Partial Differential Equations (PDEs) is the focus of this final week. PDEs arise in modeling of physical, engineering, or biological systems that demonstrate dynamics/patterns in space and time. Applying the techniques of Proper Orthogonal Decomposition (POD) can play a critical role to predict low-dimensional dynamics of systems. Lecture 26 demonstrates the Fourier modal expansion technique to solve the classic Non-Linear Schrodinger (NLS) PDE. In Lecture 27 the POD reduction technique is applied to solve the NLS, the lower-dimensional dynamics are shown to be modeled quite well using the POD. Lecture 28 illustrates the construction of a global normal form of PDEs using the POD method. After viewing Lectures 26, 27 and 28 you will have the background needed to take Quizzes 26, 27 and 28 respectively.

Mon 9 Mar 2015 8:02 AM CET

Week 9 will explore techniques for signal and image reconstruction. Lecture 23 introduces the basics of compressed sensing: the critical idea is to take advantage of sparsity of signals/images to perform their reconstruction. In Lecture 24 we will sample an audio signal using spare sampling and reconstruct the signal using compressive sensing algorithms based on the concepts introduced in the previous lecture. Lecture 25 will apply the ideas of compressed sensing to image reconstruction from sparse sampling. After viewing Lectures 23, 24 and 25 you will have the background needed to take Quizzes 23, 24 and 25 respectively.

- The Course Staff

Mon 2 Mar 2015 9:02 AM CET

Image recognition and classification are the focus of Week 8. Lecture 20 starts with highlighting the robustness of human perception and image recognition capabilities. Through the examples presented, the concept of "edge detection" is shown to be critical in the image recognition problem. As an example problem we will look at classifying images of dogs and cats. Building on the edge detection concept, in Lecture 21 an algorithm to discriminate between Cat and Dog images is formulated. Linear Discrimination Analysis (LDA) is introduced as a method for statistical discrimination between distinct data sets. In Lecture 22 all the algorithm details are implemented in MATLAB, and the results are discussed. After viewing Lectures 20, 21 and 22 you will have the background needed to take Quizzes 20, 21 and 22 respectively.

Please find the dogData.mat and catData.mat files linked below
Download: dogData.mat 

Download: catData.mat 

Thank you and we hope that you are enjoying this course.

- The Course Staff

Mon 23 Feb 2015 9:02 AM CET

Week 7 starts with a study of Independent Component Analysis (ICA), a mathematical tool used for extracting and separating mixed data sets or signals. In Lecture 17 the mathematical framework for ICA is formally defined. In Lecture 18 we will look at the mathematical details of separating two images as an example application of ICA. Lecture 19 will carry this forward to an implementation of the image separation algorithm in MATLAB. After viewing Lectures 17, 18 and 19 you will have the background needed to take Quizzes 17, 18 and 19 respectively.

- The Course Staff

Mon 16 Feb 2015 9:02 AM CET

In Week 6 we continue with the study of Principal Component Analysis (PCA), or the Proper Orthogonal mode Decomposition (POD) in the context of the model spring-mass system experiment. In Lecture 15 we will continue working with the Covariance Matrix, and tie together the concepts of diagonalization of covariance matrix, its eigen vectors and its SVD. We will also compute the Principal Components of the covariance matrix and relate it to the dynamics of the spring-mass experiment. Lecture 16 lays down the formal concepts of Proper orthogonal modes of a function and its relation to the SVD. After viewing Lectures 15 and 16 you will have the background needed to take Quizzes 15 and 16 respectively.

- The Course Staff

Mon 9 Feb 2015 9:02 AM CET

Singular Value Decomposition or SVD is the focus of Week 5. Lecture 12 presents an introduction to the SVD of a matrix. In Lecture 13 we will explore the relevant mathematical properties of SVD, and compare it to the Eigen Value decomposition. This lays the framework for one of the key applications of SVD - Principal Component Analysis (PCA), or the Proper Orthogonal mode Decomposition (POD). In Lecture 15 a simple spring-mass system experiment is formulated to illustrate the key concepts of the PCA/POD. Data collection and ordering is addressed in the context of the model experiment, and the covariance matrix is defined. After viewing Lectures 12, 13 and 14 you will have the background needed to take Quizzes 12, 13 and 14 respectively.

- The Course Staff

Mon 2 Feb 2015 9:02 AM CET

In Week 4 we start working with image processing and apply the concepts of frequency analysis and filtering to data from images. Lecture 9 surveys various applications of image processing and examines the properties of typical image data. In-built MATLAB functions used to read, examine and manipulate image data are introduced. In Lecture 10 we work on building filters to extract relevant information from noisy images. Lecture 11 introduces diffusive filtering and it's advantages in localized filtering of images. You will have the background needed to take Quizzes 9, 10 and 11 after viewing Lectures 9, 10 and 11 respectively.

- The Course Staff

Mon 26 Jan 2015 9:02 AM CET

MATLAB is the primary programming language used in this course. In Week 3 focusses on developing time-frequency analysis codes via in-class programming exercises. Work along with Dr. Kutz to develop code to compute spectrograms and Gabor transforms of data in Lecture 7. Lecture 8 explores the in-built MATLAB toolbox for time-frequency analysis, and reviews the Wavelet toolbox functionality. You will have the background needed to take Quizzes 7 and 8 after viewing Lectures 7 and 8 respectively.

- The Course Staff

Mon 19 Jan 2015 9:02 AM CET

Week 2 builds on the time-frequency analysis concepts introduced in Week 1. Windowed Fourier transforms and Gabor transforms are introduced in Lecture 4. In Lecture 5 we will be introduced to wavelet transforms of data and briefly survey some example wavelets used. Lecture 6 continues the study of wavelet transforms by examining it's properties, and it's application in resolving multiple scales in data or "Multi-resolution analysis". You will have the background needed to take Quizzes 4, 5 and 6 after viewing Lectures 4, 5 and 6 respectively.

- The Course Staff

Mon 12 Jan 2015 9:02 AM CET

Objective data analysis starts with a study of time-frequency analysis. Fourier transforms and wavelet transforms are the most powerful tools used in time-frequency analysis. Lecture 1 introduces Fourier transform, it's properties, and an efficient algorithm to compute it. Lecture 2 draws examples of noisy data from RADAR and SONAR, we will explore and construct typical RADAR signals. Lectures 2 and 3 explore in detail "Filtering" and "Averaging" as de-noising tools to extract meaningful frequency signatures from RADAR data. Example codes will be developed in-class with MATLAB. You will have the background needed to take Quizzes 1, 2 and 3 after viewing Lectures 1, 2 and 3 respectively.

- The course staff

Mon 5 Jan 2015 9:10 AM CET

Thank you for joining the Computational Methods for Data Analysis course! Please take a few moments to read through the course welcome page followed by watching the introductory and week one lecture videos. There is a lot of useful information there about the course.

For now, you should plan to allocate between five and 10 hours per week on the course. There will be roughly two hours of lectures per week, as well as weekly quizzes (graded automatically) for each lecture.

In this course you will learn how to recognize and solve numerically practical problems which may arise in your research. Given the computational nature of the course, access to MATLAB (www.mathworks.com) or Octave (www.gnu.org/software/octave) is essential. MATLAB provides student editions for $99 that can be downloaded via the web. Octave is a free (or by donation) alternative to MATLAB that can also be downloaded and installed via the web. Either software should suffice for all the needs of the course, but MATLAB is the strongly recommended alternative.

MathWorks is also pleased to provide a special license to you as a course participant to use for your Coursera course. This is a limited license for the duration of your course plus 30 days and is intended to be used only for course work and not for commercial purposes.

Below is the MATLAB download link for the "Computational Methods for Data Analysis" course software:
https://www.mathworks.com/licensecenter/classroom/compmethods

To complement the course, a set of notes detailing each individual lecture is included. The notes should be read through thoroughly and routinely as all the course content is contained therein. It is imperative that the student engage in a focused effort to learn the notes as the lectures are simply a supplement to the notes, not the other way around. You are also encouraged to interact with each other within the discussion forums in order to arrive at the various solution sets. Course Lecture Packet:
Download: Course Lecture Notes Packet 

Again, welcome, and I hope that you enjoy this course!

Dr. Nathan Kutz

Mon 5 Jan 2015 9:02 AM CET