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Welcome to Computational Methods for Data Analysis

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.

Dr. J. Nathan Kutz

About the Course

In this course you will learn 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.

Prerequisites

Solid background in ODEs and familiarity with PDEs and MATLAB.

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.

About the Instructor

J. Nathan Kutz specializes in a unified approach to applied mathematics including modeling, computation and analysis. His current focus is phenomena in dimensionality reduction and data-analysis techniques for complex systems. This includes work in laser dynamics and modelocking in fiber lasers, neuro-sensory systems and theoretical neuroscience, and gesture recognition algorithms for portable electronic devices. Kutz has authored numerous scientific articles on these subjects as well as segments of books devoted to his area of expertise.

Textbook and Notes

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- These notes are intended as the primary source of information for this Coursera course. The notes may contain errors. Any other use aside from classroom purposes and personal research is prohibited and copyrighted.

Course Outline:

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.
   • mean, variance, moments
   • probability distributions
   • significance testing, hypothesis testing
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.
   • digital signal processing
   • noise reduction and filtering
   • image processing and face recognition
   • time-frequency methods and wavelets
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.
   • Principal Component Analysis (PCA)
   • Proper Orthogonal Decomposition (POD)
   • Emperical Mode Decomposition (EMD)
   • Singular Value Decomposition (SVD)
     

Weekly Lecture Quiz attempts

• You have TWO attempts ONLY to complete the quizzes assigned.
• Quizes are timed.
• Once opened, You have 3 hours to complete them before they close; Give yourself enough time to complete the quiz.
• Quiz names are reflective of their association with each lecture.
• Before attempting, be sure that you have viewed the lectures and read the notes so that you are fully prepared to answer the questions.

Video Downloads of Lectures
The University of Washington is committed to working with some of the world's leading instructors to provide high quality, free education, globally.

We have removed the ability to download course video from Coursera for a number of reasons:

1. Our video contains functionality which only works within the Coursera environment.  Downloading it to another platform, such as YouTube, prevents this from working as designed.
   
2. Our ability to bring you a free course means that we must protect its content so that it is viewed as intended, as a component of an instructionally coherent educational program in Coursera.

We apologize if this is an inconvenience for some students who would prefer more flexibility for viewing this free content.

We hope that you understand our need to maintain a quality standard and continue to enjoy the course