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Applications of Linear Algebra Part 2

Explore applications of linear algebra in the field of data mining by learning fundamentals of search engines, clustering movies into genres and of computer graphics by posterizing an image.
This course is archived
Estimated 4 weeks
12–18 hours per week
Instructor-paced
Instructor-led on a course schedule
Free
Optional upgrade available

About this course

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Our world is in a data deluge with ever increasing sizes of datasets. Linear algebra is a tool to manage and analyze such data.

This course is part 2 of a 2-part course, with this part extending smoothly from the first. Note, however, that part 1, is not a prerequisite for part 2. In this part of the course, we'll develop the linear algebra more fully than part 1. This class has a focus on data mining with some applications of computer graphics. We'll discuss, in further depth than part 1, sports ranking and ways to rate teams from thousands of games. We’ll apply the methods to March Madness. We'll also learn methods behind web search, utilized by such companies as Google. We'll also learn to cluster data to find similar groups and also how to compress images to lower the amount of storage used to store them. The tools that we learn can be applied to applications of your interest. For instance, clustering data to find similar movies can be applied to find similar songs or friends. So, come to this course ready to investigate your own ideas.

Courses offered via edX.org are not eligible for academic credit from Davidson College. A passing score in a DavidsonX course(s) will only be eligible for a verified certificate generated by edX.org.

At a glance

  • Language: English
  • Video Transcript: English

What you'll learn

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  • How to solve least-square systems, about eigenvectors of matrix, how to Markov Chains, and the matrix decomposition called the singular value decomposition.
  • To apply the least-squares method to finding a presidential look-alike
  • To use an eigenvector to cluster a dataset into groups or downsample an image
  • To use Markov Chains to analyze a board game
  • How Markov Chains were proposed by Google as part of their search engine process
  • Applications of the singular value decomposition in image compression and data mining.
  • Explore applications with Matlab codes provided with the course.  

About the instructors

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