What do Network flows, Markov chains, discrete-time state-space models of autonomous (undriven) systems, and the PageRank™ Algorithm have in common? The answer is the mathematics that leads, in part, to what some have called Google's ''$25,000,000,000 Eigenvector''—an array of "importance scores" that Google computes and uses to present Web pages in response to each query.
In this presentation, we (i.e., you and I) will set up the basic form of Google's PageRank™ problem as a linear matrix-vector equation. We'll discuss aspects of the equation, and then add bells and whistles to the basic setup so we can explore further the richness of its underlying mathematics and the reach of its applications. You can then decide for yourself whether you agree with authors who have hinted that the centerpiece equation that leads to Google's importance-score vector might deserve a spot in a book of the most beautiful equations ever discovered.
We use PageRank™ in EECS 16A—the first in a two-course sequence in our new freshman-level introduction to EECS at UC Berkeley—to motivate the study of eigenvalues and eigenvectors. Even a casual prior exposure to the notions of linear independence, rank, and null space of a square matrix should make this talk accessible.
Babak Ayazifar joined the EECS faculty at UC Berkeley in 2005, where he is now a Teaching Professor. He earned his B.S. in EE from Caltech, and his S.M. and Ph.D. in EECS from MIT. At MIT, Babak received the Harold L. Hazen Award for outstanding teaching (1995). He advanced to the rank of Instructor-G, which conferred teaching assignments ordinarily reserved for faculty (1996). He won the Goodwin Medal—MIT's most prestigious award for a graduate student who "has performed above and beyond the norm, and whose teaching efforts can truly be characterized as 'conspicuously effective'" (1999). In spring 2002, he took leave from his graduate studies to take an appointment as a Senior Lecturer at MIT's School of Engineering, to teach a graduate course in Digital Signal Processing. From spring 2013 to spring 2014 Babak was a visiting Sr. Lecturer at MIT, while on sabbatical leave from UC Berkeley.
At Berkeley Babak has focused on teaching, student learning, curriculum development and reform, mentoring graduate and undergraduate teaching assistants, and sharing the results of his pedagogical activities at workshops and international conferences. In 2008 Babak received the UC Berkeley Electrical Engineering Division's Outstanding Teaching Award. And in 2012, he received the IEEE Education Society's Mac Van Valkenburg Early Career Teaching Award. His citation reads "For creative, lively, challenging, and caring teaching that has sparked broad excitement and engagement among his students, even in the largest core courses."
Babak's research interests are in Spectral Graph Theory and the emerging field of Graph Signal Processing.