The adjoint equation associated with a control problem is a nice shortcut to compute the gradient vector for the control variables. When the constraint in the control problem is an unsteady partial differential equation, the adjoint equation is an extremely large linear system. This project uses a random walk and Monte Carlo estimator to approximately solve the linear system quickly.

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Approximate Personal PageRank

Personal PageRank is a vector over all the pages on the web that measures their importance to your interests. Computing personal PageRank in the obvious way, however, requires disclosing your interests to a third-party, the search engine. This paper shows how motivated users can compute personal PageRank on their home PCs.

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ViMoS

ViMoS, visual movie suggestions. ViMoS allows you to visually browse through movies to find undiscovered titles you will love.

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Parallel PageRank

Fast Parallel PageRank, a linear system approach. One way to compute the PageRank value for each page on the web is to formulate the PageRank problem as a linear system. We took this approach and used parallel implementations of various linear solvers to compute the PageRank vector.

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World of Music

Visualization methods for recommender systems. Using semi-definite programming, we computed a low dimensional projection of recommendation data from Launch!. The low dimensional projection is used to place vertices of the artist-artist recommendation graph.

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PCA and ICA with Neural Networks

A review of neural networks for PCA and ICA. This was my final project for an undergraduate course in neural networks. The review includes all the necessary Matlab code to duplicate the results, as well as presentations describing the work.

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