My 10 slides of a short seminar talk on
Approximate SDP solvers, Matrix Factorizations, the Netflix Prize, and PageRank
Abstract:
We will present a new simple approximation algorithm of Hazan [Hazan LATIN '08] to solve arbitrary semidefinite programs (SDPs).
Furthermore, we will discuss matrix factorization techniques in machine learning. The task here is that given just a few of the entries of a large real matrix, we try to predict the unknown entries by building a simple factor model of the matrix. Here 'simple' either means low rank or low norm. Such matrix factorization techniques are at the core of current recommender systems as in the recently ended Netflix Prize competition [Short IEEE article, Wikipedia: Netflix Prize].
In the last part we will apply Hazan's approximate SDP solver to solve matrix factorization problems, and observe that its performance is comparable to the best existing algorithms. The performance is limited by how fast we can find the principal eigenvector of the adjacency matrix of a weighted bipartite graph.
