Nonnegative Matrix Factorization

Introduction.

In this post, I derive the nonnegative matrix factorization (NMF) algorithm as proposed by Lee and Seung (1999). I derive the multiplicative updates from a gradient descent point of view by using the treatment of Lee and Seung in their later NIPS paper Algorithms for Nonnegative Matrix Factorization. The code for this blogpost can be accessed from here.

Stochastic gradient descent

In this post, I introduce the widely used stochastic optimization technique, namely the stochastic gradient descent. I also implement the algorithm for the linear-regression problem and provide the Matlab code.

Gaussianity, Least squares, Pseudoinverse

Introduction.

In this post, we show the relationship between Gaussian observation model, Least-squares and pseudoinverse. We start with a Gaussian observation model and then move to the least-squares estimation. Then we show that the solution of the least-squares corresponds to the pseudoinverse operation.