In non-negative matrix factorization, it is difficult to find the optimal non-negative factor matrix in each iterative update. However, with the help of transformation matrix, it is able to derive the optimal non-negative factor matrix for the transformed cost function. Transformation matrix based nonnegative matrix factorization method is proposed and analyzed. It shows that this new method, w...

The non-negative matrix factorization (NMF) algorithm is a classical matrix factorization and dimension reduction method in machine learning and data mining. However, in real problems, we always have to run the algorithm for several times and use the best matrix factorization result as the final output because of the random initialization of the matrix factorization. In this paper, we proposed ...

We proposed automatic factorization method of biological signals measured by Fluorescence Correlation Spectroscopy (FCS). Since the signals are composed from several positive components, the signals are decomposed by using the idea of Non-negative matrix factorization (NMF). Each component is represented by model functions and the signals are factorized as the non-negative sum of the model func...

We prove that the earth mover’s distance problem reduces to a problem with half the number of constraints regardless of the ground distance, and propose a further reduced formulation when the ground distance comes from a graph with a homogeneous neighborhood structure. We also propose to apply our formulation to the non-negative matrix factorization.