nonnegative matrix factorization (nmf) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. methods in alternating least square (als) approach usually used to solve this non-convex minimization problem.  at each step of als algorithms two convex least square problems should be solved, which causes high com...

We present an algorithm that verifies if two unlabeled configurations of N points in Rd are or are not an orthogonal transformation of one another, and if applicable, explicitly compute that transformation. We also give a formula for the orthogonal transformation in the case of noisy measurements. AMS subject classification: 65F15, 65F35, 65G99.

The non-orthogonal boundary-fitted coordinate transformation method is applied to the solution of steady three-dimensional momentum and energy equations in laminar flow to obtain temperature field and Nusselt numbers in the thermal entry region of straight ducts of different cross sectional geometries. The conservation equations originally written in Cartesian coordinates are parabolized in the...

Orthogonal matrix has shown advantages in training Recurrent Neural Networks (RNNs), but such matrix is limited to be square for the hidden-to-hidden transformation in RNNs. In this paper, we generalize such square orthogonal matrix to orthogonal rectangular matrix and formulating this problem in feedforward Neural Networks (FNNs) as Optimization over Multiple Dependent Stiefel Manifolds (OMDSM...