  Calculating the log-determinant of a matrix is useful for statistical
computations used in machine learning, such as generative learning which uses
the log-determinant of the covariance matrix to calculate the log-likelihood of
model mixtures. The log-determinant calculation becomes challenging as the
number of variables becomes large. Therefore, finding a practical speedup for
this computation can be useful. In this study, we present a parallel matrix
condensation algorithm for calculating the log-determinant of a large matrix.
We demonstrate that in a distributed environment, Parallel Matrix Condensation
has several advantages over the well-known Parallel Gaussian Elimination. The
advantages include high data distribution efficiency and less data
communication operations. We test our Parallel Matrix Condensation against
self-implemented Parallel Gaussian Elimination as well as ScaLAPACK (Scalable
Linear Algebra Package) on 1000 x1000 to 8000x8000 for 1,2,4,8,16,32,64 and 128
processors. The results show that Matrix Condensation yields the best speed-up
among all other tested algorithms. The code is available on
https://github.com/vbvg2008/MatrixCondensation
