  In this paper we introduce a generic model for multiplicative algorithms
which is suitable for the MapReduce parallel programming paradigm. We implement
three typical machine learning algorithms to demonstrate how similarity
comparison, gradient descent, power method and other classic learning
techniques fit this model well. Two versions of large-scale matrix
multiplication are discussed in this paper, and different methods are developed
for both cases with regard to their unique computational characteristics and
problem settings. In contrast to earlier research, we focus on fundamental
linear algebra techniques that establish a generic approach for a range of
algorithms, rather than specific ways of scaling up algorithms one at a time.
Experiments show promising results when evaluated on both speedup and accuracy.
Compared with a standard implementation with computational complexity $O(m^3)$
in the worst case, the large-scale matrix multiplication experiments prove our
design is considerably more efficient and maintains a good speedup as the
number of cores increases. Algorithm-specific experiments also produce
encouraging results on runtime performance.
