  The success of semi-supervised learning crucially relies on the scalability
to a huge amount of unlabelled data that are needed to capture the underlying
manifold structure for better classification. Since computing the pairwise
similarity between the training data is prohibitively expensive in most kinds
of input data, currently, there is no general ready-to-use semi-supervised
learning method/tool available for learning with tens of millions or more data
points. In this paper, we adopted the idea of two low-rank label propagation
algorithms, GLNP (Global Linear Neighborhood Propagation) and Kernel Nystr\"om
Approximation, and implemented the parallelized version of the two algorithms
accelerated with Nesterov's accelerated projected gradient descent for Big-data
Label Propagation (BigLP).
  The parallel algorithms are tested on five real datasets ranging from 7000 to
10,000,000 in size and a simulation dataset of 100,000,000 samples. In the
experiments, the implementation can scale up to datasets with 100,000,000
samples and hundreds of features and the algorithms also significantly improved
the prediction accuracy when only a very small percentage of the data is
labeled. The results demonstrate that the BigLP implementation is highly
scalable to big data and effective in utilizing the unlabeled data for
semi-supervised learning.
