1. Partially labeled classification with Markov random walks
A discussion on
Partially labeled classification with Markov random walks
By M. Szummer and T. Jaakkola
Xuejun Liao
15 June 2006

2. Neighborhood graph (undirected)
Wik gives the (on-step) connection strength datum i and k
The graph induces a Markov random walk with one-step transitions
t-step Markov random walk
where A is the one-step transition matrix with [A]ij=p(k|i)
Assuming uniform initial distribution p(i)

3. Transduction
Likelihood for labeled data
Maximizing the likelihood gives
E-step:
M-step:

4. Estimation based on margin maximization
where C denotes the number of classes and NC(k) gives the number of labeled points in the same class as k, and
The solution to this linear program can be found in closed form:
For each data k, choose tk as the smallest number of transitions needed to reach a labeled datum from datum k.

5. An example