Partially labeled classification with Markov random walks

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# Partially labeled classification with Markov random walks - PowerPoint PPT Presentation

A discussion on. Partially labeled classification with Markov random walks. By M. Szummer and T. Jaakkola. Xuejun Liao 15 June 2006. Neighborhood graph (undirected). W ik gives the (on-step) connection strength datum i and k.

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A discussion on

Partially labeled classification with Markov random walks

By M. Szummer and T. Jaakkola

Xuejun Liao

15 June 2006

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)

Transduction

• Likelihood for labeled data
• Maximizing the likelihood gives

E-step:

M-step:

Estimation based on margin maximization

where Cdenotes 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 tkas the smallest number of transitions needed to reach a labeled datum from datum k.