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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. Neighborhood graph (undirected). W ik gives the (on-step) connection strength datum i and k.

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Partially labeled classification with Markov random walks

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  1. 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 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.

  5. An example

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