Download
1 / 5
50 likes | 152 Views
This paper explores the methodology of partially labeled classification using Markov random walks. It delves into the construction of an undirected neighborhood graph that enables one-step connection strength calculations. The Markov random walk is analyzed through its one-step and t-step transitions, emphasizing the initial uniform distribution. The approach also covers transduction and likelihood maximization for labeled data, introducing processes such as E-step and M-step for estimation. Additionally, the paper presents a closed-form solution for linear programming in this context, illustrating the methodology with relevant examples.
E N D
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.
