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An approach to semi-supervised learning is proposed that is based on a Gaussian random field model. Labeled and unlabeled data are represented as vertices in a weighted graph, with edge weights encoding the similarity between instances. The learning problem is then formulated in terms of a Gaussian random field on this graph, where the mean of the field is… (More)

We investigate the use of unlabeled data to help labeled data in classification. We propose a simple iterative algorithm, label propagation, to propagate labels through the dataset along high density areas defined by unlabeled data. We analyze the algorithm, show its solution, and its connection to several other algorithms. We also show how to learn… (More)

- Xiaojin Zhu, Andrew B. Goldberg
- Introduction to Semi-Supervised Learning
- 2009

- Xiaojin Zhu, John D. Lafferty, Zoubin Ghahramaniy
- 2003

Active and semi-supervised learning are important techniques when labeled data are scarce. We combine the two under a Gaussian random field model. Labeled and unlabeled data are represented as vertices in a weighted graph, with edge weights encoding the similarity between instances. The semi-supervised learning problem is then formulated in terms of a… (More)

We present an algorithm based on convex optimization for constructing kernels for semi-supervised learning. The kernel matrices are derived from the spectral decomposition of graph Laplacians, and combine labeled and unlabeled data in a systematic fashion. Unlike previous work using diffusion kernels and Gaussian random field kernels, a nonparametric kernel… (More)

- David Andrzejewski, Xiaojin Zhu, Mark Craven
- ICML
- 2009

Users of topic modeling methods often have knowledge about the composition of words that should have high or low probability in various topics. We incorporate such domain knowledge using a novel Dirichlet Forest prior in a Latent Dirichlet Allocation framework. The prior is a mixture of Dirichlet tree distributions with special structures. We present its… (More)

We pose transductive classification as a matrix completion problem. By assuming the underlying matrix has a low rank, our formulation is able to handle three problems simultaneously: i) multi-label learning, where each item has more than one label, ii) transduction, where most of these labels are unspecified, and iii) missing data, where a large number of… (More)

- Xiaojin Zhu, Andrew B. Goldberg, Jurgen Van Gael, David Andrzejewski
- HLT-NAACL
- 2007

We introduce a novel ranking algorithm called GRASSHOPPER, which ranks items with an emphasis on diversity. That is, the top items should be different from each other in order to have a broad coverage of the whole item set. Many natural language processing tasks can benefit from such diversity ranking. Our algorithm is based on random walks in an absorbing… (More)

- John D. Lafferty, Xiaojin Zhu, Yan Liu
- ICML
- 2004

Kernel conditional random fields (KCRFs) are introduced as a framework for discriminative modeling of graph-structured data. A representer theorem for conditional graphical models is given which shows how kernel conditional random fields arise from risk minimization procedures defined using Mercer kernels on labeled graphs. A procedure for greedily… (More)

We present a graph-based semi-supervised learning algorithm to address the sentiment analysis task of rating inference. Given a set of documents (e.g., movie reviews) and accompanying ratings (e.g., “4 stars”), the task calls for inferring numerical ratings for unlabeled documents based on the perceived sentiment expressed by their text. In particular, we… (More)