Label Propagation

Label Propagation

Label Propagation is a semi-supervised learning method that propagates labels from labeled data points to unlabeled ones in a dataset. It’s a graph-based technique that leverages the structure of the data to predict labels for unlabeled instances.


Label Propagation is based on the assumption that similar data points are likely to share the same label. It constructs a similarity graph where each node represents a data point, and edges connect similar instances. The strength of the connection (edge weight) is determined by the similarity between the instances.

Initially, all labeled instances propagate their labels to their neighbors. The unlabeled instances receive a label based on the weighted majority vote of their neighbors. This process is iteratively repeated until the labels converge or a predefined number of iterations is reached.

Use Cases

Label Propagation is particularly useful when labeled data is scarce or expensive to obtain. It’s widely used in various domains such as:

  • Text Classification: Label Propagation can classify documents by propagating labels from a few labeled documents to similar unlabeled ones.
  • Image Segmentation: It can segment images by propagating pixel labels to neighboring pixels.
  • Social Network Analysis: Label Propagation can identify communities by propagating user labels within the network.


  • Efficiency: Label Propagation is computationally efficient as it only requires matrix multiplication operations.
  • Scalability: It can handle large datasets due to its linear time complexity.
  • Flexibility: It can work with any similarity measure and is not restricted to Euclidean distance.


  • Sensitivity to Initialization: The initial labels can significantly influence the final results.
  • Noise Sensitivity: Label Propagation is sensitive to noise and outliers as they can mislead the propagation process.
  • Lack of Theoretical Guarantees: There are no theoretical guarantees for the convergence or the quality of the solution.
  • Label Spreading: A variant of Label Propagation that introduces a regularization parameter to control the label diffusion process.
  • Graph Convolutional Networks (GCNs): A deep learning approach that also uses graph structures for semi-supervised learning.


  1. Zhu, X., & Ghahramani, Z. (2002). Learning from labeled and unlabeled data with label propagation. Technical Report CMU-CALD-02-107, Carnegie Mellon University.
  2. Bengio, Y., Delalleau, O., & Roux, N. L. (2006). Label propagation and quadratic criterion. Semi-supervised Learning, 193-216.

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