An Implementation of Standard Label Propagation Algorithm

Label Propagation is a classic semi-supervised learning algorithm commonly used for node classification tasks in graph data. Its core concept involves propagating label information from labeled nodes to unlabeled nodes based on similarity within the graph structure.

The fundamental algorithm workflow consists of: first constructing a graph structure where nodes represent data samples and edges represent similarity between samples. Labeled nodes retain their initial labels, while unlabeled nodes iteratively update their labels based on the label distribution of neighboring nodes. During each iteration, each node updates its label in a weighted manner according to its neighbors' label distribution, typically using majority voting or probability diffusion strategies. In code implementation, this is often achieved through matrix operations where the label matrix is multiplied by the propagation matrix.

Three crucial aspects require attention during implementation: first, constructing the similarity matrix, commonly computed using Gaussian kernel functions to measure sample similarity; second, defining propagation rules to ensure algorithm convergence, which can be implemented using normalized graph Laplacian or random walk transitions; third, setting termination conditions, typically stopping when label changes fall below a threshold or when maximum iterations are reached. The convergence check can be implemented by calculating the norm difference between label matrices of consecutive iterations.

The advantage of label propagation lies in its simplicity and efficiency, particularly suitable for scenarios with local consistency in graphs. Its variants can be applied to tasks like community detection and anomaly detection, making it a fundamental method in graph algorithms. The algorithm can be efficiently implemented using sparse matrix operations to handle large-scale graphs.