A four-node chain with equal edge weights shows how label propagation spreads information from labeled to unlabeled points. With endpoints fixed at scores 1 and 0, iterative neighbor averaging solves f2=(1+f3)/2 and f3=f2/2, yielding f2=2/3 and f3=1/3, split by a 0.5 threshold. The animation contrasts supervised, unsupervised, and semi-supervised setups, ties the update rule to graph Laplacian smoothness, and warns that scores are not calibrated probabilities and that disconnected components cannot receive labels. Useful for first-year AI students learning semi-supervised learning foundations.
Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
# Labels travel through a graph only when its connections make sense Compare fully labeled, unlabeled, and partly labeled point clouds to introduce supervised, unsupervised, and semi-supervised learning. Explain smoothness, cluster separation, and manifold assumptions with a curved point pattern, then focus on an exact four-node chain with equal edge weights. Fix the left endpoint's score at 1 and the right endpoint's score at 0. The two unlabeled nodes repeatedly average their neighbors while the endpoints remain fixed. Solve f2=(1+f3)/2 and f3=f2/2 to obtain f2=2/3 and f3=1/3. A threshold of .5 assigns them to opposite classes. Connect this process to minimizing neighboring score differences through a graph Laplacian. Explain that these scores are not automatically calibrated probabilities, and that an unlabeled disconnected component lacks a label anchor. Use black backgrounds and cyan-to-orange node fills. Useful for seeing how graph structure supports, or misleads, label propagation. Audience: 一年级人工智能专业学生