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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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A time-series graph is a line graph with repeated measurements taken at successive intervals of time. It is also called a time series chart. To construct a time-series graph, one must look at both pieces of a paired data set. The horizontal axis is used to plot the time increments, and the vertical axis is used to plot the values of the variable that one is measuring. By using the axes in this way, each point on the graph will correspond to time and a measured quantity. The points on the graph...
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Updated: Jan 26, 2026

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UniTrain: A universal iterative semi-supervised training framework for graph representation learning.

Xinlong Chen1, Jin Li2, Yisong Huang1

  • 1College of Computer and Data Science, Fuzhou University, Fuzhou, 350108, China.

Neural Networks : the Official Journal of the International Neural Network Society
|January 24, 2026
PubMed
Summary
This summary is machine-generated.

The Universal iterative semi-supervised Training (UniTrain) framework improves graph neural networks and graph transformers in semi-supervised learning by generating high-quality pseudo-labels for unlabeled nodes, boosting performance on node classification tasks.

Keywords:
Graph neural networksGraph transformersLabel refinementSemi-supervised learning

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Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Graph Representation Learning

Background:

  • Graph neural networks (GNNs) and graph transformers (GTs) excel at graph-related tasks but struggle in semi-supervised settings due to limited labeled data.
  • Over-fitting and task gaps persist despite robust encoders and pre-training, hindering GNN and GT potential.

Purpose of the Study:

  • To introduce the Universal iterative semi-supervised Training (UniTrain) framework to enhance semi-supervised learning for GNNs and GTs.
  • To address label scarcity and improve node classification performance in graph-based machine learning.

Main Methods:

  • UniTrain constructs a semantic graph using hidden vector representations from a pre-training stage.
  • It employs label knowledge propagation with uncertainty filtering to infer and refine labels for unlabeled nodes.
  • High-confidence pseudo-labels are incorporated to mitigate noise and compensate for limited original label guidance.

Main Results:

  • UniTrain significantly improves node classification performance across seven diverse graph benchmarks (Cora, Citeseer, Pubmed, Actor, Cornell, Texas, Wisconsin).
  • The framework demonstrates substantial performance gains when applied to both GNNs and GTs.
  • Experimental results validate the effectiveness and generalization capability of the UniTrain method.

Conclusions:

  • UniTrain effectively enhances fine-tuning in existing self-supervised learning methods for graph data.
  • The framework is compatible with any GNN or GT encoder, showcasing broad applicability.
  • UniTrain offers a robust solution for improving semi-supervised learning on graphs, particularly in low-label scenarios.