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Everything about Manifold regularization

Technique for shaping training datasets

In machine learning, manifold regularization is a technique for using the shape of a dataset to constrain the functions that should be learned on that dataset. In many machine learning problems, the data to be learned do not cover the entire input space. For example, a facial recognition system may not need to classify any possible image, but only the subset of images that contain faces. The technique of manifold learning assumes that the relevant subset of data comes from a manifold, a mathematical structure with useful properties. The technique also assumes that the function to be learned is smooth: data with different labels are not likely to be close together, and so the labeling function should not change quickly in areas where there are likely to be many data points. Because of this assumption, a manifold regularization algorithm can use unlabeled data to inform where the learned function is allowed to change quickly and where it is not, using an extension of the technique of Tikhonov regularization. Manifold regularization algorithms can extend supervised learning algorithms in semi-supervised learning and transductive learning settings, where unlabeled data are available. The technique has been used for applications including medical imaging, geographical imaging, and object recognition. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Manifold regularizationA 5-minute orientation
  2. Skim a recent paper: Pairwise constraints-based semi-supervised fuzzy clustering with multi-manifold regularizationInfluential work since 2022
  3. Pick up a classic book: Introduction to 3-maniflodsThe most-reprinted book on the subject
  4. Read the landmark paper: Discriminative Semi-Supervised Feature Selection Via Manifold RegularizationCited 312 times
  5. Go sideways: Proximal gradient methods for learningA closely related topic
  6. Go sideways: Kodaira–Spencer mapA closely related topic

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  1. Manifold regularizer
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🏆 Landmark papers (most cited)

🆕 Influential since 2022

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