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Laplacian embedded regression for scalable manifold regularization.

Lin Chen, Ivor W Tsang, Dong Xu

    IEEE Transactions on Neural Networks and Learning Systems
    |May 9, 2014
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces Laplacian embedded regression for semi-supervised learning (SSL), improving scalability by efficiently handling large datasets. The new framework enhances manifold regularization algorithms, making them more computationally feasible for real-world applications.

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    Area of Science:

    • Machine Learning
    • Data Science
    • Computational Mathematics

    Background:

    • Semi-supervised learning (SSL) leverages limited labeled data with abundant unlabeled data, gaining traction in machine learning.
    • Manifold regularization frameworks, like LapSVM and LapRLS, provide theoretical underpinnings for SSL but face scalability issues due to high computational costs, particularly matrix inversion.
    • Existing SSL algorithms struggle with large-scale problems due to the computational demands of matrix operations.

    Purpose of the Study:

    • To propose a novel, scalable framework for semi-supervised learning based on manifold regularization.
    • To address the computational limitations of existing SSL algorithms for large-scale datasets.
    • To develop efficient algorithms that can effectively utilize both labeled and unlabeled data.

    Main Methods:

    • Introduced a 'Laplacian embedded regression' framework by incorporating an intermediate decision variable into manifold regularization.
    • Derived Laplacian embedded support vector regression (LapESVR) using epsilon-insensitive loss for sparse solutions and Laplacian embedded RLS (LapERLS).
    • Developed a transformed kernel (sum of original and graph kernels) and proposed projecting the decision variable into a subspace of graph Laplacian eigenvectors for efficiency and manifold representation.

    Main Results:

    • LapESVR and LapERLS exhibit a transformed kernel that simplifies computation by allowing separate handling of kernel and graph Laplacian matrices.
    • The proposed methods significantly improve computational efficiency, especially when the graph Laplacian matrix is sparse, by reducing the need for dense matrix inversion.
    • Experiments demonstrate the effectiveness and scalability of the Laplacian embedded regression framework on both toy and real-world datasets.

    Conclusions:

    • The proposed Laplacian embedded regression framework offers an effective and scalable solution for semi-supervised learning problems.
    • The novel approach enhances the practical applicability of manifold regularization techniques to large-scale machine learning tasks.
    • The methods provide a computationally efficient way to leverage manifold structures for improved learning from limited labeled data.