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    Area of Science:

    • Machine Learning
    • Computer Science

    Background:

    • Learning with label proportions (LLP) typically requires accessible label proportions for all training bags.
    • In practice, marking all bags is time-consuming, leading to the semisupervised LLP (SLLP) problem with both marked and unmarked bags.

    Purpose of the Study:

    • To address the SLLP problem by proposing the first semisupervised proportional support vector machine (SS-∝SVM).
    • To develop efficient optimization methods for the proposed SS-∝SVM model.

    Main Methods:

    • Introduced SS-∝SVM, extending the proportional SVM (∝SVM) to a semisupervised setting.
    • Developed two realizations: alter-SS-∝SVM (alternating optimization) and conv-SS-∝SVM (convex relaxation).
    • Designed a cutting plane (CP) method for conv-SS-∝SVM optimization and a fast accelerated proximal gradient method for its multiple kernel learning subproblem.

    Main Results:

    • SS-∝SVM demonstrates superiority over its supervised counterpart in classification accuracy.
    • The CP optimization of conv-SS-∝SVM shows highly competitive computational efficiency.

    Conclusions:

    • SS-∝SVM is a novel and effective approach for the SLLP problem.
    • The proposed optimization methods provide efficient solutions for training SS-∝SVM models.