The explosive growth of multimedia data on the Internet makes it essential to develop innovative machine learning algorithms for practical applications especially where only a small number of labeled samples are available. Manifold regularized semi-supervised learning (MRSSL) thus received intensive attention recently because it successfully exploits the local structure of data distribution including both labeled and unlabeled samples to leverage the generalization ability of a learning model. Although there are many representative works in MRSSL, including Laplacian regularization (LapR) and Hessian regularization, how to explore and exploit the local geometry of data manifold is still a challenging problem. In this paper, we introduce a fully efficient approximation algorithm of graph ${p}$ -Laplacian, which significantly saving the computing cost. And then we propose ${p}$ -LapR (pLapR) to preserve the local geometry. Specifically, ${p}$ -Laplacian is a natural generalization of the standard graph Laplacian and provides convincing theoretical evidence to better preserve the local structure. We apply pLapR to support vector machines and kernel least squares and conduct the implementations for scene recognition. Extensive experiments on the Scene 67 dataset, Scene 15 dataset, and UC-Merced dataset validate the effectiveness of pLapR in comparison to the conventional manifold regularization methods.

中文翻译：

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p-Laplacian正则化场景识别

互联网上多媒体数据的爆炸性增长使得必须针对实际应用开发创新的机器学习算法，尤其是在只有少量标记样本的情况下。流形正规化半监督学习（MRSSL）因此最近受到了广泛的关注，因为它成功地利用了包括标记和未标记样本在内​​的数据分布的本地结构来利用学习模型的泛化能力。尽管MRSSL中有很多代表性的作品，包括Laplacian正则化（LapR）和Hessian正则化，但是如何探索和利用数据流形的局部几何形状仍然是一个具有挑战性的问题。在本文中，我们介绍了图的一种完全有效的近似算法 $ {p} $ -Laplacian，大大节省了计算成本。然后我们提出 $ {p} $ -LapR（pLapR）保留局部几何。具体来说， $ {p} $ -Laplacian是标准图Laplacian的自然概括，并提供了令人信服的理论证据以更好地保留局部结构。我们将pLapR应用到支持向量机和内核最小二乘法，并进行场景识别的实现。与传统的流形正则化方法相比，在Scene 67数据集，Scene 15数据集和UC-Merced数据集上的大量实验验证了pLapR的有效性。