To cite this version: Xiaoyi Mai, Romain Couillet. The counterintuitive mechanism of graph-based semi-supervised learning in the big data regime. ABSTRACT In this article, a new approach is proposed to study the performance of graph-based semi-supervised learning methods, under the assumptions that the dimension of data p and their number n grow large at the same rate and that the data arise from a Gaussian mixture model. Unlike small dimensional systems, the large dimensions allow for a Taylor

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... expansion to linearize the weight (or kernel) matrix W , thereby providing in closed form the limiting performance of semi-supervised learning algorithms. This notably allows to predict the classification error rate as a function of the normalization parameters and of the choice of the kernel function. Despite the Gaussian assumption for the data, the theoretical findings match closely the performance achieved with real datasets, particularly here on the popular MNIST database.