2017/10/19 by Cem Örnek, Ornek, Cem, Elif Vural +1
Computer Science · #Face and Expression Recognition #Machine Learning and ELM #Domain Adaptation and Few-Shot Learning
paper · pdf · doi:10.48550/arxiv.1710.07120
The recovery of the intrinsic geometric structures of data collections is an\nimportant problem in data analysis. Supervised extensions of several manifold\nlearning approaches have been proposed in the recent years. Meanwhile, existing\nmethods primarily focus on the embedding of the training data, and the\ngeneralization of the embedding to initially unseen test data is rather\nignored. In this work, we build on recent theoretical results on the\ngeneralization performance of supervised manifold learning algorithms.\nMotivated by these performance bounds, we propose a supervised manifold\nlearning method that computes a nonlinear embedding while constructing a smooth\nand regular interpolation function that extends the embedding to the whole data\nspace in order to achieve satisfactory generalization. The embedding and the\ninterpolator are jointly learnt such that the Lipschitz regularity of the\ninterpolator is imposed while ensuring the separation between different\nclasses. Experimental results on several image data sets show that the proposed\nmethod outperforms traditional classifiers and the supervised dimensionality\nreduction algorithms in comparison in terms of classification accuracy in most\nsettings.\n