Abstract:
Semi-supervised learning is one of the most appealing machine learning problems. This paper introduces Semi-supervised Adaptive Local Embedding learning (SALE), a locality-preserved dimensionality reduction framework that learns a local discriminative embedding by constructing a k1 Nearest Neighbors (k1 NN) graph on labeled data to explore the intrinsic structure, i.e., sub-manifolds from non-Gaussian labeled data. Next, mapping all samples into learned embedding and constructing another k2 NN graph on all embedded data to explore the global structure of all samples. To improve embedded data discrimination, unlabeled data and their labeled neighbors can be clustered into the same sub-manifold. Using SALE framework, we propose two semi-supervised dimensionality reduction methods with orthogonal and whitening constraints. Our models use a fast alternatively iterative optimization algorithm to solve the NP-hard problem. Our methods excel at local structure exploration and classification in extensive experiments on synthetic and real-world data sets.
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