Graph Construction from Data using Non Negative Kernel regression (NNK Graphs)
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Data driven graph constructions are often used in various applications, including several machine learning tasks, where the goal is to make predictions and discover patterns. However, learning an optimal graph from data is still a challenging task. Weighted K-nearest neighbor and ϵ-neighborhood methods are among the most common graph construction methods, due to their computational simplicity but the choice of parameters such as K and ϵ associated with these methods is often ad hoc and lacks a clear interpretation. We formulate graph construction as the problem of finding a sparse signal approximation in kernel space, identifying key similarities between methods in signal approximation and existing graph learning methods. We propose non-negative kernel regression (NNK), an improved approach for graph construction with interesting geometric and theoretical properties. We show experimentally the efficiency of NNK graphs, its robustness to choice of sparsity K and better performance over state of the art graph methods in semi supervised learning tasks on real world data.
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