Abstract
Isometric feature mapping (Isomap) demonstrated noteworthy performance for nonlinear dimensionality reduction in a wide range of application domains. To improve the scalability of the algorithm a fast variant, called Landmark Isomap (L-Isomap), has been proposed in which time-consuming computations are performed on a subset of points referred to as landmarks. In this paper we present a novel method for landmark selection to be framed within the L-Isomap procedure. It is based on a mixed-integer problem aimed at finding a set of landmarks which are representative of dense regions of points in the input space which mostly contain samples of the same class. The optimization model is solved by a heuristic algorithm based on Lagrangian relaxation with subgradient method. Computational experiments performed on benchmark data sets highlighted the effectiveness of the proposed landmark selection algorithm which, combined with L-Isomap, provided promising results in terms of classification accuracy and computational effort.
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Orsenigo, C., Vercellis, C. (2013). Landmark Selection for Isometric Feature Mapping Based on Mixed-Integer Optimization. In: Torra, V., Narukawa, Y., Navarro-Arribas, G., MegÃas, D. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2013. Lecture Notes in Computer Science(), vol 8234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41550-0_23
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DOI: https://doi.org/10.1007/978-3-642-41550-0_23
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