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For their ability to capture non-linearities in the data and to scale tolarge training sets, local Support Vector Machines (SVMs) have received aspecial attention during the past decade. In this paper, we introduce a newlocal SVM method, called L$^3$-SVMs, which clusters the input space, carriesout dimensionality reduction by projecting the data on landmarks, and jointlylearns a linear combination of local models. Simple and effective, ouralgorithm is also theoretically well-founded. Using the framework of UniformStability, we show that our SVM formulation comes with generalizationguarantees on the true risk. The experiments based on the simplestconfiguration of our model (i.e. landmarks randomly selected, linearprojection, linear kernel) show that L$^3$-SVMs is very competitive w.r.t. thestate of the art and opens the door to new exciting lines of research.

L$^3$-SVMs: Landmarks-based Linear Local Support Vectors Machines