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Very recently, an adaptive projection algorithm was introduced for the online classification task with sparsification in reproducing kernel Hilbert spaces (RKHS). This paper presents another sparsification method for the projection-based approach by generating a sequence of linear subspaces in RKHS. Projection mappings give a geometrical flavor to the design; classification is performed by metric projection mappings, sparsification is achieved by orthogonal projections, while the online system's memory and tracking requirements are attained by oblique projections. The resulting sparsification scheme shows strong similarities with the classical sliding window adaptive schemes. Validation is performed by considering the adaptive equalization problem of a nonlinear communication channel. Although here the classification scheme is considered, the method is readily extended to regression tasks. Furthermore its generality allows for a number of cost functions including non-differentiable ones.