Resolvent and new activation functions for linear programming kernel sparse learning

The resolvent operator and the corresponding Green’s function occupy a central position in realms of differential integral equations, theory, particular modern physics. However, field machine learning, when confronted with complex highly challenging learning tasks from real world, prowess is rarely explored exploited. This paper aims at innovating conventional translation-invariant kernels rotation-invariant kernels, through theoretical investigation into new view constructing kernel functions by means its function. From practical perspective, newly developed are applied for robust signal recovery noise corrupted data scenario linear programming support vector learning. In particular, monotonic non-monotonic activation used design to improve representation capability. this manner, dimension given kernel-based sparse following two aspects: firstly, framework bridging gap between mathematical subtleties theory construction; secondly, concretization fusion neural networks nonlinear design. Finally, experimental study demonstrates potential superiority multiscale modeling, as one step towards removing apparent boundaries processing computational intelligence.