5,744 research outputs found
RMSE-ELM: Recursive Model based Selective Ensemble of Extreme Learning Machines for Robustness Improvement
Extreme learning machine (ELM) as an emerging branch of shallow networks has
shown its excellent generalization and fast learning speed. However, for
blended data, the robustness of ELM is weak because its weights and biases of
hidden nodes are set randomly. Moreover, the noisy data exert a negative
effect. To solve this problem, a new framework called RMSE-ELM is proposed in
this paper. It is a two-layer recursive model. In the first layer, the
framework trains lots of ELMs in different groups concurrently, then employs
selective ensemble to pick out an optimal set of ELMs in each group, which can
be merged into a large group of ELMs called candidate pool. In the second
layer, selective ensemble is recursively used on candidate pool to acquire the
final ensemble. In the experiments, we apply UCI blended datasets to confirm
the robustness of our new approach in two key aspects (mean square error and
standard deviation). The space complexity of our method is increased to some
degree, but the results have shown that RMSE-ELM significantly improves
robustness with slightly computational time compared with representative
methods (ELM, OP-ELM, GASEN-ELM, GASEN-BP and E-GASEN). It becomes a potential
framework to solve robustness issue of ELM for high-dimensional blended data in
the future.Comment: Accepted for publication in Mathematical Problems in Engineering,
09/22/201
On the Inequivalence of Renormalization and Self-Adjoint Extensions for Quantum Singular Interactions
A unified S-matrix framework of quantum singular interactions is presented
for the comparison of self-adjoint extensions and physical renormalization. For
the long-range conformal interaction the two methods are not equivalent, with
renormalization acting as selector of a preferred extension and regulator of
the unbounded Hamiltonian.Comment: 19 pages, including 2 figures. The title and abstract were changed to
more accurately reflect the content. The text was rearranged into sections,
with several equations and multiple paragraphs added for clarity; and a few
typos were corrected. The central equations and concepts remain unchanged
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