Sentence examples for using the representer theorem from inspiring English sources

In this paper, we interpret the robustness of the R-LSSVM from a re-weighted viewpoint and develop a primal R-LSSVM using the representer theorem.

The least-square problem thus defined is developed by using the representer approach.

The representer theorem [ 32] is used to find the optimal g.

To overcome this problem we have devised a primal SVM method with the following properties: (1) it solves for the SVM representation without the need to invoke the representer theorem, (2) forward and backward selections are combined to approach the final globally optimal solution, and (3) a criterion is introduced for identification of support vectors leading to a much reduced support vector set.

This fact is known as the representer theorem in [12].

However, derivation of the representer theorem in a multiple kernel case is not so straightforward.

Since most generative dimensionality reduction algorithms exploit the representer theorem for reproducing kernel Hilbert spaces, their computational costs grow at least quadratically in the number n of data.

We give basic explanations of some key concepts the so-called kernel trick, the representer theorem and regularization which may open up the possibility that insights from machine learning can feed back into psychology.

Yet, according to the representer theorem [43] the evaluation of f at point x i is given by a linear combination of kernel functions: f ( x i ) = ∑ i = 1 m β i k x i, x j. (6).

In non-parametric regression, the search space is infinite, but the representer theorem allows confining the search to a specific set of functions.

Coupled with the representer theorem, the diffusion kernel allows casting underlying graph structures into a regression on the real line under a Hilbert space.