Name
Title | ||
|---|---|---|
Piece-wise quadratic lego set for constructing arbitrary error potentials and their fast optimization. |
Abstract | ||
|---|---|---|
Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrate many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited the properties of non-quadratic error functionals based on L1 norm or even sub-linear potentials corresponding to fractional norms. The back side of these approaches is tremendous increase in computational cost for optimization. Till so far, no approaches have been suggested to deal with {it arbitrary} error functionals, in a flexible and computationally efficient framework. In this paper, we develop the theory and basic universal data approximation algorithms ($k$-means, principal components, principal manifolds and graphs), based on piece-wise quadratic error potentials of subquadratic growth (PQSQ potentials). We develop a new and universal framework to minimize {it arbitrary sub-quadratic error potentials} using an algorithm with guaranteed fast convergence to the local or global error minimum. The approach can be applied in most of existing machine learning methods, including methods of data approximation and regularized regression, leading to the improvement in the computational cost/accuracy trade-off. |
Year | Venue | Field |
|---|---|---|
2016 | arXiv: Learning | Convergence (routing),Mathematical optimization,Square (algebra),Quadratic equation,Curse of dimensionality,Artificial intelligence,Quadratic programming,Principal component analysis,Piecewise,Machine learning,Manifold,Mathematics |
DocType | Volume | Citations |
Journal | abs/1605.06276 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alexander N Gorban | 1 | 90 | 16.13 |
| Eugenij Moiseevich Mirkes | 2 | 11 | 3.08 |
| Andrei Yu. Zinovyev | 3 | 93 | 11.87 |