Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
MODELLING OF KERNEL MACHINES BY INFINITE AND SEMI-INFINITE PROGRAMMING
Date
2009-06-03
Author
Ozogur-Akyuz, S.
Weber, Gerhard Wilhelm
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
267
views
0
downloads
Cite This
In Machine Learning (ML) algorithms, one of the crucial issues is the representation of the data. As the data become heterogeneous and large-scale, single kernel methods become insufficient to classify nonlinear data. The finite combinations of kernels are limited up to a finite choice. In order to overcome this discrepancy, we propose a novel method of "infinite" kernel combinations for learning problems with the help of infinite and semi-infinite programming regarding all elements in kernel space. Looking at all infinitesimally fine convex combinations of the kernels from the infinite kernel set, the margin is maximized subject to an infinite number of constraints with a compact index set and an additional (Riemann-Stieltjes) integral constraint due to the combinations. After a parametrization in the space of probability measures, it becomes semi-infinite. We analyze the regularity conditions which satisfy the Reduction Ansatz and discuss the type of distribution functions within the structure of the constraints and our bi-level optimization problem.
Subject Keywords
Machine learning
,
Kernel machines
,
Kernel machines
,
Semi-infinite optimization
,
Infinite programming
,
Support vector machines
,
Continuous optimization
,
Data mining
URI
https://hdl.handle.net/11511/55001
Collections
Graduate School of Applied Mathematics, Conference / Seminar
Suggestions
OpenMETU
Core
On numerical optimization theory of infinite kernel learning
Ozogur-Akyuz, S.; Weber, Gerhard Wilhelm (2010-10-01)
In Machine Learning algorithms, one of the crucial issues is the representation of the data. As the given data source become heterogeneous and the data are large-scale, multiple kernel methods help to classify "nonlinear data". Nevertheless, the finite combinations of kernels are limited up to a finite choice. In order to overcome this discrepancy, a novel method of "infinite" kernel combinations is proposed with the help of infinite and semi-infinite programming regarding all elements in kernel space. Look...
Adapted Infinite Kernel Learning by Multi-Local Algorithm
Akyuz, Sureyya Ozogur; Ustunkar, Gurkan; Weber, Gerhard Wilhelm (2016-05-01)
The interplay of machine learning (ML) and optimization methods is an emerging field of artificial intelligence. Both ML and optimization are concerned with modeling of systems related to real-world problems. Parameter selection for classification models is an important task for ML algorithms. In statistical learning theory, cross-validation (CV) which is the most well-known model selection method can be very time consuming for large data sets. One of the recent model selection techniques developed for supp...
A Bayesian Approach to Learning Scoring Systems
Ertekin Bolelli, Şeyda (2015-12-01)
We present a Bayesian method for building scoring systems, which are linear models with coefficients that have very few significant digits. Usually the construction of scoring systems involve manual efforthumans invent the full scoring system without using data, or they choose how logistic regression coefficients should be scaled and rounded to produce a scoring system. These kinds of heuristics lead to suboptimal solutions. Our approach is different in that humans need only specify the prior over what the ...
Machine Learning over Encrypted Data With Fully Homomorphic Encyption
Kahya, Ayşegül; Cenk, Murat; Department of Cryptography (2022-8-26)
When machine learning algorithms train on a large data set, the result will be more realistic. Big data, distribution of big data, and the study of learning algorithms on distributed data are popular research topics of today. Encryption is a basic need, especially when storing data with a high degree of confidentiality, such as medical data. Classical encryption methods cannot meet this need because when texts encrypted with classical encryption methods are distributed, and the distributed data set is decry...
Multiobjective evolutionary feature subset selection algorithm for binary classification
Deniz Kızılöz, Firdevsi Ayça; Coşar, Ahmet; Dökeroğlu, Tansel; Department of Computer Engineering (2016)
This thesis investigates the performance of multiobjective feature subset selection (FSS) algorithms combined with the state-of-the-art machine learning techniques for binary classification problem. Recent studies try to improve the accuracy of classification by including all of the features in the dataset, neglecting to determine the best performing subset of features. However, for some problems, the number of features may reach thousands, which will cause too much computation power to be consumed during t...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
S. Ozogur-Akyuz and G. W. Weber, “MODELLING OF KERNEL MACHINES BY INFINITE AND SEMI-INFINITE PROGRAMMING,” 2009, vol. 1159, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/55001.