MODELLING OF KERNEL MACHINES BY INFINITE AND SEMI-INFINITE PROGRAMMING

2009-06-03
Ozogur-Akyuz, S.
Weber, Gerhard Wilhelm
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.

Suggestions

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...
Time series classification using deep learningTime series classification using deep learning
Hatipoğlu, Poyraz Umut; İyigün, Cem; Department of Industrial Engineering (2016)
Deep learning is a fast-growing and interesting field due to the need to represent statistical data in a more complex and abstract way. Development in the processors and graphics processing unit technology effects undeniably that the deep networks get that popularity. The main purpose of this work is to develop robust and full functional time series classification method. To achieve this intent a deep learning based novel methods are proposed. Because time series data can have complex and variable structure...
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...
Improvement of Hyperspectral Classification Accuracy with Limited Training Data Using Meanshift Segmentation
Özdemir, Okan Bilge; Çetin, Yasemin (2014-04-25)
In this study, the performance of hyperspectral classification algorithms with limited training data investigated. Support Vector Machines (SVM) with Gaussian kernel is used. Principle Component Analysis (PCA) is employed for preprocessing and meanshift segmentation is used to incorporate spatial information with spectral information to observe the effect spatial information. Pattern search algorithm is used to optimize meanshift segmentation parameters. The performance of the algorithm is demonstrated on h...
Citation Formats
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.