Learning and optimization of 'fhe kernel functions from insufficiently labeled data
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Date
2010
Authors
Abbasnejad, M.Ehsan
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Abstract
Amongst all the machine learning techniques, kernel methods are increasingly becoming
popular due to their efficiency, accuracy and ability to handle high-dimensional
data. The fundamental problem related to these learning techniques is the selection of
the kernel function. Therefore, learning the kernel as a procedure in which the kernel
function is selected for a particular dataset is highly important. In this thesis, two approaches
to learn the kernel function are proposed: transferred learning of the kernel
and an unsupervised approach to learn the kernel. The first approach uses transferred
knowledge from unlabeled data to cope with situations where training examples are
scarce. Unlabeled data is used in conjunction with labeled data to construct an optimized
kernel using Fisher discriminant analysis and maximum mean discrepancy. The
accuracy of classification which indicates the number of correctly predicted test examples
from the base kernels and the optimized kernel are compared in two datasets
involving satellite images and synthetic data where proposed approach produces better
results. The second approach is an unsupervised method to learn a linear combination
of kernel functions. Here, the global intrinsic structure of the unlabeled data is inferred
through a measure called influence, which is computed by constructing a weighted
graph and performing a random walk upon it. The measure of influence in the feature
space is probabilistically related to the input space that yields an optimization
problem to be solved. The optimization problem is formulated in two different convex
settings, namely linear and semidefinite programming, depending on the type of
kernel combination considered. Here, the contributions are twofold: first, a novel unsupervised
approach to learn the kernel function, and second, a method to infer the
local similarity represented by the kernel function by measuring the global influence
of each point towards the structure of the dataset. The proposed approach focuses on
the kernel selection which is independent of the kernel-based learning algorithm. The
empirical evaluation of the proposed approach on image and text classification shows
the effectiveness of the algorithm in obtaining more accurate results.
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Keywords
Kernel functions , Labeled data