Abstract |
The information explosion triggered by the creation of vast amounts of data anytime, anywhere,
around the globe implies that we are certainly living in an era of data deluge. Although traditional
flat-view matrix modeling methods are usually suitable for their processing, when data dimensionality
scales up as a direct consequence of their multi-factor creation mechanisms, their limitations
become apparent and may jeopardize subsequent efficient processing. This calls for the design of
modern high-dimensional tensor-based methods and frameworks, tailored especially to exploit existing
correlations in the inherent dimensions of the data. The prevailing contribution of this thesis is
therefore to develop a novel framework for processing high-dimensional data, as well as to show its
practical utility in several applications of signal processing and machine learning.
Towards that end, in the first part of this dissertation we initially consider the fundamental concepts
of modeling and processing high-dimensional data, namely tensors and their decompositions.
These higher-order processing workhorses, made it feasible to model, treat and process efficiently
high dimensional data in real-world problems, in the quest of deriving new results in various application
domains of interest. In particular, we adopted tensor-based approaches for efficiently imputing
missing measurements and compared them with state-of-the-art matrix-based ones in the context of
supervised classification. In that way, we were able to prove that concrete merits are made available
when higher-order tensor processing structures are employed, and hence high-dimensional data
processing in their nominal dimensions paves the way for clearly enhanced performance results.
Since deep learning approaches have dominated the machine learning field in several interesting
low and high-dimensional tasks, in the second part of this thesis we initially elucidate their theoretical
foundations in order to familiarize with their key processing mechanisms to be used in upcoming
applications. We focus on convolutional neural networks, specially tailored for imaging tasks, by
reviewing every building block of them to be used and extended in this thesis. Subsequently, we cope
with several lower-order supervised learning applications of signal processing flavor, by formulating
the respective problems at hand as instances of low-order convolutional neural networks classification
tasks. Throughout this process we were able to show that low-order convolutional neural networks
are excellent feature learners as the dimensionality of their input data scales up, and, hence, their
extension for addressing higher-order supervised learning tasks is worthwhile.
Combining the theoretical and the application-based intuition obtained from the aforementioned
parts, the last part of the dissertation focuses on extending existing low-order convolutional neural
networks to their higher-order analogues, in order to efficiently cope with high-dimensional supervised
learning regimes arising in practice. More precisely, we introduce the notion of N-dimensional
convolutional neural networks, by extending the key concept of convolution to the general case. The respective extension is performed via tensor decompositions as well as stacked convolutions, with the
pros and cons of each method being highlighted towards their integration in modern deep learning
systems. Capitalizing on the designed core-functionality extension, we subsequently verify its performance
in several inherently high-dimensional supervised machine learning tasks in remote sensing,
ranging from classification to regression. The obtained experimental results clearly demonstrate that
tensor signal modeling in conjunction with convolutional neural networks architectures offer concrete
merits towards efficient high-dimensional data processing and learning in the context of novel deep
learning systems.
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