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Identifier 000455823
Title Tensor learning for high-dimensional signal acquisition and analysis
Alternative Title Εκμάθηση τανυστών για απόκτηση και ανάλυση σημάτων υψηλών διαστάσεων
Author Αϊδίνη, Αναστασία Ν.
Thesis advisor Τσακαλίδης, Παναγιώτης
Reviewer Αργυρός, Αντώνιος
Sidiropoulos, Nikolaos
Beferull-Lozano, Baltasar
Δημητρόπουλος, Ξενοφώντας
Ροντογιάννης, Αθανάσιος
Τσαγκατάκης, Γρηγόριος
Abstract Many signal processing applications rely on multidimensional signals, which require demanding acquisition and analysis procedures. Tensors, which are multidimensional arrays indexed by multiple variables, are a natural way to represent these signals. Despite the complexities involved in handling and manipulating tensors, tools for tensor analysis can effectively overcome the limitations of traditional processing models. This thesis presents innovative tensor learning techniques that tackle the challenges associated with high-dimensional signal acquisition and analysis. During the data acquisition process, a common issue is the corruption or loss of a significant number of measurements due to communication failures. Additionally, the available measurements are often quantized to a specific number of bits for transmission purposes. To enable further analysis, a quantization model for high-dimensional data is proposed, along with formal methods for recovering a tensor from partially quantized and potentially corrupted measurements. The study also investigates the relationship between quantization and sampling, as well as the identification of possible anomalies or outliers in higher-order signals. Experiments conducted on satellite-derived observations indicate that it is more effective to consider the discrete nature of the quantized measurements rather than treating them as real values. The compression process is another critical step in signal acquisition that aims to reduce the required number of bits for representation without significant loss. To this end, we introduce end-to-end compression algorithms for high-dimensional data that include quantization and coding to bitstreams, allowing them to be directly applied in real-world scenarios. In these schemes, we populate the relevant representation subspaces and utilize tensor decomposition techniques within a machine-learning framework to exploit the data characteristics of available training samples. Subsequently, each new sample can be mapped to the learned decompositions, necessitating only the transmission of associated coefficients. Consequently, high compression ratios can be achieved, and the correlations among all variables are simultaneously removed. While these algorithms are evaluated on third- and fourth-order remote sensing multispectral image sequences, they can handle arbitrary-high-dimensional data, providing a mathematically concrete solution for encoding multiple sources of observations simultaneously. Multidimensional measurements have also significant implications for their analysis, including classification. Therefore, this dissertation proposes a general machine-learning approach for supervised classification based on tensor decomposition. The problem is for mulated as a tensor completion task, where the tensor of scores for various classes and all possible samples, is completed. By integrating classification loss functions with tensor decomposition techniques, the proposed method is effectively utilized in several real-world classification tasks. In conclusion, the proposed schemes effectively tackle numerous challenges associated with high-dimensional signal acquisition and processing. However, the main contribution of this thesis lies in the integration of tensor models with machine learning techniques. By leveraging the advantages of both tensor decomposition and machine learning, we can concurrently exploit their benefits and provide a novel framework for multidimensional signal processing that overcomes the constraints of conventional models.
Language English
Subject Classification
Compression
Quantization
Tensor Completion
Ανάλυση τανυστών
Αποσύνθεση τανυστών
Κβάντιση
Ολοκλήρωση τανυστών
Συμπίεση
Σήματα υψηλών διαστάσεων
Ταξινόμηση
Issue date 2023-07-21
Collection   School/Department--School of Sciences and Engineering--Department of Computer Science--Doctoral theses
  Type of Work--Doctoral theses
Permanent Link https://elocus.lib.uoc.gr//dlib/1/4/1/metadata-dlib-1687251215-714351-725.tkl Bookmark and Share
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