Classification methods using Dictionary Learning algorithms
This work contributes to the field by addressing the problem of Classification and Anomaly Detection using Sparse Representations and Dictionary Learning algorithms. These techniques offer unique advantages for classification problems and anomaly detection, as they efficiently capture the underlying structure of data. By leveraging the inherent sparsity in data, these methods aim to represent data samples as sparse linear combinations of a few basis elements.
In classification problems, sparse representation and dictionary learning enable the construction of discriminative features that enhance the accuracy and robustness of classifiers. The learned dictionary captures essential patterns and structures in the data, enabling efficient extraction and selection of features.
In anomaly detection, sparse representation and dictionary learning stand out by identifying deviations from normal patterns. By learning a dictionary that represents the normal behavior of the data, anomalies are detected as samples that cannot be sparsely represented using the learned dictionary.
In this thesis, the main contributions revolve around the development and application of innovative strategies in sparse representation and dictionary learning. The research spans various domains, including Sparse representation with Infinite Set Atoms, Incoherent frames design, Incoherent Dictionary Learning, Reduced Kernel Dictionary Learning, and their applications to anomaly detection and classification.
Chapters 1 and 2 present the general problems of sparse representation and dictionary learning. Here, we also outline the main motivation for using these methods for classification and anomaly detection problems.
Chapter 3 introduces the idea of sparse representation using infinite set atoms. For this framework, we provide two examples: the first one benefits of Gaussian (probability distributions) atoms, while the second one considers the use of Cone atoms. These types of sparse representations are beneficial for problems that involve outlier detection.
In Chapter 4, we present several Incoherence strategies for the design of incoherent frames or incoherent dictionaries. These strategies are useful for several key applications and areas within signal processing, machine learning, and data representation. On the other hand, the incoherent dictionary learning problem improves the representation capabilities, which can also be used in classification.
The Kernel Dictionary Learning problem is addressed in Chapter 5. Here, we outline the problem of reducing the kernel space.
Chapter 6 outlines other relevant contributions with respect to the classification and anomaly detection problems. Using the previous incoherence strategies, we adapt them for contrastive learning, with the main application to classification problems. Here, we also address the problem of dictionary initialization.
For the anomaly detection problem, we include a selection procedure that is used for the dictionary update stage. This demonstrates to be beneficial for the outlier detection problem. We also demonstrate that dictionary learning can also be used in other anomaly detection algorithms to enhance the results.
Chapter 7 ends the thesis with a recap discussion about all the obtained results. This chapter outlines the main contributions of this thesis.