System identification and artificial neural networks (ANN) are families of algorithms used in systems engineering and machine learning respectively that use structure detection and learning strategies to build models of complex systems by taking advantage of input-output type data. These models play an essential role in science and engineering because they fill the gap in those cases where we know the input-output behaviour of a system, but there is not a mathematical model to understand and predict its changes in future or even prevent threats. In this context, the nonlinear approximation of systems is nowadays very popular since it better describes complex instances. On the other hand, digital image processing is an area of systems engineering that is expanding the analysis dimension level in a variety of real-life problems while it is becoming more attractive and affordable over time. Medicine has made the most of it by supporting important human decision-making processes through computer-aided diagnosis (CAD) systems.
This thesis presents three different frameworks for breast cancer detection, with approaches ranging from nonlinear system identification, nonlinear system identification coupled with simple neural networks, to multilayer neural networks. In particular, the nonlinear system identification approaches termed the Nonlinear AutoRegressive with eXogenous inputs (NARX) model and the MultiScales Radial Basis Function (MSRBF) neural networks appear for the first time in image processing. Along with the above contributions takes place the presentation of the Multilayer-Fuzzy Extreme Learning Machine (ML-FELM) neural network for faster training and more accurate image classification.
A central research aim is to take advantage of nonlinear system identification and multilayer neural networks to enhance the feature extraction process, while the classification in CAD systems is bolstered. In the case of multilayer neural networks, the extraction is carried throughout stacked autoencoders, a bottleneck network architecture that promotes a data transformation between layers. In the case of nonlinear system identification, the goal is to add flexible models capable of capturing distinctive features from digital images that might be shortly recognised by simpler approaches. The purpose of detecting nonlinearities in digital images is complementary to that of linear models since the goal is to extract features in greater depth, in which both linear and nonlinear elements can be captured. This aim is relevant because, accordingly to previous work cited in the first chapter, not all spatial relationships existing in digital images can be explained appropriately with linear dependencies.
Experimental results show that the methodologies based on system identification produced reliable images models with customised mathematical structure. The models came to include nonlinearities in different proportions, depending upon the case under examination. The information about nonlinearity and model structure was used as part of the whole image model. It was found that, in some instances, the models from different clinical classes in the breast cancer detection problem presented a particular structure. For example, NARX models of the malignant class showed higher non-linearity percentage and depended more on exogenous inputs compared to other classes.
Regarding classification performance, comparisons of the three new CAD systems with existing methods had variable results. As for the NARX model, its performance was superior in three cases but was overcame in two. However, the comparison must be taken with caution since different databases were used. The MSRBF model was better in 5 out of 6 cases and had superior specificity in all instances, overcoming in 3.5% the closest model in this line. The ML-FELM model was the best in 6 out of 6 cases, although it was defeated in accuracy by 0.6% in one case and specificity in 0.22% in another one.
