Maximum Entropy Linear Manifold for Learning Discriminative Low-dimensional Representation

Representation learning is currently a very hot topic in modern machine learning, mostly due to the great success of the deep learning methods. In particular low-dimensional representation which discriminates classes can not only enhance the classification procedure, but also make it faster, while contrary to the high-dimensional embeddings can be efficiently used for visual based exploratory data analysis. In this paper we propose Maximum Entropy Linear Manifold (MELM), a multidimensional generalization of Multithreshold Entropy Linear Classifier model which is able to find a low-dimensional linear data projection maximizing discriminativeness of projected classes. As a result we obtain a linear embedding which can be used for classification, class aware dimensionality reduction and data visualization. MELM provides highly discriminative 2D projections of the data which can be used as a method for constructing robust classifiers. We provide both empirical evaluation as well as some interesting theoretical properties of our objective function such us scale and affine transformation invariance, connections with PCA and bounding of the expected balanced accuracy error.Comment: submitted to ECMLPKDD 201

Numerical Modeling of Flexible Structures in Open Ocean Environment

The dissertation presents advancements in numerical modeling of offshore aquaculture and harbor protection structures in the open ocean environment. The advancements were implemented in the finite element software Hydro-FE that expands the Morison equation approach previously incorporated in Aqua-FE software developed at the University of New Hampshire. The concept of equivalent dropper was introduced and validated on the example of a typical mussel longline design. Parametric studies for mussel dropper drag coefficients and bending stiffness contributions were performed for different environmental conditions. To model kelp aggregates in macroalgae aquaculture, a corresponding numerical technique was developed. The technique proposes a modified Morison-type approach calibrated in full-scale physical tow tank experiments conducted at Hydromechanics Laboratory of the United States Naval Academy. In addition to the numerical modeling techniques, an advanced methodology for multidimensional approximation of the current velocity fields around offshore installations was proposed. The methodology was applied to model a response of a kelp farm by utilizing tidal-driven acoustic Doppler current profiler measurements. Finally, a numerical model of a floating protective barrier was built in the Hydro-FE software to evaluate its seaworthiness. The model was validated by comparison to measurements obtained in scaled physical wave tank tests and field deployments

Dimension-reduction and discrimination of neuronal multi-channel signals

Dimensionsreduktion und Trennung neuronaler Multikanal-Signale

A Theory of Networks for Appxoimation and Learning

Learning an input-output mapping from a set of examples, of the type that many neural networks have been constructed to perform, can be regarded as synthesizing an approximation of a multi-dimensional function, that is solving the problem of hypersurface reconstruction. From this point of view, this form of learning is closely related to classical approximation techniques, such as generalized splines and regularization theory. This paper considers the problems of an exact representation and, in more detail, of the approximation of linear and nolinear mappings in terms of simpler functions of fewer variables. Kolmogorov's theorem concerning the representation of functions of several variables in terms of functions of one variable turns out to be almost irrelevant in the context of networks for learning. We develop a theoretical framework for approximation based on regularization techniques that leads to a class of three-layer networks that we call Generalized Radial Basis Functions (GRBF), since they are mathematically related to the well-known Radial Basis Functions, mainly used for strict interpolation tasks. GRBF networks are not only equivalent to generalized splines, but are also closely related to pattern recognition methods such as Parzen windows and potential functions and to several neural network algorithms, such as Kanerva's associative memory, backpropagation and Kohonen's topology preserving map. They also have an interesting interpretation in terms of prototypes that are synthesized and optimally combined during the learning stage. The paper introduces several extensions and applications of the technique and discusses intriguing analogies with neurobiological data

A Review of Kernel Methods for Feature Extraction in Nonlinear Process Monitoring

Kernel methods are a class of learning machines for the fast recognition of nonlinear patterns in any data set. In this paper, the applications of kernel methods for feature extraction in industrial process monitoring are systematically reviewed. First, we describe the reasons for using kernel methods and contextualize them among other machine learning tools. Second, by reviewing a total of 230 papers, this work has identified 12 major issues surrounding the use of kernel methods for nonlinear feature extraction. Each issue was discussed as to why they are important and how they were addressed through the years by many researchers. We also present a breakdown of the commonly used kernel functions, parameter selection routes, and case studies. Lastly, this review provides an outlook into the future of kernel-based process monitoring, which can hopefully instigate more advanced yet practical solutions in the process industries

Some Advances in Nonlinear Speech Modeling Using Modulations, Fractals, and Chaos

In this paper we briefly summarize our on-going work on modeling nonlinear structures in speech signals, caused by modulation and turbulence phenomena, using the theories of modulation, fractals, and chaos as well as suitable nonlinear signal analysis methods. Further, we focus on two advances: i) AM-FM modeling of fricative sounds with random modulation signals of the 1/f-noise type and ii) improved methods for speech analysis and prediction on reconstructed multidimensional attractors. 1

Dynamic non-linear system modelling using wavelet-based soft computing techniques

The enormous number of complex systems results in the necessity of high-level and cost-efficient modelling structures for the operators and system designers. Model-based approaches offer a very challenging way to integrate a priori knowledge into the procedure. Soft computing based models in particular, can successfully be applied in cases of highly nonlinear problems. A further reason for dealing with so called soft computational model based techniques is that in real-world cases, many times only partial, uncertain and/or inaccurate data is available. Wavelet-Based soft computing techniques are considered, as one of the latest trends in system identification/modelling. This thesis provides a comprehensive synopsis of the main wavelet-based approaches to model the non-linear dynamical systems in real world problems in conjunction with possible twists and novelties aiming for more accurate and less complex modelling structure. Initially, an on-line structure and parameter design has been considered in an adaptive Neuro- Fuzzy (NF) scheme. The problem of redundant membership functions and consequently fuzzy rules is circumvented by applying an adaptive structure. The growth of a special type of Fungus (Monascus ruber van Tieghem) is examined against several other approaches for further justification of the proposed methodology. By extending the line of research, two Morlet Wavelet Neural Network (WNN) structures have been introduced. Increasing the accuracy and decreasing the computational cost are both the primary targets of proposed novelties. Modifying the synoptic weights by replacing them with Linear Combination Weights (LCW) and also imposing a Hybrid Learning Algorithm (HLA) comprising of Gradient Descent (GD) and Recursive Least Square (RLS), are the tools utilised for the above challenges. These two models differ from the point of view of structure while they share the same HLA scheme. The second approach contains an additional Multiplication layer, plus its hidden layer contains several sub-WNNs for each input dimension. The practical superiority of these extensions is demonstrated by simulation and experimental results on real non-linear dynamic system; Listeria Monocytogenes survival curves in Ultra-High Temperature (UHT) whole milk, and consolidated with comprehensive comparison with other suggested schemes. At the next stage, the extended clustering-based fuzzy version of the proposed WNN schemes, is presented as the ultimate structure in this thesis. The proposed Fuzzy Wavelet Neural network (FWNN) benefitted from Gaussian Mixture Models (GMMs) clustering feature, updated by a modified Expectation-Maximization (EM) algorithm. One of the main aims of this thesis is to illustrate how the GMM-EM scheme could be used not only for detecting useful knowledge from the data by building accurate regression, but also for the identification of complex systems. The structure of FWNN is based on the basis of fuzzy rules including wavelet functions in the consequent parts of rules. In order to improve the function approximation accuracy and general capability of the FWNN system, an efficient hybrid learning approach is used to adjust the parameters of dilation, translation, weights, and membership. Extended Kalman Filter (EKF) is employed for wavelet parameters adjustment together with Weighted Least Square (WLS) which is dedicated for the Linear Combination Weights fine-tuning. The results of a real-world application of Short Time Load Forecasting (STLF) further re-enforced the plausibility of the above technique