Abstract: "Max and min operations have interesting properties that facilitate the exchange of information between the symbolic and real- valued domains. As such, neural networks that employ max-min activation functions have been a subject of interest in recent years. Since max-min functions are not strictly differentiable, many ad hoc learning methods for such max-min neural networks have been proposed in the literature. In this technical report, we propose a mathematically sound learning method based on using Fourier convergence analysis to derive a gradient descent technique for max-min error functions. This method is then applied to two models: a feedforward fuzzy-neural network and a recurrent max-min neural network. We show how a 'typical' fuzzy-neural network model employing max- min activation functions can be trained to perform function approximation; its performance was found to be better than that of a conventional feedforward neural network. We also propose a novel recurrent max-min neural network model which is trained to perform grammatical inference as an application example. Comparisons are made between this model and recurrent neural networks that use conventional sigmoidal activation fuctions; such recurrent sigmoidal networks are known to be difficult to train and generalize poorly on long strings. The comparisons show that our model not only performs better in terms of learning speed and generalization, its final weight configuration allows a DFQ to be extracted in a straighforward manner. However, it has a potential drawback: the minimal network size required for successful convergence grows with increasing language depth and complexity. Nevertheless, we are able to demonstrate that our proposed gradient descent technique does allow max-min neural networks to learn effectively. Our leaning method should be extensible to other neural networks that have non-differentiable activation functions."

Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.

This book discusses chemometric methods for spectroscopy analysis including NIR, MIR, Raman, NMR, and LIBS, from the perspective of practical applied spectroscopy. It covers all aspects of chemometrics associated with analytical spectroscopy, including representative sample selection algorithm, outlier detection algorithm, model updating and maintenance algorithm and strategy and calibration performance evaluation methods.To provide a systematic and comprehensive overview the latest progress of chemometric methods including recent scientific research and practical applications are presented. In addition the book also highlights the improvement of classical algorithms and the extension of common strategies. It is therefore useful as a reference book for researchers engaged in analytical spectroscopy technology, chemometrics, analytical instruments and other related fields.

Artificial neural networks and genetic algorithms both are areas of research which have their origins in mathematical models constructed in order to gain understanding of important natural processes. By focussing on the process models rather than the processes themselves, significant new computational techniques have evolved which have found application in a large number of diverse fields. This diversity is reflected in the topics which are subjects of the contributions to this volume. There are contributions reporting successful applications of the technology to the solution of industrial/commercial problems. This may well reflect the maturity of the technology, notably in the sense that 'real' users of modelling/prediction techniques are prepared to accept neural networks as a valid paradigm. Theoretical issues also receive attention, notably in connection with the radial basis function neural network. Contributions in the field of genetic algorithms reflect the wide range of current applications, including, for example, portfolio selection, filter design, frequency assignment, tuning of nonlinear PID controllers. These techniques are also used extensively for combinatorial optimisation problems.