An Overview of Classifier Fusion Methods

A number of classifier fusion methods have been recently developed opening an alternative approach leading to a potential improvement in the classification performance. As there is little theory of information fusion itself, currently we are faced with different methods designed for different problems and producing different results. This paper gives an overview of classifier fusion methods and attempts to identify new trends that may dominate this area of research in future. A taxonomy of fusion methods trying to bring some order into the existing “pudding of diversities” is also provided

An Overview of Classifier Fusion Methods

A number of classifier fusion methods have been recently developed opening an alternative approach leading to a potential improvement in the classification performance. As there is little theory of information fusion itself, currently we are faced with different methods designed for different problems and producing different results. This paper gives an overview of classifier fusion methods and attempts to identify new trends that may dominate this area of research in future. A taxonomy of fusion methods trying to bring some order into the existing “pudding of diversities” is also provided

Efficient Data Driven Multi Source Fusion

Data/information fusion is an integral component of many existing and emerging applications; e.g., remote sensing, smart cars, Internet of Things (IoT), and Big Data, to name a few. While fusion aims to achieve better results than what any one individual input can provide, often the challenge is to determine the underlying mathematics for aggregation suitable for an application. In this dissertation, I focus on the following three aspects of aggregation: (i) efficient data-driven learning and optimization, (ii) extensions and new aggregation methods, and (iii) feature and decision level fusion for machine learning with applications to signal and image processing. The Choquet integral (ChI), a powerful nonlinear aggregation operator, is a parametric way (with respect to the fuzzy measure (FM)) to generate a wealth of aggregation operators. The FM has 2N variables and N(2N − 1) constraints for N inputs. As a result, learning the ChI parameters from data quickly becomes impractical for most applications. Herein, I propose a scalable learning procedure (which is linear with respect to training sample size) for the ChI that identifies and optimizes only data-supported variables. As such, the computational complexity of the learning algorithm is proportional to the complexity of the solver used. This method also includes an imputation framework to obtain scalar values for data-unsupported (aka missing) variables and a compression algorithm (lossy or losselss) of the learned variables. I also propose a genetic algorithm (GA) to optimize the ChI for non-convex, multi-modal, and/or analytical objective functions. This algorithm introduces two operators that automatically preserve the constraints; therefore there is no need to explicitly enforce the constraints as is required by traditional GA algorithms. In addition, this algorithm provides an efficient representation of the search space with the minimal set of vertices. Furthermore, I study different strategies for extending the fuzzy integral for missing data and I propose a GOAL programming framework to aggregate inputs from heterogeneous sources for the ChI learning. Last, my work in remote sensing involves visual clustering based band group selection and Lp-norm multiple kernel learning based feature level fusion in hyperspectral image processing to enhance pixel level classification

A Fuzzy-based Framework to Support Multicriteria Design of Mechatronic Systems

Designing a mechatronic system is a complex task since it deals with a high number of system components with multi-disciplinary nature in the presence of interacting design objectives. Currently, the sequential design is widely used by designers in industries that deal with different domains and their corresponding design objectives separately leading to a functional but not necessarily an optimal result. Consequently, the need for a systematic and multi-objective design methodology arises. A new conceptual design approach based on a multi-criteria profile for mechatronic systems has been previously presented by the authors which uses a series of nonlinear fuzzy-based aggregation functions to facilitate decision-making for design evaluation in the presence of interacting criteria. Choquet fuzzy integrals are one of the most expressive and reliable preference models used in decision theory for multicriteria decision making. They perform a weighted aggregation by the means of fuzzy measures assigning a weight to any coalition of criteria. This enables the designers to model importance and also interactions among criteria thus covering an important range of possible decision outcomes. However, specification of the fuzzy measures involves many parameters and is very difficult when only relying on the designer's intuition. In this paper, we discuss three different methods of fuzzy measure identification tailored for a mechatronic design process and exemplified by a case study of designing a vision-guided quadrotor drone. The results obtained from each method are discussed in the end

Insights and Characterization of l1-norm Based Sparsity Learning of a Lexicographically Encoded Capacity Vector for the Choquet Integral

This thesis aims to simultaneously minimize function error and model complexity for data fusion via the Choquet integral (CI). The CI is a generator function, i.e., it is parametric and yields a wealth of aggregation operators based on the specifics of the underlying fuzzy measure. It is often the case that we desire to learn a fusion from data and the goal is to have the smallest possible sum of squared error between the trained model and a set of labels. However, we also desire to learn as “simple’’ of solutions as possible. Herein, L1-norm regularization of a lexicographically encoded capacity vector relative to the CI is explored. The impact of regularization is explored in terms of what capacities and aggregation operators it induces under different common and extreme scenarios. Synthetic experiments are provided in order to illustrate the propositions and concepts put forth

Fuzzy control turns 50: 10 years later

In 2015, we celebrate the 50th anniversary of Fuzzy Sets, ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in FSS, see [1]. Ten years is at the same time a long period and short time thinking to the inner dynamics of research. This paper, presented for these 50 years of Fuzzy Sets is taking into account both thoughts. A first part presents a quick recap of the history of fuzzy control: from model-free design, based on human reasoning to quasi-LPV (Linear Parameter Varying) model-based control design via some milestones, and key applications. The second part shows where we arrived and what the improvements are since the milestone of the first 40 years. A last part is devoted to discussion and possible future research topics.Guerra, T.; Sala, A.; Tanaka, K. (2015). Fuzzy control turns 50: 10 years later. Fuzzy Sets and Systems. 281:162-182. doi:10.1016/j.fss.2015.05.005S16218228

Learning weights in the generalized OWA operators

This paper discusses identification of parameters of generalized ordered weighted averaging (GOWA) operators from empirical data. Similarly to ordinary OWA operators, GOWA are characterized by a vector of weights, as well as the power to which the arguments are raised. We develop optimization techniques which allow one to fit such operators to the observed data. We also generalize these methods for functional defined GOWA and generalized Choquet integral based aggregation operators.<br /

Use of aggregation functions in decision making

A key component of many decision making processes is the aggregation step, whereby a set of numbers is summarised with a single representative value. This research showed that aggregation functions can provide a mathematical formalism to deal with issues like vagueness and uncertainty, which arise naturally in various decision contexts

Advanced Mathematics and Computational Applications in Control Systems Engineering

Control system engineering is a multidisciplinary discipline that applies automatic control theory to design systems with desired behaviors in control environments. Automatic control theory has played a vital role in the advancement of engineering and science. It has become an essential and integral part of modern industrial and manufacturing processes. Today, the requirements for control precision have increased, and real systems have become more complex. In control engineering and all other engineering disciplines, the impact of advanced mathematical and computational methods is rapidly increasing. Advanced mathematical methods are needed because real-world control systems need to comply with several conditions related to product quality and safety constraints that have to be taken into account in the problem formulation. Conversely, the increment in mathematical complexity has an impact on the computational aspects related to numerical simulation and practical implementation of the algorithms, where a balance must also be maintained between implementation costs and the performance of the control system. This book is a comprehensive set of articles reflecting recent advances in developing and applying advanced mathematics and computational applications in control system engineering