Stochastic Stepwise Ensembles for Variable Selection

Ensembles methods such as AdaBoost, Bagging and Random Forest have attracted much attention in the statistical learning community in the last 15 years. Zhu and Chipman (2006) proposed the idea of using ensembles for variable selection. Their implementation used a parallel genetic algorithm (PGA). In this thesis, I propose a stochastic stepwise ensemble for variable selection, which improves upon PGA. Traditional stepwise regression (Efroymson 1960) combines forward and backward selection. One step of forward selection is followed by one step of backward selection. In the forward step, each variable other than those already included is added to the current model, one at a time, and the one that can best improve the objective function is retained. In the backward step, each variable already included is deleted from the current model, one at a time, and the one that can best improve the objective function is discarded. The algorithm continues until no improvement can be made by either the forward or the backward step. Instead of adding or deleting one variable at a time, Stochastic Stepwise Algorithm (STST) adds or deletes a group of variables at a time, where the group size is randomly decided. In traditional stepwise, the group size is one and each candidate variable is assessed. When the group size is larger than one, as is often the case for STST, the total number of variable groups can be quite large. Instead of evaluating all possible groups, only a few randomly selected groups are assessed and the best one is chosen. From a methodological point of view, the improvement of STST ensemble over PGA is due to the use of a more structured way to construct the ensemble; this allows us to better control over the strength-diversity tradeoff established by Breiman (2001). In fact, there is no mechanism to control this fundamental tradeoff in PGA. Empirically, the improvement is most prominent when a true variable in the model has a relatively small coefficient (relative to other true variables). I show empirically that PGA has a much higher probability of missing that variable

Cooperative Training in Multiple Classifier Systems

Multiple classifier system has shown to be an effective technique for classification. The success of multiple classifiers does not entirely depend on the base classifiers and/or the aggregation technique. Other parameters, such as training data, feature attributes, and correlation among the base classifiers may also contribute to the success of multiple classifiers. In addition, interaction of these parameters with each other may have an impact on multiple classifiers performance. In the present study, we intended to examine some of these interactions and investigate further the effects of these interactions on the performance of classifier ensembles. The proposed research introduces a different direction in the field of multiple classifiers systems. We attempt to understand and compare ensemble methods from the cooperation perspective. In this thesis, we narrowed down our focus on cooperation at training level. We first developed measures to estimate the degree and type of cooperation among training data partitions. These evaluation measures enabled us to evaluate the diversity and correlation among a set of disjoint and overlapped partitions. With the aid of properly selected measures and training information, we proposed two new data partitioning approaches: Cluster, De-cluster, and Selection (CDS) and Cooperative Cluster, De-cluster, and Selection (CO-CDS). In the end, a comprehensive comparative study was conducted where we compared our proposed training approaches with several other approaches in terms of robustness of their usage, resultant classification accuracy and classification stability. Experimental assessment of CDS and CO-CDS training approaches validates their robustness as compared to other training approaches. In addition, this study suggests that: 1) cooperation is generally beneficial and 2) classifier ensembles that cooperate through sharing information have higher generalization ability compared to the ones that do not share training information

Optimising multimodal fusion for biometric identification systems

Biometric systems are automatic means for imitating the human brain’s ability of identifying and verifying other humans by their behavioural and physiological characteristics. A system, which uses more than one biometric modality at the same time, is known as a multimodal system. Multimodal biometric systems consolidate the evidence presented by multiple biometric sources and typically provide better recognition performance compared to systems based on a single biometric modality. This thesis addresses some issues related to the implementation of multimodal biometric identity verification systems. The thesis assesses the feasibility of using commercial offthe-shelf products to construct deployable multimodal biometric system. It also identifies multimodal biometric fusion as a challenging optimisation problem when one considers the presence of several configurations and settings, in particular the verification thresholds adopted by each biometric device and the decision fusion algorithm implemented for a particular configuration. The thesis proposes a novel approach for the optimisation of multimodal biometric systems based on the use of genetic algorithms for solving some of the problems associated with the different settings. The proposed optimisation method also addresses some of the problems associated with score normalization. In addition, the thesis presents an analysis of the performance of different fusion rules when characterising the system users as sheep, goats, lambs and wolves. The results presented indicate that the proposed optimisation method can be used to solve the problems associated with threshold settings. This clearly demonstrates a valuable potential strategy that can be used to set a priori thresholds of the different biometric devices before using them. The proposed optimisation architecture addressed the problem of score normalisation, which makes it an effective “plug-and-play” design philosophy to system implementation. The results also indicate that the optimisation approach can be used for effectively determining the weight settings, which is used in many applications for varying the relative importance of the different performance parameters

Coevolutionary fuzzy modeling

This thesis presents Fuzzy CoCo, a novel approach for system design, conducive to explaining human decisions. Based on fuzzy logic and coevolutionary computation, Fuzzy CoCo is a methodology for constructing systems able to accurately predict the outcome of a human decision-making process, while providing an understandable explanation of the underlying reasoning. Fuzzy logic provides a formal framework for constructing systems exhibiting both good numeric performance (precision) and linguistic representation (interpretability). From a numeric point of view, fuzzy systems exhibit nonlinear behavior and can handle imprecise and incomplete information. Linguistically, they represent knowledge in the form of rules, a natural way for explaining decision processes. Fuzzy modeling —meaning the construction of fuzzy systems— is an arduous task, demanding the identification of many parameters. This thesis analyses the fuzzy-modeling problem and different approaches to coping with it, focusing on evolutionary fuzzy modeling —the design of fuzzy inference systems using evolutionary algorithms— which constitutes the methodological base of my approach. In order to promote this analysis the parameters of a fuzzy system are classified into four categories: logic, structural, connective, and operational. The central contribution of this work is the use of an advanced evolutionary technique —cooperative coevolution— for dealing with the simultaneous design of connective and operational parameters. Cooperative coevolutionary fuzzy modeling succeeds in overcoming several limitations exhibited by other standard evolutionary approaches: stagnation, convergence to local optima, and computational costliness. Designing interpretable systems is a prime goal of my approach, which I study thoroughly herein. Based on a set of semantic and syntactic criteria, regarding the definition of linguistic concepts and their causal connections, I propose a number of strategies for producing more interpretable fuzzy systems. These strategies are implemented in Fuzzy CoCo, resulting in a modeling methodology providing high numeric precision, while incurring as little a loss of interpretability as possible. After testing Fuzzy CoCo on a benchmark problem —Fisher's Iris data— I successfully apply the algorithm to model the decision processes involved in two breast-cancer diagnostic problems: the WBCD problem and the Catalonia mammography interpretation problem. For the WBCD problem, Fuzzy CoCo produces systems both of high performance and high interpretability, comparable (if not better) than the best systems demonstrated to date. For the Catalonia problem, an evolved high-performance system was embedded within a web-based tool —called COBRA— for aiding radiologists in mammography interpretation. Several aspects of Fuzzy CoCo are thoroughly analyzed to provide a deeper understanding of the method. These analyses show the consistency of the results. They also help derive a stepwise guide to applying Fuzzy CoCo, and a set of qualitative relationships between some of its parameters that facilitate setting up the algorithm. Finally, this work proposes and explores preliminarily two extensions to the method: Island Fuzzy CoCo and Incremental Fuzzy CoCo, which together with the original CoCo constitute a family of coevolutionary fuzzy modeling techniques. The aim of these extensions is to guide the choice of an adequate number of rules for a given problem. While Island Fuzzy CoCo performs an extended search over different problem sizes, Incremental Fuzzy CoCo bases its search power on a mechanism of incremental evolution