Research On Multi-objective Granular Vector Machines And Their Applications

The research focus and emphasis on machine learning lie in how to improve the generalization ability, training speed, and intelligibility of learning machines. Granular computing (granular model) divides the complex task into some sub-tasks, so that people observe and analyze the research objectives from microcosmic, and the complexity, such as training complexity, is reduced. Conversely, for the microcosmic and simple task, the complexity caused dealing with multiple simple tasks is reduced by the gradual integration approach of sub-tasks in the view of macroscopic. For users, misclassified rate and training complexity are two conflict objectives used to evaluate the classification algorithms, and forming the classification algorithm with the minimal misclassified rate and minimal training complexity is a multi-objective optimization problem. In recent years, multi-objective optimization is embedded into machine learning field, which is applied to achieve a group of learning methods on the given training set, these learning methods can satisfy the user's selection in terms of their requirements. For support vector machines, different training samples have different contributions to the training process, and the sample being easily misclassified makes bigger contribution than the sample being classified correctly. It is a usual method to reduce the training complexity by training support vector machines on the reduced training set induced by their contributions.In this dissertation, fuzzy lattice-based granular computing, multi-objective granular computing, and granular support vector machines are proposed based on the fusion of granular computing, multi-objective optimization, and support vector machines. The innovative works are as follows:The inconsistency, between two partial order relations on vector set and granule set, is eliminated by the isomorphic mapping between lattice and its dual lattice. Fuzzy lattice-based granular computing classification algorithm is formed on the conditional union in terms of the granularity of united granule and fuzzy inclusion measure induced by the isomorphic mapping and positive valuation function. The feasibility of granular computing classification algorithm is proved in the view of algebraic system. Experimental results show that the proposed algorithms not only speed up the training process but also achieve the better generalization ability compared with SVMs and KNN algorithms.According to the redundancy granules generated by granular computing, Importance-based Pareto (IPareto) dominance is used to compare two individuals based on Pareto dominance and different importance between the misclassification rate and the number of granules. The multi-objective granular computing model including the number of granules and misclassification rate is proposed, and the corresponding evolutionary algorithm is designed based on IPareto dominance. The evolutionary algorithm represents the individual by two-level structure, designs crossover, mutation, and union operators to search the IPareto front by guide of prior information. Compared with the traditional granular computing, experimental results show that the multi-objective granular computing algorithms achieved a group of classifiers for users, and each classifier is the granule set with the minimal size corresponding to the misclassification rate.The granular model is formed by the contribution of samples to the training process, support vectors and non-support vectors are estimated by their distribution or contribution. A great deal of non-support vectors causing higher training complexity are discarded, and granular support vector machines are formed by the samples with higher contributions. The granular model of training set is formed by the equivalence relation induced by the discreterization of attribute value, and the boundary of rough set including samples with different class labels is used to form granular support vector machines. Granular support vector machines are formed by reduction or granular model of attribute set induced by significance of attribute. Experimental results show that the granular support vector machines not only downsize the training complexity but also achieve the better generalization ability compared with SVMs algorithms.The proposed hyperbox granular computing classification algorithm (HBGrCCA) is used to estimate location of sensors in wireless sensor network. Firstly, the communication measure between reference points and other points is composed of training set. Secondly, localization problem is transformed into corresponding classification problem by gridding of localization area. Experimental results show that HBGrCCA, used to estimate the location of blind nodes in wireless sensor network, achieved the acceptable localization precision.