Multi-class problem is the class of problems having more than one classes in the data set. Bayesian Network (BN) is a well-known algorithm handling the multi-class problem and is applied to different areas. But BN cannot handle continuous values. In contrast, Genetic Programming (GP) can handle continuous values and produces classification rules. However, GP is possible to produce cyclic rules representing tautologic, in which are useless for inference and expert systems. Co-evolutionary Rule-chaining Genetic Programming (CRGP) is the first variant of GP handling the multi-class problem and produces acyclic classification rules [16]. It employs backward chaining inference to carry out classification based on the acquired acyclic rule set. It can handle multi-classes; it can avoid cyclic rules; it can handle input attributes with continuous values; and it can learn complex relationships among the attributes. In this paper, we propose a novel algorithm, the Chaining Genetic Programming (CGP) learning a set of acyclic rules and to produce better results than the CRGP's. The experimental results demonstrate that the proposed algorithm has the shorter learning process and can produce more accurate acyclic classification rules.

Classification rule is a useful model in data mining. Given variable values, rules classify data items into different classes. Different rule learning algorithms are proposed, like Genetic Algorithm (GA) and Genetic Programming (GP). Rules can also be extracted from Bayesian Network (BN) and decision trees. However, all of them have disadvantages and may fail to get the best results. Both of GA and GP cannot handle cooperation among rules and thus, the learnt rules are likely to have many overlappings, i. e. more than one rules classify the same data items and different rules have different predictions. The conflicts among the rules reduce their understandability and increase their usage difficulty for expert systems. In contrast, rules extracted from BN and decision trees have no overlapping in nature. But BN can handle discrete values only and cannot represent higher-order relationships among variables. Moreover, the search space for decision tree learning is huge and thus, it is difficult to reach the global optimum. In this paper, we propose to use Functional Dependency Network (FDN) and MDL Genetic Programming (MDLGP) to learn a set of non-overlapping classification rules [17]. The FDN is an extension of BN; it can handle all kind of values; it can represent higher-order relationships among variables; and its learning search space is smaller than decision trees’. The experimental results demonstrate that the proposed method can successfully discover the target rules, which have no overlapping and have the highest classification accuracies.

Bayesian Network (BN) is a powerful network model, which represents a set of variables in the domain and provides the probabilistic relationships among them. But BN can handle discrete values only; it cannot handle continuous, interval and ordinal ones, which must be converted to discrete values and the order information is lost. Thus, BN tends to have higher network complexity and lower understandability. In this paper, we present a novel dependency network which can handle discrete, continuous, interval and ordinal values through functions; it has lower network complexity and stronger expressive power; it can represent any kind of relationships; and it can incorporate a-priori knowledge though user-defined functions. We also propose a novel Genetic Programming (GP) to learn dependency networks. The novel GP does not use any knowledge-guided nor application-oriented operator, thus it is robust and easy to replicate. The experimental results demonstrate that the novel GP can successfully discover the target novel dependency networks, which have the highest accuracy and the lowest network complexity.

The self-organizing map (SOM) is a powerful tool in the exploratory phase of data mining. However, due to the dimensional conflict, neighborhood preservation cannot always lead to perfect topology preservation. In this paper we establish an expanding SOM (ESOM) to detect and preserve better topology correspondence between the two spaces. Our experiment results demonstrate that the ESOM constructs better mappings than the classic SOM in terms of both topological and quantization errors. Furthermore, clustering results generated by the ESOM are more accurate than those of the SOM.