Fuzzy rule weight modification with particle swarm optimisation

The most challenging problem in developing fuzzy rule-based classification systems is the construction of a fuzzy rule base for the target problem. In many practical applications, fuzzy sets that are of particular linguistic meanings, are often predefined by domain experts and required to be maintained in order to ensure interpretability of any subsequent inference results. However, learning fuzzy rules using fixed fuzzy quantity space without any qualification will restrict the accuracy of the resulting rules. Fortunately, adjusting the weights of fuzzy rules can help improve classification accuracy without degrading the interpretability. There have been different proposals for fuzzy rule weight tuning through the use of various heuristics with limited success. This paper proposes an alternative approach using Particle Swarm Optimisation in the search of a set of optimal rule weights, entailing high classification accuracy. Systematic experimental studies are carried out using common benchmark data sets, in comparison to popular rule based learning classifiers. The results demonstrate that the proposed approach can boost classification performance, especially when the size of the initially built rule base is relatively small, and is competitive to popular rule-based learning classifiers.     

On the quest for optimal rule learning heuristics

The primary goal of the research reported in this paper is to identify what criteria are responsible for the good performance of a heuristic rule evaluation function in a greedy top-down covering algorithm. We first argue that search heuristics for inductive rule learning algorithms typically trade off consistency and coverage, and we investigate this trade-off by determining optimal parameter settings for five different parametrized heuristics. In order to avoid biasing our study by known functional families, we also investigate the potential of using metalearning for obtaining alternative rule learning heuristics. The key results of this experimental study are not only practical default values for commonly used heuristics and a broad comparative evaluation of known and novel rule learning heuristics, but we also gain theoretical insights into factors that are responsible for a good performance. For example, we observe that consistency should be weighted more heavily than coverage, presumably because a lack of coverage can later be corrected by learning additional rules.     

融入差异性的帕累托集成剪枝方法

相比于集成学习,集成剪枝方法是在多个分类器中搜索最优子集从而改善分类器的泛化性能,简化集成过程。帕累托集成剪枝方法同时考虑了分类器的精准度及集成规模两个方面,并将二者均作为优化的目标。然而帕累托集成剪枝算法只考虑了基分类器的精准度与集成规模,忽视了分类器之间的差异性,从而导致了分类器之间的相似度比较大。本文提出了融入差异性的帕累托集成剪枝算法,该算法将分类器的差异性与精准度综合为第1个优化目标,将集成规模作为第2个优化目标,从而实现多目标优化。实验表明,当该改进的集成剪枝算法与帕累托集成剪枝算法在集成规模相当的前提下,由于差异性的融入该改进算法能够获得较好的性能。     

Unified fusion rules for multisensor multihypothesis network decision systems

In this paper, we present a fusion rule for distributed multihypothesis decision systems where communication patterns among sensors are given and the fusion center may also observe data. It is a specific form of the most general fusion rule, independent of statistical characteristics of observations and decision criteria, and thus, is called a unified fusion rule of the decision system. To achieve globally optimum performance, only sensor rules need to be optimized under the proposed fusion rule for the given conditional distributions of observations and decision criterion. Following this idea, we present a systematic and efficient scheme for generating optimum sensor rules and hence, optimum fusion rules, which reduce computation tremendously as compared with the commonly used exhaustive search. Numerical examples are given, which support the above results and provide a guideline on how to assign sensors to nodes in a signal detection networks with a given communication pattern. In addition, performance of parallel and tandem networks is compared.     

On Mining Instance-Centric Classification Rules

Many studies have shown that rule-based classifiers perform well in classifying categorical and sparse high-dimensional databases. However, a fundamental limitation with many rule-based classifiers is that they find the rules by employing various heuristic methods to prune the search space and select the rules based on the sequential database covering paradigm. As a result, the final set of rules that they use may not be the globally best rules for some instances in the training database. To make matters worse, these algorithms fail to fully exploit some more effective search space pruning methods in order to scale to large databases. In this paper, we present a new classifier, HARMONY, which directly mines the final set of classification rules. HARMONY uses an instance-centric rule-generation approach and it can assure that, for each training instance, one of the highest-confidence rules covering this instance is included in the final rule set, which helps in improving the overall accuracy of the classifier. By introducing several novel search strategies and pruning methods into the rule discovery process, HARMONY also has high efficiency and good scalability. Our thorough performance study with some large text and categorical databases has shown that HARMONY outperforms many well-known classifiers in terms of both accuracy and computational efficiency and scales well with regard to the database size     

Learning decision trees with taxonomy of propositionalized attributes

We consider the problem of exploiting a taxonomy of propositionalized attributes in order to learn compact and robust classifiers. We introduce propositionalized attribute taxonomy guided decision tree learner (PAT-DTL), an inductive learning algorithm that exploits a taxonomy of propositionalized attributes as prior knowledge to generate compact decision trees. Since taxonomies are unavailable in most domains, we also introduce propositionalized attribute taxonomy learner (PAT-Learner) that automatically constructs taxonomy from data. PAT-DTL uses top-down and bottom-up search to find a locally optimal cut that corresponds to the literals of decision rules from data and propositionalized attribute taxonomy. PAT-Learner propositionalizes attributes and hierarchically clusters the propositionalized attributes based on the distribution of class labels that co-occur with them to generate a taxonomy. Our experimental results on UCI repository data sets show that the proposed algorithms can generate a decision tree that is generally more compact than and is sometimes comparably accurate to those produced by standard decision tree learners.     

The maximal likelihood enumeration method for the problem of classifying piecewise regular objects

We study the recognition problem for composite objects based on a probabilistic model of a piecewise regular object with thousands of alternative classes. Using the model’s asymptotic properties, we develop a new maximal likelihood enumeration method which is optimal (in the sense of choosing the most likely reference for testing on every step) in the class of “greedy” algorithms of approximate nearest neighbor search. We show experimental results for the face recognition problem on the FERET dataset. We demonstrate that the proposed approach lets us reduce decision making time by several times not only compared to exhaustive search but also compared to known approximate nearest neighbors techniques.     

Impact of error estimation on feature selection

Given a large set of potential features, it is usually necessary to find a small subset with which to classify. The task of finding an optimal feature set is inherently combinatoric and therefore suboptimal algorithms are typically used to find feature sets. If feature selection is based directly on classification error, then a feature-selection algorithm must base its decision on error estimates. This paper addresses the impact of error estimation on feature selection using two performance measures: comparison of the true error of the optimal feature set with the true error of the feature set found by a feature-selection algorithm, and the number of features among the truly optimal feature set that appear in the feature set found by the algorithm. The study considers seven error estimators applied to three standard suboptimal feature-selection algorithms and exhaustive search, and it considers three different feature-label model distributions. It draws two conclusions for the cases considered: (1) depending on the sample size and the classification rule, feature-selection algorithms can produce feature sets whose corresponding classifiers possess errors far in excess of the classifier corresponding to the optimal feature set; and (2) for small samples, differences in performances among the feature-selection algorithms are less significant than performance differences among the error estimators used to implement the algorithms. Moreover, keeping in mind that results depend on the particular classifier-distribution pair, for the error estimators considered in this study, bootstrap and bolstered resubstitution usually outperform cross-validation, and bolstered resubstitution usually performs as well as or better than bootstrap.     

Constrained dynamic rule induction learning

One of the known classification approaches in data mining is rule induction (RI). RI algorithms such as PRISM usually produce If-Then classifiers, which have a comparable predictive performance to other traditional classification approaches such as decision trees and associative classification. Hence, these classifiers are favourable for carrying out decisions by users and therefore they can be utilised as decision making tools. Nevertheless, RI methods, including PRISM and its successors, suffer from a number of drawbacks primarily the large number of rules derived. This can be a burden especially when the input data is largely dimensional. Therefore, pruning unnecessary rules becomes essential for the success of this type of classifiers. This article proposes a new RI algorithm that reduces the search space for candidate rules by early pruning any irrelevant items during the process of building the classifier. Whenever a rule is generated, our algorithm updates the candidate items frequency to reflect the discarded data examples associated with the rules derived. This makes items frequency dynamic rather static and ensures that irrelevant rules are deleted in preliminary stages when they don't hold enough data representation. The major benefit will be a concise set of decision making rules that are easy to understand and controlled by the decision maker. The proposed algorithm has been implemented in WEKA (Waikato Environment for Knowledge Analysis) environment and hence it can now be utilised by different types of users such as managers, researchers, students and others. Experimental results using real data from the security domain as well as sixteen classification datasets from University of California Irvine (UCI) repository reveal that the proposed algorithm is competitive in regards to classification accuracy when compared to known RI algorithms. Moreover, the classifiers produced by our algorithm are smaller in size which increase their possible use in practical applications.     

强化属性依赖关系的K阶贝叶斯分类模型

经典K阶贝叶斯分类模型(KDB)进行属性排序时,仅考虑类变量与决策属性间的直接相关,而忽略以决策属性为条件二者之间的条件相关.针对以上问题,在KDB结构的基础上,以充分表达属性间的依赖信息为原则,强化属性间的依赖关系,提升决策属性对分类的决策表达,利用类变量与决策属性间的条件互信息优化属性次序,融合属性约简策略剔除冗余属性,降低模型结构复杂带来的过拟合风险,根据贪婪搜索策略选择最优属性并构建模型结构.在UCI机器学习数据库中数据集的实验结果表明,该模型相比于KDB而言,具有更好的分类精度和突出的鲁棒性.     

Theoretical and practical considerations of uncertainty andcomplexity in automated knowledge acquisition

Inductive machine learning has become an important approach to automated knowledge acquisition from databases. The disjunctive normal form (DNF), as the common analytic representation of decision trees and decision tables (rules), provides a basis for formal analysis of uncertainty and complexity in inductive learning. A theory for general decision trees is developed based on C. Shannon's (1949) expansion of the discrete DNF, and a probabilistic induction system PIK is further developed for extracting knowledge from real world data. Then we combine formal and practical approaches to study how data characteristics affect the uncertainty and complexity in inductive learning. Three important data characteristics, namely, disjunctiveness, noise and incompleteness, are studied. The combination of leveled pruning, leveled condensing and resampling estimation turns out to be a very powerful method for dealing with highly disjunctive and inadequate data. Finally the PIK system is compared with other recent inductive learning systems on a number of real world domains     

Genetic rule induction at an intermediate level

Lists of if–then rules (i.e. ordered rule sets) are among the most expressive and intelligible representations for inductive learning algorithms. Two extreme strategies searching for such a list of rules can be distinguished: (i) local strategies primarily based on a step-by-step search for the optimal list of rules, and (ii) global strategies primarily based on a one-strike search for the optimal list of rules. Both approaches have their disadvantages. In this paper we present an intermediate strategy. A sequential covering strategy is combined with a one-strike genetic search for the next most promising rule. To achieve this, a new rule-fitness function is introduced. Experimental results on benchmark problems are presented and the performance of our intermediate approach is compared with other rule learning algorithms. Finally, GeSeCo's performance is compared to a more local strategy on a set of tasks in which the information value of individual attributes is varied.     

ENDER: a statistical framework for boosting decision rules

Induction of decision rules plays an important role in machine learning. The main advantage of decision rules is their simplicity and human-interpretable form. Moreover, they are capable of modeling complex interactions between attributes. In this paper, we thoroughly analyze a learning algorithm, called ENDER, which constructs an ensemble of decision rules. This algorithm is tailored for regression and binary classification problems. It uses the boosting approach for learning, which can be treated as generalization of sequential covering. Each new rule is fitted by focusing on examples which were the hardest to classify correctly by the rules already present in the ensemble. We consider different loss functions and minimization techniques often encountered in the boosting framework. The minimization techniques are used to derive impurity measures which control construction of single decision rules. Properties of four different impurity measures are analyzed with respect to the trade-off between misclassification (discrimination) and coverage (completeness) of the rule. Moreover, we consider regularization consisting of shrinking and sampling. Finally, we compare the ENDER algorithm with other well-known decision rule learners such as SLIPPER, LRI and RuleFit.     

Multiobjective genetic fuzzy rule selection of single granularity-based fuzzy classification rules and its interaction with the lateral tuning of membership functions

Multiobjective genetic fuzzy rule selection is based on the generation of a set of candidate fuzzy classification rules using a preestablished granularity or multiple fuzzy partitions with different granularities for each attribute. Then, a multiobjective evolutionary algorithm is applied to perform fuzzy rule selection. Since using multiple granularities for the same attribute has been sometimes pointed out as to involve a potential interpretability loss, a mechanism to specify appropriate single granularities at the rule extraction stage has been proposed to avoid it but maintaining or even improving the classification performance. In this work, we perform a statistical study on this proposal and we extend it by combining the single granularity-based approach with a lateral tuning of the membership functions, i.e., complete contexts learning. In this way, we analyze in depth the importance of determining the appropriate contexts for learning fuzzy classifiers. To this end, we will compare the single granularity-based approach with the use of multiple granularities with and without tuning. The results show that the performance of the obtained classifiers can be even improved by obtaining the appropriate variable contexts, i.e., appropriate granularities and membership function parameters.     

Inductive rule generation and interpretation

Abstract

The problem of knowledge acquisition has been recognized as the major bottleneck in the development of knowledge-based systems. An encouraging approach to alleviate this problem is inductive learning. Inductive learning systems accept, as input, a set of data that represent instances of the problem domain and produce, as output, the rules of the knowledge base. Each data item is described by a set of attribute values and is assigned to a unique decision class. A common characteristic of the existing inductive learning systems, is that they are empirical in nature and do not take into account the implications of the inductive rule generation process on the performance of the resulting set of rules. That performance is assessed when the rules are used to classify new unlabelled data. This paper demonstrates that the performance of a rule set is a function of the rule generation and rule interpretation processes. These two processes are interrelated and should not be considered separately. The interrelation of rule generation and rule interpretation is analysed and suggestions to improve the performance of existing inductive learning systems, are forwarded.     

The effects of combining classifiers with the same training statistics using Bayesian decision rules

Multiple classifier systems (MCS) are attracting increasing interest in the field of pattern recognition and machine learning. Recently, MCS are also being introduced in the remote sensing field where the importance of classifier diversity for image classification problems has not been examined. In this article, Satellite Pour l'Observation de la Terre (SPOT) IV panchromatic and multispectral satellite images are classified into six land cover classes using five base classifiers: contextual classifier, k-nearest neighbour classifier, Mahalanobis classifier, maximum likelihood classifier and minimum distance classifier. The five base classifiers are trained with the same feature sets throughout the experiments and a posteriori probability, derived from the confusion matrix of these base classifiers, is applied to five Bayesian decision rules (product rule, sum rule, maximum rule, minimum rule and median rule) for constructing different combinations of classifier ensembles. The performance of these classifier ensembles is evaluated for overall accuracy and kappa statistics. Three statistical tests, the McNemar's test, the Cochran's Q test and the Looney's F-test, are used to examine the diversity of the classification results of the base classifiers compared to the results of the classifier ensembles. The experimental comparison reveals that (a) significant diversity amongst the base classifiers cannot enhance the performance of classifier ensembles; (b) accuracy improvement of classifier ensembles can only be found by using base classifiers with similar and low accuracy; (c) increasing the number of base classifiers cannot improve the overall accuracy of the MCS and (d) none of the Bayesian decision rules outperforms the others.     

A genetic algorithm-based rule extraction system

Individual classifiers predict unknown objects. Although, these are usually domain specific, and lack the property of scaling up prediction while handling data sets with huge size and high-dimensionality or imbalance class distribution. This article introduces an accuracy-based learning system called DTGA (decision tree and genetic algorithm) that aims to improve prediction accuracy over any classification problem irrespective to domain, size, dimensionality and class distribution. More specifically, the proposed system consists of two rule inducing phases. In the first phase, a base classifier, C4.5 (a decision tree based rule inducer) is used to produce rules from training data set, whereas GA (genetic algorithm) in the next phase refines them with the aim to provide more accurate and high-performance rules for prediction. The system has been compared with competent non-GA based systems: neural network, Naïve Bayes, rule-based classifier using rough set theory and C4.5 (i.e., the base classifier of DTGA), on a number of benchmark datasets collected from UCI (University of California at Irvine) machine learning repository. Empirical results demonstrate that the proposed hybrid approach provides marked improvement in a number of cases.     

Distributed learning with bagging-like performance

Bagging forms a committee of classifiers by bootstrap aggregation of training sets from a pool of training data. A simple alternative to bagging is to partition the data into disjoint subsets. Experiments with decision tree and neural network classifiers on various datasets show that, given the same size partitions and bags, disjoint partitions result in performance equivalent to, or better than, bootstrap aggregates (bags). Many applications (e.g., protein structure prediction) involve use of datasets that are too large to handle in the memory of the typical computer. Hence, bagging with samples the size of the data is impractical. Our results indicate that, in such applications, the simple approach of creating a committee of n classifiers from disjoint partitions each of size 1/n (which will be memory resident during learning) in a distributed way results in a classifier which has a bagging-like performance gain. The use of distributed disjoint partitions in learning is significantly less complex and faster than bagging.