Attribute Reduction of Hybrid Decision Information Systems Based on Fuzzy Conditional Information Entropy

The presence of numerous uncertainties in hybrid decision information systems(HDISs)renders attribute reduction a formidable task.Currently available attribute reduction algorithms,including those based on Pawlak attribute importance,Skowron discernibility matrix,and information entropy,struggle to effectively manages multiple uncertainties simultaneously in HDISs like the precise measurement of disparities between nominal attribute values,and attributes with fuzzy boundaries and abnormal values.In order to address the aforementioned issues,this paper delves into the study of attribute reduction withinHDISs.First of all,a novel metric based on the decision attribute is introduced to solve the problem of accurately measuring the differences between nominal attribute values.The newly introduced distance metric has been christened the supervised distance that can effectively quantify the differences between the nominal attribute values.Then,based on the newly developed metric,a novel fuzzy relationship is defined from the perspective of“feedback on parity of attribute values to attribute sets”.This new fuzzy relationship serves as a valuable tool in addressing the challenges posed by abnormal attribute values.Furthermore,leveraging the newly introduced fuzzy relationship,the fuzzy conditional information entropy is defined as a solution to the challenges posed by fuzzy attributes.It effectively quantifies the uncertainty associated with fuzzy attribute values,thereby providing a robust framework for handling fuzzy information in hybrid information systems.Finally,an algorithm for attribute reduction utilizing the fuzzy conditional information entropy is presented.The experimental results on 12 datasets show that the average reduction rate of our algorithm reaches 84.04%,and the classification accuracy is improved by 3.91%compared to the original dataset,and by an average of 11.25%compared to the other 9 state-of-the-art reduction algorithms.The comprehensive analysis of these research results clearly indicates that our algorithm is highly effective in managing the intricate uncertainties inherent in hybrid data.

CONDITION MONITOR OF DEEP-HOLE DRILLING BASED ON MULTI-SENSOR INFORMATION FUSION

A condition monitoring method of deep-hole drilling based on multi-sensor information fusion is discussed. The signal of vibration and cutting force are collected when the condition of deep-hole drilling on stainless steel 0Cr17Ni4Cu4Nb is normal or abnormal. Four eigenvectors are extracted on time-domain and frequency-domain analysis of the signals. Then the four eigenvectors are combined and sent to neural networks to dispose. The fusion results indicate that multi-sensor information fusion is superior to single-sensor information, and that cutting force signal can reflect the condition of cutting tool better than vibration signal.

Double-layer Bayesian Classifier Ensembles Based on Frequent Itemsets

Numerous models have been proposed to reduce the classification error of Naive Bayes by weakening its attribute independence assumption and some have demonstrated remarkable error performance. Considering that ensemble learning is an effective method of reducing the classifmation error of the classifier, this paper proposes a double-layer Bayesian classifier ensembles （DLBCE） algorithm based on frequent itemsets. DLBCE constructs a double-layer Bayesian classifier （DLBC） for each frequent itemset the new instance contained and finally ensembles all the classifiers by assigning different weight to different classifier according to the conditional mutual information. The experimental results show that the proposed algorithm outperforms other outstanding algorithms.

Nonlinear Analysis of Physiological Time Series

The heart rate variability could be explained by a low-dimensional governing mechanism. There has been increasing interest in verifying and understanding the coupling between the respiration and the heart rate. In this paper we use the nonlinear detection method to detect the nonlinear deterministic component in the physiological time series by a single variable series and two variables series respectively, and use the conditional information entropy to analyze the correlation between the heart rate, the respiration and the blood oxygen concentration. The conclusions are that there is the nonlinear deterministic component in the heart rate data and respiration data, and the heart rate and the respiration are two variables originating from the same underlying dynamics.

LEARNING MULTIVARIATE TIME SERIES CAUSAL GRAPHS BASED ON CONDITIONAL MUTUAL INFORMATION

Detection and clarification of cause-effect relationships among variables is an important problem in time series analysis.This paper provides a method that employs both mutual information and conditional mutual information to identify the causal structure of multivariate time series causal graphical models.A three-step procedure is developed to learn the contemporaneous and the lagged causal relationships of time series causal graphs.Contrary to conventional constraint-based algorithm, the proposed algorithm does not involve any special kinds of distribution and is nonparametric.These properties are especially appealing for inference of time series causal graphs when the prior knowledge about the data model is not available.Simulations and case analysis demonstrate the effectiveness of the method.

The information content of rules and rule sets and its application

The information content of rules is categorized into inner mutual information content and outer impartation information content. Actually, the conventional objective interestingness measures based on information theory are all inner mutual information, which represent the confidence of rules and the mutual information between the antecedent and consequent. Moreover, almost all of these measures lose sight of the outer impartation information, which is conveyed to the user and help the user to make decisions. We put forward the viewpoint that the outer impartation information content of rules and rule sets can be represented by the relations from input universe to output universe. By binary relations, the interaction of rules in a rule set can be easily represented by operators： union and intersection. Based on the entropy of relations, the outer impartation information content of rules and rule sets are well measured. Then, the conditional information content of rules and rule sets, the independence of rules and rule sets and the inconsistent knowledge of rule sets are defined and measured. The properties of these new measures are discussed and some interesting results are proven, such as the information content of a rule set may be bigger than the sum of the information content of rules in the rule set, and the conditional information content of rules may be negative. At last, the applications of these new measures are discussed. The new method for the appraisement of rule mining algorithm, and two rule pruning algorithms, λ-choice and RPClC, are put forward. These new methods and algorithms have predominance in satisfying the need of more efficient decision information.

LEARNING GRANGER CAUSALITY GRAPHS FOR MULTIVARIATE NONLINEAR TIME SERIES

An information theory method is proposed to test the. Granger causality and contemporaneous conditional independence in Granger causality graph models. In the graphs, the vertex set denotes the component series of the multivariate time series, and the directed edges denote causal dependence, while the undirected edges reflect the instantaneous dependence. The presence of the edges is measured by a statistics based on conditional mutual information and tested by a permutation procedure. Furthermore, for the existed relations, a statistics based on the difference between general conditional mutual information and linear conditional mutual information is proposed to test the nonlinearity. The significance of the nonlinear test statistics is determined by a bootstrap method based on surrogate data. We investigate the finite sample behavior of the procedure through simulation time series with different dependence structures, including linear and nonlinear relations.

LEARNING CAUSAL GRAPHS OF NONLINEAR STRUCTURAL VECTOR AUTOREGRESSIVE MODEL USING INFORMATION THEORY CRITERIA

Detection and clarification of cause-effect relationships among variables is an important problem in time series analysis. Traditional causality inference methods have a salient limitation that the model must be linear and with Gaussian noise. Although additive model regression can effectively infer the nonlinear causal relationships of additive nonlinear time series, it suffers from the limitation that contemporaneous causal relationships of variables must be linear and not always valid to test conditional independence relations. This paper provides a nonparametric method that employs both mutual information and conditional mutual information to identify causal structure of a class of nonlinear time series models, which extends the additive nonlinear times series to nonlinear structural vector autoregressive models. An algorithm is developed to learn the contemporaneous and the lagged causal relationships of variables. Simulations demonstrate the effectiveness of the nroosed method.

Detecting Lags in Nonlinear Models Using General Mutual Information

The general mutual information （GMI） and general conditional mutual information （GCMI） are considered to measure lag dependences in nonlinear time series. Both of the measures have the property of invariance with transform. The statistics based on GMI and GCMI are estimated using the correlation integral. Under the hypothesis of independent series, the estimators have Gaussian asymptotic distributions. Simulations applied to generated nonlinear series demonstrate that the methods appear to find frequently the correct lags.