A MIC-Based Empirical Study of Attribute Reduction

The presence of missing data is a common problem that affects almost all clinical datasets. Since most available data mining and machine learning algorithms require complete datasets, accurately imputing (i.e. "filling in") the missing data is an essential step. This paper presents a methodology for the missing data imputation of longitudinal clinical data based on the integration of linear interpolation and a weighted K-Nearest Neighbours (KNN) algorithm. The Maximal Information Coefficient (MIC) values among features are employed as weights for the distance computation in the KNN algorithm in order to integrate intra- and inter-patient information. An interpolation-based imputation approach was also employed and tested both independently and in combination with the KNN algorithm. The final imputation is carried out by applying the best performing method for each feature. The methodology was validated on a dataset of clinical laboratory test results of 13 commonly measured analytes of patients in an intensive care unit (ICU) setting. The performance results are compared with those of 3D-MICE, a state-of-the-art imputation method for cross-sectional and longitudinal patient data. This work was presented in the context of the 2019 ICHI Data Analytics Challenge on Missing data Imputation (DACMI).

Gene expression profile data have high-dimensionality with a small number of samples. These data characteristics lead to a long training time and low performance in predictive model construction. To address this issue, the paper proposes a feature selection algorithm using non-dominant feature-guide search. The algorithm adopts a filtering framework based on feature sorting and search strategy to overcome the problems of long training time and poor performance. First, the feature pre-selection is completed according to the calculated feature category correlation. Second, a multi-objective optimization feature selection model is constructed. Non-dominant features are defined according to the Pareto dominance theory. Combined with the bidirectional search strategy, the Pareto dominance features under the current category maximum relevance feature are removed one by one. Finally, the optimal feature subset with maximum correlation and minimum redundancy is obtained. Experimental results on six gene expression data sets show that the algorithm is much better than Fisher score, maximum information coefficient, composition of feature relevancy, mini-batch K-means normalized mutual information feature inclusion, and max-Relevance and Min-Redundancy algorithms. Compared to feature selection method based on maximum information coefficient and approximate Markov blanket, the algorithm not only has high computational efficiency but also can obtain better classification capabilities in a smaller dimension.

Genetic Programming (GP) is a powerful evolutionary algorithm that has a wide range of real-world applications. High-dimensional symbolic regression (HDSR) is an important yet challenging application of GP. In this paper, a comparative study is conducted to investigate and to discuss the effectiveness of dimensionality reduction (DR) techniques in assisting GP for HDSR problems. Three popular DR techniques, which are the Pearson Correlation Coefficient (PCC), the Principal Component Analysis (PCA), and the Maximal Information Coefficient (MIC), are selected for comparison and discussion. The experimental results showed that considering only correlation during DR is not effective enough to provide a suitable reduced set of problem dimensions, and that GP with DR may perform worse than its counterpart without DR. Meanwhile, we propose a novel two-phase DR method, considering both correlation and redundancy. The proposed method can give a more reasonable set of reduced dimensions, which can effectively improve the performance of GP on HDSR problems.

An incremental approach to attribute reduction from dynamic incomplete decision systems in rough set theory

Attribute Reduction problem is an important content in Rough Set theory, which has been proven to be NP-hard. It tends to find a subset of attributes that preserve the same discriminatory power as the entire attributes. Heuristics methods are used to find the minimum attribute subset. In this paper, we use three typical heuristic methods to do Attribute Reduction. They are positive-region-based, discernibility-matrix-based and mutual-information-based Attribute Reduction algorithm. Experimental results validate that all the three algorithms have good performance on classification for symbolic data. However, the computational complexity of the three Attribute Reduction algorithms are all O(n^2), so it s hard to apply them to massive data. In order to improve the efficiency of the three Attribute Reduction algorithms, we remodel the objective of them from the perspective of Submodular Function Optimization with submodular optimization strategies. We first optimize the attribute selection process with Lazy-Greedy strategy and then extend the serial algorithm to a parallel version according to the parallel optimization strategy of submodular functions. Experimental results validate that the efficiency of the proposed Attribute Reduction algorithms.

Dominance-based rough set approach (DRSA) has attracted much attention in multi-criteria decision-making problems for data with preference-ordered relations since its inception. However, in the real world, there is often the challenge of incomplete information. This paper addresses approaches to attribute reduction in an incomplete ordered decision system (IODS). Attribute evaluation is crucial in the attribute reduction process. Traditional evaluation functions primarily depend on the relationships between features, neglecting their impact on classification, and incur high computational costs when calculating lower and upper approximations. To address these issues, this paper proposes whole inter-class non-dominance as the criterion for attribute importance. First, we define the concepts of inter-class proximity and inter-class non-dominance in an IODS, with whole inter-class non-dominance serving as the evaluation index for attribute importance. Next, we propose a method for calculating inter-class non-dominance based on the expanded dominance matrix. Finally, combined with the heuristic search strategy, an attribute reduction algorithm based on inter-class non-dominance (HANDR) was designed, and experiments on various datasets from the University of California at Irvine (UCI) demonstrate that the proposed algorithm significantly improves running time and classification accuracy.

Attribute reduction plays an important role in knowledge discovery and data mining. Confronted with data characterized by the interval and missing values in many data analysis tasks, it is interesting to research the attribute reduction for interval-valued data with missing values. Uncertainty measures can supply efficient viewpoints, which help us to disclose the substantive characteristics of such data. Therefore, this paper addresses the attribute reduction problem based on uncertainty measure for interval-valued data with missing values. At first, an uncertainty measure is provided for measuring candidate attributes, and then an efficient attribute reduction algorithm is developed for the interval-valued data with missing values. To improve the efficiency of attribute reduction, the objects that fall within the positive region are deleted from the whole object set in the process of selecting attributes. Finally, experimental results demonstrate that the proposed algorithm can find a subset of attributes in much shorter time than existing attribute reduction algorithms without losing the classification performance.

Attribute reduction (feature selection) has become an important challenge in areas of pattern recognition, machine learning, data mining and knowledge discovery. Based on attribute reduction, one can extract fuzzy decision rules from a fuzzy decision table. As consistency is one of several criteria for evaluating the decision performance of a decision-rule set, in this paper, we devote to present a consistency-preserving attribute reduction in fuzzy rough set framework. Through constructing the membership function of an object, we first introduce a consistency measure to assess the consistencies of a fuzzy target set and a fuzzy decision table, which underlies a foundation for attribute reduction algorithm. Then, we derive two attribute significance measures based on the proposed consistency measure and design a forward greedy algorithm (ARBC) for attribute reduction from both numerical and nominal data sets. Numerical experiments show the validity of the proposed algorithm from search strategy and heuristic function in the meaning of consistency. Number of the selected features is the least for a given threshold of consistency measure.

As an effective tool for knowledge acquisition, attribute reduction is one of the key issues in rough set theory. In current research, most researchers choose to reduce redundant attributes as many as possible through some attribution reduction algorithms. However, the misclassification cost induced by attribute reduction is ignored. Thus, it is worth studying that how to reduce redundant attributes based on preserving the misclassification cost. Firstly, in this paper, the degree of minimum misclassification is defined. Then, by introducing decision process into variable precision rough set, a new model which is based on minimum misclassification cost with variable precision rough set (VPRS) is proposed. Moreover, based on the minimum misclassification cost, a heuristic attribute reduction algorithm is proposed. Finally, the simulation result shows that a feasible and reliable set of attributes can be obtained with our algorithm. These results further enrich attribute reduction to effectively deal with the uncertain classification problems.

Rough set theory is emerging as a powerful toll for reasoning about data. Attribute reduction is one of important topics in the research on the rough set theory. Heuristic, discernibility matrix and matrix method are three usually methods for designing attribute reduction algorithm in attribute reduction based on rough set. Some researchers use matrix method to design attribute reduction algorithm. The time complexity of the algorithm is O(|C| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> |U| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), and the computation of the algorithm is time consuming. To lower the time complexity, it was first proposed a new matrix, and provided an attribute reduction definition based on the new matrix. Then it was proved that the new attribute reduction definition is the same as the old reduction. At last, we used the matrix of attribute to define the significance of attribute, and designed a new attribute reduction algorithm, which time complexity is cut to O(|C||U|)+O(|C| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> |U/C| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ). At the same time, an example was used to illustrate the new algorithm.

In the coupling state of rotor unbalance fault and bearing defect fault for rotor system, the signals contain multiple fault components, and the fault diagnosis of the rotor system needs to contain comprehensive multidimensional feature quantities. However, irrelevant feature information in the multi-dimensional feature quantities increases the complexity of classification calculation and affects the efficiency and accuracy of diagnosis. In order to eliminate redundant and irrelevant features in the feature information, and achieve the goal of fewer diagnostic features and good diagnostic results, this paper proposes an adaptive feature selection based on the maximum information coefficient FF-FC-MIC (Feature-to-Feature and Feature-to-Category Maximum Information Coefficient) method. Firstly, the sparse representation algorithm is used to reconstruct the original signal to improve the signal-to-noise ratio, and the multi-dimensional feature quantity of the reconstructed signal is calculated; Secondly, calculate the correlation between features and features through MIC to obtain a feature set of weak correlation between features; thirdly, use MIC to calculate the correlation between features and signal categories to obtain a feature set with strong correlation between features and signals; Finally, the FF-FC-MIC feature selection method is used for feature adaptive selection and input into SVM to complete fault diagnosis. The method is analyzed by simulation signals and the real experiment signals. The results show that the method can effectively remove redundant and disclosed features in the coupling fault, reducing the characteristic dimension to reduce the fault classification time, and improve classification accuracy. Different experimental cases and various feature selection comparison methods further verify the accuracy and applicability of the proposed method.

A novel measure of attribute significance with complexity weight

As the object of study incomplete decision table, with the study of the notion of conflict region, the definition of attribution reduction based on conflict region in incomplete decision table is provided. it is proved that the attribute reduction is equivalent to the attribute reduction based on positive region, at the same time ,a new attribute reduction algorithm which is in incomplete decision table is designed, whose time complexity is O(|K||C|2|U|)(|K| = max{|T c (x i )|,x i ∈ U}) .Finally, an example is used to illustrate the efficiency of the new algorithm.

Attribute reduction is a key step in processing large-scale datasets, where the Granular Ball Neighborhood Rough Set (GBNRS) can significantly enhance the performance of attribute reduction compared to the traditional Neighborhood Rough Set (NRS). However, the GBNRS algorithm faces such challenges as a sharp increase in computational costs in high-dimensional spaces. To address these issues, this study introduces a new granular ball quality index to judge the separability degree of decision classes, and on the basis of this index, a rapid variable granular ball generation model (RVGBGM) is proposed. Compared with GBNRS, RVGBGM has the following advantages: (1) it reduces the number of granular balls and can quickly reflect the separability degree of different decision classes with few granular balls, (2) it constructs granular balls by using label information and shortens the time of granular ball construction, and (3) it can adjust the radius of granular balls adaptively by using parameters to determine the optimal granular ball radius for different datasets. Finally, we compare the RVGBGM algorithm with classical attribute reduction algorithms and the current state-of-the-art granular ball algorithm on 11 datasets. The proposed algorithm significantly improves algorithm efficiency while maintaining high accuracy. • A variable granular ball is defined. • A novel performance measure called separability degree between two variable granular balls is presented. • An efficient attribute reduction algorithm based on variable granular ball is devised and verified.

This study investigates brain-heart dynamics during visual emotional elicitation in healthy subjects through linear and nonlinear coupling measures of EEG spectrogram and instantaneous heart rate estimates. To this extent, affective pictures including different combinations of arousal and valence levels, gathered from the International Affective Picture System, were administered to twenty-two healthy subjects. Time-varying maps of cortical activation were obtained through EEG spectral analysis, whereas the associated instantaneous heartbeat dynamics was estimated using inhomogeneous point-process linear models. Brain-Heart linear and nonlinear coupling was estimated through the Maximal Information Coefficient (MIC), considering EEG time-varying spectra and point-process estimates defined in the time and frequency domains. As a proof of concept, we here show preliminary results considering EEG oscillations in the θ band (4-8 Hz). This band, indeed, is known in the literature to be involved in emotional processes. MIC highlighted significant arousal-dependent changes, mediated by the prefrontal cortex interplay especially occurring at intermediate arousing levels. Furthermore, lower and higher arousing elicitations were associated to not significant brain-heart coupling changes in response to pleasant/unpleasant elicitations.