基于邻域粗糙集和帝王蝶优化的特征选择算法

针对经典的帝王蝶优化（MBO）算法不能很好地处理连续型数据,以及粗糙集模型对于大规模、高维复杂的数据处理能力不足等问题,提出了基于邻域粗糙集（NRS）和MBO的特征选择算法。首先,将局部扰动和群体划分策略与MBO算法结合,并构建传输机制以形成一种二进制MBO（BMBO）算法;其次,引入突变算子增强算法的探索能力,设计了基于突变算子的BMBO（BMBOM）算法;然后,基于NRS的邻域度构造适应度函数,并对初始化的特征子集的适应度值进行评估并排序;最后,使用BMBOM算法通过不断迭代搜索出最优特征子集,并设计了一种元启发式特征选择算法。在基准函数上评估BMBOM算法的优化性能,并在UCI数据集上评价所提出的特征选择算法的分类能力。实验结果表明,在5个基准函数上,BMBOM算法的最优值、最差值、平均值以及标准差明显优于MBO和粒子群优化（PSO）算法;在UCI数据集上,与基于粗糙集的优化特征选择算法、结合粗糙集与优化算法的特征选择算法、结合NRS与优化算法的特征选择算法、基于二进制灰狼优化的特征选择算法相比,所提特征选择算法在分类精度、所选特征数和适应度值这3个指标上表现良好,能够选择特征数少且分类精度高的最优特征子集。     

An efficient accelerator for attribute reduction from incomplete data in rough set framework

Feature selection (attribute reduction) from large-scale incomplete data is a challenging problem in areas such as pattern recognition, machine learning and data mining. In rough set theory, feature selection from incomplete data aims to retain the discriminatory power of original features. To address this issue, many feature selection algorithms have been proposed, however, these algorithms are often computationally time-consuming. To overcome this shortcoming, we introduce in this paper a theoretic framework based on rough set theory, which is called positive approximation and can be used to accelerate a heuristic process for feature selection from incomplete data. As an application of the proposed accelerator, a general feature selection algorithm is designed. By integrating the accelerator into a heuristic algorithm, we obtain several modified representative heuristic feature selection algorithms in rough set theory. Experiments show that these modified algorithms outperform their original counterparts. It is worth noting that the performance of the modified algorithms becomes more visible when dealing with larger data sets.     

基于自适应鲸鱼优化算法和容错邻域粗糙集的特征选择算法

针对传统鲸鱼优化算法(WOA)不能有效处理连续型数据、邻域粗糙集对噪声数据的容错性较差等问题,文中提出基于自适应WOA和容错邻域粗糙集的特征选择算法.首先,为了避免WOA过早陷入局部最优,基于迭代周期构建分段式动态惯性权重,改进WOA的收缩包围和螺旋捕食行为,设计自适应WOA.然后,为了解决邻域粗糙集对噪声数据缺乏容错性的问题,引入邻域内相同决策特征所占的比例,定义容错邻域上下近似集、容错近似精度和近似粗糙度、容错依赖度及容错近似条件熵.最后,基于容错邻域粗糙集构造适应度函数,使用自适应WOA,不断迭代以获取最优子群.高维数据集上采用费雪评分算法进行初步降维,降低算法的时间复杂度.在8个低维UCI数据集和6个高维基因数据集上的实验表明,文中算法可有效选择特征个数较少且分类精度较高的特征子集.     

一种基于粗糙集理论的最简决策规则挖掘算法

研究粗糙集理论中可辨识矩阵，扩展了类别特征矩阵，提出一种基于粗糙集理论的最筒决策规则算法．该算法根据决策属性将原始决策表分成若干个等价子决策表．借助核属性和属性频率函数对各类别特征矩阵挖掘出最简决策规则．与可辨识矩阵相比，采用类别特征矩阵可有效减少存储空间和时间复杂度。增强规则的泛化能力．实验结果表明，采用所提出的算法获得的规则更为简洁和高效．     

Positive approximation: An accelerator for attribute reduction in rough set theory

Feature selection is a challenging problem in areas such as pattern recognition, machine learning and data mining. Considering a consistency measure introduced in rough set theory, the problem of feature selection, also called attribute reduction, aims to retain the discriminatory power of original features. Many heuristic attribute reduction algorithms have been proposed however, quite often, these methods are computationally time-consuming. To overcome this shortcoming, we introduce a theoretic framework based on rough set theory, called positive approximation, which can be used to accelerate a heuristic process of attribute reduction. Based on the proposed accelerator, a general attribute reduction algorithm is designed. Through the use of the accelerator, several representative heuristic attribute reduction algorithms in rough set theory have been enhanced. Note that each of the modified algorithms can choose the same attribute reduct as its original version, and hence possesses the same classification accuracy. Experiments show that these modified algorithms outperform their original counterparts. It is worth noting that the performance of the modified algorithms becomes more visible when dealing with larger data sets.     

基于粗糙集的火灾图像特征选择与识别

针对图像型火灾探测方法检测准确度和实时性间的矛盾,提出了基于粗糙集的火灾图像特征选择和识别算法。首先通过对火焰图像特征的深入研究发现,在燃烧能量的驱动下火焰的上边缘极不规则,出现明显的震动现象,而下边缘却恰恰相反; 基于此特点,可利用上下边缘抖动投影个数比作为火焰区别于边缘形状较规则的干扰。然后,选择火焰的6个显著特征构造训练样本,在火灾分类能力不受影响的前提下,使用实验所得的特征量归类表对训练样本进行属性约简,并将约简后的信息系统属性训练支持向量机模型,实现火灾探测。最后与传统支持向量机火灾探测算法做了比较。实验结果表明:将粗糙集作为支持向量机分类器的前置系统,把粗糙集理论的属性约简引入到支持向量机中,可以大大消除样本集冗余属性,降低了火灾图像特征空间的维数,减少了分类器训练和检测数据,在保证识别精度的同时,提高了算法的速度和泛化能力。     

Neighborhood rough set based heterogeneous feature subset selection

Feature subset selection is viewed as an important preprocessing step for pattern recognition, machine learning and data mining. Most of researches are focused on dealing with homogeneous feature selection, namely, numerical or categorical features. In this paper, we introduce a neighborhood rough set model to deal with the problem of heterogeneous feature subset selection. As the classical rough set model can just be used to evaluate categorical features, we generalize this model with neighborhood relations and introduce a neighborhood rough set model. The proposed model will degrade to the classical one if we specify the size of neighborhood zero. The neighborhood model is used to reduce numerical and categorical features by assigning different thresholds for different kinds of attributes. In this model the sizes of the neighborhood lower and upper approximations of decisions reflect the discriminating capability of feature subsets. The size of lower approximation is computed as the dependency between decision and condition attributes. We use the neighborhood dependency to evaluate the significance of a subset of heterogeneous features and construct forward feature subset selection algorithms. The proposed algorithms are compared with some classical techniques. Experimental results show that the neighborhood model based method is more flexible to deal with heterogeneous data.     

基于粗糙集和改进鲸鱼优化算法的特征选择方法

随着互联网和物联网技术的发展,数据的收集变得越发容易。但是,高维数据中包含了很多冗余和不相关的特征,直接使用会徒增模型的计算量,甚至会降低模型的表现性能,故很有必要对高维数据进行降维处理。特征选择可以通过减少特征维度来降低计算开销和去除冗余特征,以提高机器学习模型的性能,并保留了数据的原始特征,具有良好的可解释性。特征选择已经成为机器学习领域中重要的数据预处理步骤之一。粗糙集理论是一种可用于特征选择的有效方法,它可以通过去除冗余信息来保留原始特征的特性。然而,由于计算所有的特征子集组合的开销较大,传统的基于粗糙集的特征选择方法很难找到全局最优的特征子集。针对上述问题,文中提出了一种基于粗糙集和改进鲸鱼优化算法的特征选择方法。为避免鲸鱼算法陷入局部优化,文中提出了种群优化和扰动策略的改进鲸鱼算法。该算法首先随机初始化一系列特征子集,然后用基于粗糙集属性依赖度的目标函数来评价各子集的优劣,最后使用改进鲸鱼优化算法,通过不断迭代找到可接受的近似最优特征子集。在UCI数据集上的实验结果表明,当以支持向量机为评价所用的分类器时,文中提出的算法能找到具有较少信息损失的特征子集,且具有较高的分类精度。因此,所提算法在特征选择方面具有一定的优势。     

基于模糊粗糙集信息熵的蚁群特征选择方法

目前针对高维数据特征选择提出的启发式算法多数容易陷入局部最优,无法对整个特征空间进行有效搜索。为了提高对特征域的并行搜索能力,基于模糊粗糙集的信息熵原理,对蚁群模型的搜索策略、信息素更新和状态转移规则等进行了改进,提出蚁群特征选择方法。经UCI数据实验验证,该算法比传统的特征选择算法具有更好的选择效果,是有效的。     

Soft rough fuzzy sets and soft fuzzy rough sets

Fuzzy set theory, soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related. Feng et al. introduced the notions of rough soft set, soft rough set and soft rough fuzzy set by combining fuzzy set, rough set and soft set all together. This paper is devoted to the further discussion of the combinations of fuzzy set, rough set and soft set. A new soft rough set model is proposed and its properties are derived. Furthermore, fuzzy soft set is employed to granulate the universe of discourse and a more general model called soft fuzzy rough set is established. The lower and upper approximation operators are presented and their related properties are surveyed.     

A rough margin based support vector machine

By introducing the rough set theory into the support vector machine (SVM), a rough margin based SVM (RMSVM) is proposed to deal with the overfitting problem due to outliers. Similar to the classical SVM, the RMSVM searches for the separating hyper-plane that maximizes the rough margin, defined by the lower and upper margin. In this way, more data points are adaptively considered rather than the few extreme value points used in the classical SVM. In addition, different support vectors may have different effects on the learning of the separating hyper-plane depending on their positions in the rough margin. Points in the lower margin have more effects than those in the boundary of the rough margin. From experimental results on six benchmark datasets, the classification accuracy of this algorithm is improved without additional computational expense compared with the classical ν-SVM.     

A hybrid decision support system based on rough set and extreme learning machine for diagnosis of hepatitis disease

Hepatitis is a disease which is seen at all levels of age. Hepatitis disease solely does not have a lethal effect, but the early diagnosis and treatment of hepatitis is crucial as it triggers other diseases. In this study, a new hybrid medical decision support system based on rough set (RS) and extreme learning machine (ELM) has been proposed for the diagnosis of hepatitis disease. RS-ELM consists of two stages. In the first one, redundant features have been removed from the data set through RS approach. In the second one, classification process has been implemented through ELM by using remaining features. Hepatitis data set, taken from UCI machine learning repository has been used to test the proposed hybrid model. A major part of the data set (48.3%) includes missing values. As removal of missing values from the data set leads to data loss, feature selection has been done in the first stage without deleting missing values. In the second stage, the classification process has been performed through ELM after the removal of missing values from sub-featured data sets that were reduced in different dimensions. The results showed that the highest 100.00% classification accuracy has been achieved through RS-ELM and it has been observed that RS-ELM model has been considerably successful compared to the other methods in the literature. Furthermore in this study, the most significant features have been determined for the diagnosis of the hepatitis. It is considered that proposed method is to be useful in similar medical applications.     

Feature selection based on rough sets and particle swarm optimization

We propose a new feature selection strategy based on rough sets and particle swarm optimization (PSO). Rough sets have been used as a feature selection method with much success, but current hill-climbing rough set approaches to feature selection are inadequate at finding optimal reductions as no perfect heuristic can guarantee optimality. On the other hand, complete searches are not feasible for even medium-sized datasets. So, stochastic approaches provide a promising feature selection mechanism. Like Genetic Algorithms, PSO is a new evolutionary computation technique, in which each potential solution is seen as a particle with a certain velocity flying through the problem space. The Particle Swarms find optimal regions of the complex search space through the interaction of individuals in the population. PSO is attractive for feature selection in that particle swarms will discover best feature combinations as they fly within the subset space. Compared with GAs, PSO does not need complex operators such as crossover and mutation, it requires only primitive and simple mathematical operators, and is computationally inexpensive in terms of both memory and runtime. Experimentation is carried out, using UCI data, which compares the proposed algorithm with a GA-based approach and other deterministic rough set reduction algorithms. The results show that PSO is efficient for rough set-based feature selection.     

Soft sets and soft rough sets

In this study, we establish an interesting connection between two mathematical approaches to vagueness: rough sets and soft sets. Soft set theory is utilized, for the first time, to generalize Pawlak’s rough set model. Based on the novel granulation structures called soft approximation spaces, soft rough approximations and soft rough sets are introduced. Basic properties of soft rough approximations are presented and supported by some illustrative examples. We also define new types of soft sets such as full soft sets, intersection complete soft sets and partition soft sets. The notion of soft rough equal relations is proposed and related properties are examined. We also show that Pawlak’s rough set model can be viewed as a special case of the soft rough sets, and these two notions will coincide provided that the underlying soft set in the soft approximation space is a partition soft set. Moreover, an example containing a comparative analysis between rough sets and soft rough sets is given.     

A hybrid genetic algorithm for feature subset selection in rough set theory

Rough set theory has been proven to be an effective tool to feature subset selection. Current research usually employ hill-climbing as search strategy to select feature subset. However, they are inadequate to find the optimal feature subset since no heuristic can guarantee optimality. Due to this, many researchers study stochastic methods. Since previous works of combination of genetic algorithm and rough set theory do not show competitive performance compared with some other stochastic methods, we propose a hybrid genetic algorithm for feature subset selection in this paper, called HGARSTAR. Different from previous works, HGARSTAR embeds a novel local search operation based on rough set theory to fine-tune the search. This aims to enhance GA’s intensification ability. Moreover, all candidates (i.e. feature subsets) generated in evolutionary process are enforced to include core features to accelerate convergence. To verify the proposed algorithm, experiments are performed on some standard UCI datasets. Experimental results demonstrate the efficiency of our algorithm.     

基于邻域粗糙集的高维类不平衡数据在线流特征选择

在许多实际应用中,数据经常呈现高维不平衡特征,特征还根据需求在不同时间段动态生成.基于此种情况,文中提出基于邻域粗糙集的高维类不平衡数据的在线流特征选择算法.算法设计基于小类重要度的粗糙依赖度计算公式,同时,提出在线相关性分析、在线冗余度分析、在线重要度分析三种策略,用于选择在大类和小类之间具有高可分离性的特征.在7个高维类不平衡数据集上的实验表明,文中算法可以有效选择一个较好的特征子集,性能较优.     

Supervised hybrid feature selection based on PSO and rough sets for medical diagnosis

Medical datasets are often classified by a large number of disease measurements and a relatively small number of patient records. All these measurements (features) are not important or irrelevant/noisy. These features may be especially harmful in the case of relatively small training sets, where this irrelevancy and redundancy is harder to evaluate. On the other hand, this extreme number of features carries the problem of memory usage in order to represent the dataset. Feature Selection (FS) is a solution that involves finding a subset of prominent features to improve predictive accuracy and to remove the redundant features. Thus, the learning model receives a concise structure without forfeiting the predictive accuracy built by using only the selected prominent features. Therefore, nowadays, FS is an essential part of knowledge discovery. In this study, new supervised feature selection methods based on hybridization of Particle Swarm Optimization (PSO), PSO based Relative Reduct (PSO-RR) and PSO based Quick Reduct (PSO-QR) are presented for the diseases diagnosis. The experimental result on several standard medical datasets proves the efficiency of the proposed technique as well as enhancements over the existing feature selection techniques.     

基于最大决策边界的高维类不平衡数据在线流特征选择

数据的特征空间常随时间动态变化,而训练样本的数量固定不变,数据的特征空间在呈现超高维特点的同时通常伴随决策空间的类别不平衡问题.对此,文中提出基于最大决策边界的高维类不平衡数据在线流特征选择算法.借助邻域粗糙集模型,在充分考虑边界样本影响的基础上, 定义自适应邻域关系,设计基于最大决策边界的粗糙依赖度计算公式.同时,提出三种在线特征子集评估指标,用于选择在大类和小类之间具有强区分能力的特征.在 11 个高维类不平衡数据集上的实验表明,在相同的实验环境及特征数量下,文中算法综合性能较优.     

基于粗糙集相对分类信息熵和粒子群优化的特征选择方法

特征选择是指从初始特征全集中,依据既定规则筛选出特征子集的过程,是数据挖掘的重要预处理步骤。通过剔除冗余属性,以达到降低算法复杂度和提高算法性能的目的。针对离散值特征选择问题,提出了一种将粗糙集相对分类信息熵和粒子群算法相结合的特征选择方法,依托粒子群算法,以相对分类信息熵作为适应度函数,并与其他基于进化算法的特征选择方法进行了实验比较,实验结果表明本文提出的方法具有一定的优势。     

Spark下的分布式粗糙集属性约简算法

属性约简（特征选择）作为数据预处理的重要环节,大多以属性依赖作为筛选属性子集的标准。设计了一种快速依赖计算方法FDC,通过直接寻找基于相对正域的对象来计算依赖度,而不需要预先求出相对正域,相比传统方法在速度上有明显的性能提升。另外,改进鲸鱼优化算法（WOA）使其能够有效应用于粗糙集属性约简。结合上述两个方法,提出一种基于Spark的分布式粗糙集属性约简算法SP-WOFRST,并在两组人工合成的大数据集上与另一种基于Spark的粗糙集属性约简算法SP-RST进行对比实验。实验结果表明所提出的SP-WOFRST算法在精度和速度上均优于SP-RST。