基于邻域信息熵度量数值属性快速约简算法

阐述邻域粗糙集和邻域信息熵的基本定义及性质,为避免数值属性信息系统属性约简过程中,属性离散化造成特征信息的丢失,提出一种新的基于邻域信息熵度量数值属性约简算法。扩展邻域信息系统核属性集生成约简属性集,邻域信息熵度量不仅关注约简属性集正域变化,而且考察负域样本空间约简属性邻域等价类在决策属性划分的分布,具备更好的邻域关系度量细粒度。实验表明,对比邻域粗糙集近似度量、邻域有效信息率度量、邻域软间隔度量的属性约简方法,该算法能有效进行邻域信息系统属性约简的同时,也保持了约简属性集更好的分类精度。     

基于邻域粗糙集组合度量的混合数据属性约简算法

属性约简是一种重要的数据挖掘方法。为了对混合型信息系统达到更好的属性约简性能,提出一种邻域组合度量的启发式属性约简算法。邻域依赖度是构造混合信息系统属性约简的常用方法,根据粒计算的视角,在混合信息系统中提出邻域知识粒度用于评估属性的粒化能力。将邻域依赖度与邻域知识粒度进行结合,提出混合信息系统下的邻域组合度量,并将该度量方法作为启发式函数,提出一种属性约简算法。实验分析表明,该算法比混合信息系统的其他相关属性约简算法具有更高的约简性能。     

基于邻域粒化的数值信息系统的知识约简

数值信息系统在实际生活中有很广的应用。基于邻域粒化的思想,提出了数值信息系统上的分布约简,分配约简和规则约简,同时给出了邻域关系上的近似分类精度等概念。最后通过区间化的形式描述了决策规则的获取方法,这是对Pawlak知识发现的推广。     

混合不完备数据的新型双邻域粗糙集分类方法

针对混合不完备数据集,提出了一种新型双邻域粗糙集分类方法。首先,定义一个无参数的邻域联系度距离,并建立基于无参数邻域联系度距离的双邻域粗糙集模型;其次,基于所构建的模型,给出基于覆盖约简的双邻域粗糙集规则约简方法,获得约简后的上近似规则集和下近似规则集;再次,基于约简后的上、下近似规则集,给出最近邻分类方法;最后,取7个UCI公共测试集做实验分析,通过与混合距离HEOM、带参数邻域联系度距离的双邻域粗糙集分类方法对比,结果表明提出的分类方法仍然取得了优异的分类效果,其突出的优势是不再需要通过大量实验来确定其参数值。     

基于集值决策属性的集值信息系统

定义了决策属性也是集合子集的集值决策信息系统,给出了基于集值决策属性的协调集值决策信息系统的定义,得到了协调集值决策信息系统属性约简的判定定理和辨识矩阵,并讨论了在属性约简中起不同作用的属性分类及其特征。定义了不协调集值决策信息系统的分配协调集,给出了基于集值决策属性的不协调集值决策信息系统属性约简的方法。     

基于邻域粒化的数值信息系统的知识约简

数值信息系统在实际生活中有很广的应用.基于邻域粒化的思想,提出了数值信息系统上的分布约简,分配约简和规则约简,同时给出了邻域关系上的近似分类精度等概念.最后通过区间化的形式描述了决策规则的获取方法,这是对Pawlak知识发现的推广.     

集值信息系统基于变精度相容关系的知识约简

借助于属性集值的相似程度在集值信息系统上定义了一种变精度相容关系,给出了这种变精度相容关系下目标协调集值信息系统的知识约简与判定,并讨论了相容水平对目标协调集值信息系统的知识约简的影响。     

集值决策信息系统的知识约简与属性特征

本文定义了集值决策信息系统中的一种新的关系,给出了在这种关系下协调集值决策信息系统属性约简的判定定理和辨识矩阵,从而得到了知识约简的具体操作方法,并讨论了在属性约简中起不同作用的属性分类及其特征。定义了不协调集值决策信息系统的分配协调集,给出了一种将不协调集值决策信息系统转化为广义协调近似空间的方法,并证明了不协调集值决策信息系统的分配协调集就是广义协调近似表示空间的协调集。     

基于扩展容差关系的不完备信息系统属性约简

针对当前的邻域粗糙集多用于处理完备的信息系统,而非不完备的信息系统这一问题,提出了一种可用于处理不完备混合信息系统的扩展容差关系,并给出相关定义,使用容差完备度和邻域阈值作为限制条件计算扩展容差邻域,以此邻域为基础选择决策正域得到系统的属性重要性,并以该重要性作为启发因子给出基于扩展容差关系的属性约简算法。采用UCI数据集中的7组不同类型的数据集进行仿真实验,并分别与扩展邻域关系（EN）、容差邻域熵（TRE）、邻域粗糙集（NR）的方法进行比较,实验结果表明,该方法在保证分类精度的同时能够约简得到更少的属性。最后讨论了在扩展容差关系中改变邻域阈值对分类精度产生的影响。     

混合值不完备决策信息系统的粗糙分类方法

针对混合值不完备决策信息系统,提出一种将邻域联系度粗糙集与贝叶斯理论相结合的分类方法。定义了一种新的属性辨识矩阵——同异反辨识矩阵,给出了基于同异反辨识矩阵的t分配约简算法,以及对约简后的决策信息系统建立基于邻域联系度粗糙集的最小错误率贝叶斯决策准则,用于对含有混合属性值以及不完备数据的对象进行分类。实验表明所提出的方法是客观有效的。     

Multi-label feature selection based on neighborhood mutual information

Multi-label learning deals with data associated with a set of labels simultaneously. Like traditional single-label learning, the high-dimensionality of data is a stumbling block for multi-label learning. In this paper, we first introduce the margin of instance to granulate all instances under different labels, and three different concepts of neighborhood are defined based on different cognitive viewpoints. Based on this, we generalize neighborhood information entropy to fit multi-label learning and propose three new measures of neighborhood mutual information. It is shown that these new measures are a natural extension from single-label learning to multi-label learning. Then, we present an optimization objective function to evaluate the quality of the candidate features, which can be solved by approximating the multi-label neighborhood mutual information. Finally, extensive experiments conducted on publicly available data sets verify the effectiveness of the proposed algorithm by comparing it with state-of-the-art methods.     

Neighborhood systems and approximate retrieval

An approximate retrieval model is proposed based on the notion of neighborhood systems. The knowledge used in the model consists of an information table, in which each object is represented by its values on a finite set of attributes, and neighborhood systems on attribute values, which provide semantic similarity or closeness of different values. An information table can be used for exact retrieval. With the introduction of neighborhood systems to information tables, one is able to perform approximate retrieval. Operations on neighborhood systems are introduced based on power algebras. An ordering relation representing the information of a neighborhood system is suggested and examined. Approximate retrieval is carried out by the relaxation of the original query using neighborhood systems, and the combination of intermediate results using neighborhood system operations. The final retrieval results are presented according to the proposed ordering relation. In contrast to many existing systems, a main advantage of the proposed model is that the retrieval results are a non-linear ordering of objects.     

邻域信息系统基于同态的数据压缩

用同态的概念作为处理部域信息系统中数据压缩的工具。给出了部域信息系统和诱导的部域信息系统概 念,并在此基础上定义了一种新的协调函数,研究了在同态映射下部域信息系统的一些重要性质,证明了原部域信息 系统与同态象部域信息系统约简的等价性,从而得到一种通过计算数据量较少的象信息系统的约简来对原系统进行 数据压缩的方法.     

Three-way decision reduction in neighborhood systems

Rough set reduction has been used as an important preprocessing tool for pattern recognition, machine learning and data mining. As the classical Pawlak rough sets can just be used to evaluate categorical features, a neighborhood rough set model is introduced to deal with numerical data sets. Three-way decision theory proposed by Yao comes from Pawlak rough sets and probability rough sets for trading off different types of classification error in order to obtain a minimum cost ternary classifier. In this paper, we discuss reduction questions based on three-way decisions and neighborhood rough sets. First, the three-way decision reducts of positive region preservation, boundary region preservation and negative region preservation are introduced into the neighborhood rough set model. Second, three condition entropy measures are constructed based on three-way decision regions by considering variants of neighborhood classes. The monotonic principles of entropy measures are proved, from which we can obtain the heuristic reduction algorithms in neighborhood systems. Finally, the experimental results show that the three-way decision reduction approaches are effective feature selection techniques for addressing numerical data sets.     

基于边界域的邻域知识距离度量模型

粗糙集的不确定性度量在知识获取中扮演着非常重要的角色。在邻域粗糙集理论中,当前不确定性度量方面的研究工作主要专注于度量单个知识空间的不确定性及其随粒度变化的单调性规律,其仍存在以下缺点:1)邻域粗糙集不确定性来自于邻域粒中属于目标概念的元素和不属于目标概念的元素,当前的方法没有同时考虑每个邻域信息粒的这两部分;2)不能反映不同知识空间对目标概念刻画能力的差异性;3)由于当前的知识距离包含了粒度划分的信息,已有方法在一些应用场合下不够准确,例如属性约简中的知识启发式搜索及其粒度选择。对此,文中首先构建了一种更加直观准确的邻域粗糙集的不确定性度量方法——邻域熵,并证明了不确定性度量随着粒度的细化具有单调性;为了反映不同邻域信息粒对目标概念刻画能力的差异性,提出了一种带近似描述能力的邻域粒距离,称为相对邻域粒距离,并介绍了它的相关性质;针对分层递阶的多粒度知识空间中的粒度选择问题,建立了基于边界域的邻域知识距离度量模型,该知识距离可以反映不同邻域知识空间对目标概念的刻画能力的差异性。     

一种基于邻域协同表达的分类方法

邻域粗糙集模型中,随着信息粒尺寸的增长,基于多数投票原则的邻域分类器(NC)容易对未知样本的类别产生误判。为了缓解该问题,在协同表达分类(CRC)思想的基础上,提出了一种基于邻域协同表达的分类方法,即邻域协同分类器(NCC)。NCC首先借助邻域粗糙集模型对分类学习任务进行特征选择,然后找出被选特征下未知样本的邻域空间,最后在邻域空间内采用协同表达来代替多数投票原则,找出与未知样本具有最小重构误差的类别作为预测的类别标记。在4组UCI数据集上的实验结果表明:1)与NC相比,所提NCC在大尺寸信息粒下获得了较为满意的分类效果;2)与CRC相比,所提NCC在保持良好分类精度的同时,极大地降低了字典样本的规模,进而提高了分类的效率。     

基于邻域粒化和遗传算法的数值型属性约简方法

针对现实中含有数值型属性的决策系统的约简问题,提出了基于邻域粒化和遗传算法的约简方法。该方法采用基于邻域等价关系建立的粗糙集模型,用邻域等价关系度量粗糙集不可分辨关系,通过邻域信息粒子逼近论域空间。构造了遗传约简算法,论述了遗传算法适应度函数的选择,设计了自适应交叉概率,给出了算法的具体实现。对经典数据集和UCI数据库中4个数据库约简的结果证明了算法的有效性和可行性。     

邻域系统层次结构的粗糙集刻画方法研究

以邻域系统为研究对象,根据邻域系统中邻域与目标之间的包含及相交关系,分析了两种不同类型的邻域系统粗糙集模型。根据这两种邻域系统粗糙集模型,分别提出了邻域系统层次单调变化的2套性质描述,并提出了2种拟序关系用以描述不同邻域系统之间的粗细关系。研究结果证明了这2种拟序关系与邻域系统层次单调变化的2套性质之间的对应关系。     

Heterogeneous object modeling through direct face neighborhood alteration

Two recent advances—the use of functionally gradient materials in parts and layered manufacturing technology—have brought to the forefront the need for design and fabrication methodologies for heterogeneous objects. However, current solid modeling systems, a core component of computer-aided design and fabrication tools, are typically purely geometry based, and only after the modeling of product geometry, can a part's non-geometric attributes such as material composition be modeled. This sequential order of modeling leads to unnecessary operations and over-segmented 3D regions during heterogeneous object modeling processes.

To enable an efficient design of heterogeneous objects, we propose a novel method, direct face neighborhood operation. This approach combines the geometry and material decisions into a common computational framework as opposed to separate and sequential operations in existing modeling systems. We present theories and algorithms for direction face neighborhood alteration, which enables direct alteration of face neighborhood before 3D regions are formed. This alteration is based on set membership classification (SMC) and region material semantics. The SMC is computationally enhanced by the usage of topological characteristics of heterogeneous objects. After the SMC, boundary evaluation is performed according to the altered face neighborhood. In comparison with other solid modeling methods, the direct face neighborhood alteration method is computationally effective, allows direct B-Rep operations, and is efficient for persistent region naming. A prototype system has been implemented to validate the method and some examples are presented.