区间值模糊Lukasiewicz蕴涵的研究

Lukasiewicz蕴涵是一个常用的重要蕴涵。在区间值模糊集合上给出了交并等几个运算的概念,证明了是有界格、分配格、完备格和有余格,其中,c>是有余格诱导的代数系统。重新构造了一种区间值模糊Lukasiewicz蕴涵,讨论了该蕴涵的正则、单调和代数等重要性质。     

基于Lukasiewicz三角模及其剩余蕴涵的模糊粗糙集

讨论基于Lukasiewicz三角模及其剩余蕴涵的模糊粗糙集模型,研究了相应模糊粗糙集的代数性质,证明了自反模糊关系下该模型中的下近似集构成一个模糊拓扑,且上、下近似算子恰为其闭包及内部算子。     

双论域下粗糙集数据约简方法研究

将变精度粗糙集理论与关系数据库理论相结合,分析了用关系数据库中常用的“连接”或“并”对两个信息系统（论域）作为对使用粗糙集理论进行分析时预处理操作可能带来的问题,提出了用“外连接”来替代“连接”运算;在此基础上给出了从外连接到数据泛化与数据补齐,再到使用变精度粗糙集模型进行分析的全过程,并给出了详细的约简实例。     

A data reduction approach for resolving the imbalanced data issue in functional genomics

Learning from imbalanced data occurs frequently in many machine learning applications. One positive example to thousands of negative instances is common in scientific applications. Unfortunately, traditional machine learning techniques often treat rare instances as noise. One popular approach for this difficulty is to resample the training data. However, this results in high false positive predictions. Hence, we propose preprocessing training data by partitioning them into clusters. This greatly reduces the imbalance between minority and majority instances in each cluster. For moderate imbalance ratio, our technique gives better prediction accuracy than other resampling method. For extreme imbalance ratio, this technique serves as a good filter that reduces the amount of imbalance so that traditional classification techniques can be deployed. More importantly, we have successfully applied our techniques to splice site prediction and protein subcellular localization problem, with significant improvements over previous predictors.     

基于数据约减的聚类有效性分析

聚类分析中利用有效性指标判断数据集的正确类数极易受到噪声数据、类之间分离性以及聚类算法的影响,所确定类数的正确性难以得到保证.为克服这个问题,以文献[1]中的数据约减方法为基础,对原数据集和约减后的数据集利用有效性指标进行正确类数判别.实验表明:该方法能增大类之间的分离性,有效判断数据集的最优类数.     

基于概念格的图像特征数据降维*

高维图像特征数据不利于图像数据挖掘。为了降低图像特征数据维数,提出了基于概念格的降维算法,该算法将图像的HSV颜色特征转换为图像形式背景,再对背景的概念格进行属性约简。实验结果表明,该降维方法比较有效,并且较主成分分析具有明显的优势。     

A global clustering approach to point cloud simplification with a specified data reduction ratio

This paper studies the problem of point cloud simplification by searching for a subset of the original input data set according to a specified data reduction ratio (desired number of points). The unique feature of the proposed approach is that it aims at minimizing the geometric deviation between the input and simplified data sets. The underlying simplification principle is based on clustering of the input data set. The cluster representation essentially partitions the input data set into a fixed number of point clusters and each cluster is represented by a single representative point. The set of the representatives is then considered as the simplified data set and the resulting geometric deviation is evaluated against the input data set on a cluster-by-cluster basis. Due to the fact that the change to a representative selection only affects the configuration of a few neighboring clusters, an efficient scheme is employed to update the overall geometric deviation during the search process. The search involves two interrelated steps. It first focuses on a good layout of the clusters and then on fine tuning the local composition of each cluster. The effectiveness and performance of the proposed approach are validated and illustrated through case studies using synthetic as well as practical data sets.     

基于二叉树搜索空间缩减的测试数据生成

为了减小适应度函数计算量, 提高测试数据自动生成效率, 提出一种基于二叉树表示的搜索空间数据缩减方法。利用二叉树编码, 记录全空间中的覆盖路径和路径长度; 将目标路径和测试路径长度进行对比, 去除路径长度相差较大的路径; 利用遗传算法生成测试数据并同已有两种方法进行比较。实验结果表明, 在保证软件测试数据正确生成的情况下, 该方法在进化代数和运行时间上有明显优势, 生成测试数据效率高。     

A note on variable threshold concept lattices: Threshold-based operators are reducible to classical concept-forming operators

The present paper deals with formal concept analysis of data with fuzzy attributes. We clarify several points of a new approach of [S.Q. Fan, W.X. Zhang, Variable threshold concept lattice, Inf. Sci., accepted for publication] which is based on using thresholds in concept-forming operators. We show that the extent- and intent-forming operators from [S.Q. Fan, W.X. Zhang, Inf. Sci., accepted for publication] can be defined in terms of basic fuzzy set operations and the original operators as introduced and studied e.g. in [R. Belohlavek, Fuzzy Galois connections, Math. Logic Quarterly 45 (4) (1999) 497-504; R. Belohlavek, Concept lattices and order in fuzzy logic, Ann. Pure Appl. Logic 128 (2004) 277-298; S. Pollandt, Fuzzy Begriffe, Springer-Verlag, Berlin/Heidelberg, 1997]. As a consequence, main properties of the new operators from [S.Q. Fan, W.X. Zhang, Inf. Sci., accepted for publication], including the properties studied in [S.Q. Fan, W.X. Zhang, Inf. Sci., accepted for publication], can be obtained as consequences of the original operators from [R. Belohlavek, 1999; R. Belohlavek, 2004; S. Pollandt, 1997].     

数据维数消减方法研究

对高维数据集合的维数消减方法及其应用进行了分类研究.将数据维数消减方法主要分为两类：子集选择法和数据变换法.基于统计数学和现有的数据挖掘模型,给出了这两类中的一些典型的维数消减方法,并对这些方法的主要特性和有效应用进行了分析、探讨,给出了一些可行的方法实现策略.     

基于非平衡数据下不完备混合型信息系统的属性约简

完备混合型信息系统下的粗糙集模型是传统粗糙集模型的重要扩展,目前关于非平衡数据属性约简的研究仅限于完备混合型的粗糙集模型。针对这一问题,提出一种基于不完备混合型信息系统的非平衡数据属性约简。本文首先将传统的粗糙集模型进行推广,提出不完备混合型信息系统下的粗糙集模型;然后针对数据的非平衡性,根据上下边界区域和类分布的不均匀性定义了一种新的属性重要度;在基于区别矩阵的基础上设计出一种非平衡数据的属性约简算法。实验分析表明该算法针对不完备非平衡数据的属性约简具有一定的有效性和优越性。     

基于分层向量距离的实时多媒体数据挖掘模型

论文构造了一个实时多媒体数据挖掘模型,提出了一种原始视频数据进行数据挖掘的新机制,主要采用分层向量距离来进行动态可控序列分析分割、段内特征提取,使用粒子群K均值进行段间聚集,在一定程度上,解决了多媒体数据挖掘各方面的特殊要求。挖掘模型中各个部分与提出的技术相结合,基本上能满足实时情况下处理原始视频数据的要求。     

基于块非负稀疏重构嵌入的高光谱数据降维

为了在充分利用高光谱信息的同时减少因数据冗余带来的分类精度降低,提出一种块非负稀疏重构嵌入降维算法。首先,将传统超完备字典转化成超完备块字典;然后,通过计算每个超完备块字典对应样本的最小重构误差,得到块非负稀疏重构权重矩阵;最后,在低维嵌入时,通过同时最小化局部和最大化非局部高光谱数据的非负稀疏信息,得到全局最优的低维子空间高光谱数据。通过3组高光谱数据的实验结果验证了所提出方法的可行性和有效性。     

基于核主成分分析的数据流降维研究

分析了数据流降维算法PCA和KPCA的原理和实现方法。针对在大型数据集上PCA线性降维无法有效实现降维且KPCA的降维效率差,提出了一种新的降维策略GKPCA算法。该算法将数据集先分组,对每一组执行KPCA,然后过滤重新组合数据集,再次应用KPCA算法,达到简化样本空间,降低了时间复杂度和空间复杂度。实验分析表明,GKPCA算法不仅能取得良好的降维效果,而且时间消耗少。     

基于用户兴趣度的数据归约效果评估方法

面对特定数据归约方案,不同的用户对归约效果具有不同的评价,针对目前数据归约效果评估方法缺乏针对性、忽视用户个性化需求的问题,基于现有的指标体系,提出基于用户兴趣度的数据归约效果评估方法。通过定义用户兴趣度的权重子空间,根据用户对数据集归约方案评价的历史数据计算用户对指标的偏好,利用蒙特卡洛仿真近似计算出用户对数据归约效果的可接受程度作为评估归约效果的参数,实现面向不同用户的数据归约效果评估方法,为面向不同关注点的系统用户推荐不同数据归约方案提供定量依据。     

A robust optimization approach for imprecise data envelopment analysis

Crisp input and output data are fundamentally indispensable in traditional data envelopment analysis (DEA). However, the input and output data in real-world problems are often imprecise or ambiguous. Some researchers have proposed interval DEA (IDEA) and fuzzy DEA (FDEA) to deal with imprecise and ambiguous data in DEA. Nevertheless, many real-life problems use linguistic data that cannot be used as interval data and a large number of input variables in fuzzy logic could result in a significant number of rules that are needed to specify a dynamic model. In this paper, we propose an adaptation of the standard DEA under conditions of uncertainty. The proposed approach is based on a robust optimization model in which the input and output parameters are constrained to be within an uncertainty set with additional constraints based on the worst case solution with respect to the uncertainty set. Our robust DEA (RDEA) model seeks to maximize efficiency (similar to standard DEA) but under the assumption of a worst case efficiency defied by the uncertainty set and it’s supporting constraint. A Monte-Carlo simulation is used to compute the conformity of the rankings in the RDEA model. The contribution of this paper is fourfold: (1) we consider ambiguous, uncertain and imprecise input and output data in DEA; (2) we address the gap in the imprecise DEA literature for problems not suitable or difficult to model with interval or fuzzy representations; (3) we propose a robust optimization model in which the input and output parameters are constrained to be within an uncertainty set with additional constraints based on the worst case solution with respect to the uncertainty set; and (4) we use Monte-Carlo simulation to specify a range of Gamma in which the rankings of the DMUs occur with high probability.     

一种非相容决策表的属性值与属性约简方法*

针对非相容决策表,本文提出一种新的属性值约简与属性约简方法,与传统数据约简方法不同的是,本文方法考虑属性值约简与属性约简之间的关联,该方法首先进行属性值约简,然后进行属性约简。这种数据约简方法在属性值约简阶段不需要频繁地与引起非相容的个体集比较,在属性约简阶段也不需要频繁地判断非相容性是否是由于非相容性的个体集所引起的,本文所要做的仅仅是执行一次删除操作。本文并证明其正确性,分析了其时间复杂度与空间复杂度,本文方法是有效可行的。     

基于张开角测度的数据约简

数据约简是包括数据压缩、数据调整和特征提取在内的数据挖掘技术中的重要课题,但已有的数据约简方法主要聚焦在特征或者维度的约简,而针对样本个数的约简方法,往往是针对具体的数据集开发,缺乏一般性.针对数据集中数据分布的一般特征,定义一种新的基于张开角的测度.该测度能够区分数据集中核心对象和边界对象分布的本质区别,实现数据集中以核心对象为中心的数据压缩.通过对UCI公共测试平台上20个具有不同特征的典型样本集进行数据约简和测试,结果表明:约简能够有效地提取数据集中的核心目标;通过对约简前后数据集采用经典K均值算法聚类,发现约简后数据集中聚类正确率明显高于约简前数据集.     

基于改进多层次模糊关联规则的定量数据挖掘算法

针对单一层次结构实现规则提取具有规则提取准确性不高、算法运行时间长、难以满足用户使用需求的问题,提出一种基于改进多层次模糊关联规则的定量数据挖掘算法。采用高频项目集合,通过不断深化迭代的方法形成自顶向下的挖掘过程,整合模糊集合理论、数据挖掘算法以及多层次分类技术,从事务数据集中寻找模糊关联规则,挖掘出储存在多层次结构事务数据库中定量值信息的隐含知识,实现用户的定制化信息挖掘需求。实验结果表明,提出的数据挖掘算法在挖掘精度和运算时间方面相较于其他算法具有突出优势,可为多层次关联规则提取方法的实际应用带来新的发展空间。