This paper presents not only practical but also instructive mathematical models to simulate tree network formation using the Poisson equation and the Finite Difference Method (FDM). Then, the implications for entropic...This paper presents not only practical but also instructive mathematical models to simulate tree network formation using the Poisson equation and the Finite Difference Method (FDM). Then, the implications for entropic theories are discussed from the viewpoint of Maximum Entropy Production (MEP). According to the MEP principle, open systems existing in the state far from equilibrium are stabilized when entropy production is maximized, creating dissipative structures with low entropy such as the tree-shaped network. We prepare two simulation models: one is the Poisson equation model that simulates the state far from equilibrium, and the other is the Laplace equation model that simulates the isolated state or the state near thermodynamic equilibrium. The output of these equations is considered to be positively correlated to entropy production of the system. Setting the Poisson equation model so that entropy production is maximized, tree network formation is advanced. We suppose that this is due to the invocation of the MEP principle, that is, entropy of the system is lowered by emitting maximal entropy out of the system. On the other hand, tree network formation is not observed in the Laplace equation model. Our simulation results will offer the persuasive evidence that certifies the effect of the MEP principle.展开更多
挖掘最大频繁项目集是多种数据挖掘应用中的关键问题,之前的很多研究都是采用Apriori类的候选项目集生成-检验方法.然而,候选项目集产生的代价是很高的,尤其是在存在大量强模式和/或长模式的时候.提出了一种快速的基于频繁模式树(FP-tr...挖掘最大频繁项目集是多种数据挖掘应用中的关键问题,之前的很多研究都是采用Apriori类的候选项目集生成-检验方法.然而,候选项目集产生的代价是很高的,尤其是在存在大量强模式和/或长模式的时候.提出了一种快速的基于频繁模式树(FP-tree)的最大频繁项目集挖掘DMFIA(discover maximum frequent itemsets algorithm)及其更新算法UMFIA(update maximum frequent itemsets algorithm).算法UMFIA将充分利用以前的挖掘结果来减少在更新的数据库中发现新的最大频繁项目集的费用.展开更多
为了解决最大频繁项目集算法DMFIA(discover maximum frequent itemsets algorithm)在挖掘候选项目集维数较大而最大频繁项目集维数较小的情况下产生大量候选项目集的问题,提出一种改进的基于FP-Tree(frequent pattern tree)的最大频繁...为了解决最大频繁项目集算法DMFIA(discover maximum frequent itemsets algorithm)在挖掘候选项目集维数较大而最大频繁项目集维数较小的情况下产生大量候选项目集的问题,提出一种改进的基于FP-Tree(frequent pattern tree)的最大频繁项目集挖掘的FP-EMFIA算法;该算法在挖掘过程中根据项目头表,采用自上而下和自下而上的双向搜索策略,并通过条件模式基中的频繁项目和较小维数的非频繁项目集对候选项目集进行降维和剪枝,以减少候选项目集的数量,加速对候选集计数的操作。在经典数据集mushroom、chess和connect上的实验结果表明,FP-EMFIA算法在支持度较小时的时间效率优于DMFIA、IDMFIA(improved algorithm of DMFIA)和BDRFI(algorithm for mining frequent itemsets based on decreasing dimensionality reduction of frequent itemsets)算法的,说明FP-EMFIA算法在候选项目集维数较大时有相对优势。展开更多
Order Table FPMax是基于有序FP-tree结构和二维表的最大频繁模式挖掘算法.有序FP-tree结构可以减少空间的浪费.基于树结构的有序性,算法在挖掘数据时可以减少挖掘事务项的数量,加快挖掘效率.算法采用二维表存储挖据事务项的路径信息及...Order Table FPMax是基于有序FP-tree结构和二维表的最大频繁模式挖掘算法.有序FP-tree结构可以减少空间的浪费.基于树结构的有序性,算法在挖掘数据时可以减少挖掘事务项的数量,加快挖掘效率.算法采用二维表存储挖据事务项的路径信息及交集,采用相应的计算方法可以在不产生条件子树的情况下快速得到最大频繁项集,并避免没必要的挖掘过程减少超集检测,既减少了空间的浪费,又加快了执行效率.展开更多
文摘This paper presents not only practical but also instructive mathematical models to simulate tree network formation using the Poisson equation and the Finite Difference Method (FDM). Then, the implications for entropic theories are discussed from the viewpoint of Maximum Entropy Production (MEP). According to the MEP principle, open systems existing in the state far from equilibrium are stabilized when entropy production is maximized, creating dissipative structures with low entropy such as the tree-shaped network. We prepare two simulation models: one is the Poisson equation model that simulates the state far from equilibrium, and the other is the Laplace equation model that simulates the isolated state or the state near thermodynamic equilibrium. The output of these equations is considered to be positively correlated to entropy production of the system. Setting the Poisson equation model so that entropy production is maximized, tree network formation is advanced. We suppose that this is due to the invocation of the MEP principle, that is, entropy of the system is lowered by emitting maximal entropy out of the system. On the other hand, tree network formation is not observed in the Laplace equation model. Our simulation results will offer the persuasive evidence that certifies the effect of the MEP principle.
文摘挖掘最大频繁项目集是多种数据挖掘应用中的关键问题,之前的很多研究都是采用Apriori类的候选项目集生成-检验方法.然而,候选项目集产生的代价是很高的,尤其是在存在大量强模式和/或长模式的时候.提出了一种快速的基于频繁模式树(FP-tree)的最大频繁项目集挖掘DMFIA(discover maximum frequent itemsets algorithm)及其更新算法UMFIA(update maximum frequent itemsets algorithm).算法UMFIA将充分利用以前的挖掘结果来减少在更新的数据库中发现新的最大频繁项目集的费用.
文摘为了解决最大频繁项目集算法DMFIA(discover maximum frequent itemsets algorithm)在挖掘候选项目集维数较大而最大频繁项目集维数较小的情况下产生大量候选项目集的问题,提出一种改进的基于FP-Tree(frequent pattern tree)的最大频繁项目集挖掘的FP-EMFIA算法;该算法在挖掘过程中根据项目头表,采用自上而下和自下而上的双向搜索策略,并通过条件模式基中的频繁项目和较小维数的非频繁项目集对候选项目集进行降维和剪枝,以减少候选项目集的数量,加速对候选集计数的操作。在经典数据集mushroom、chess和connect上的实验结果表明,FP-EMFIA算法在支持度较小时的时间效率优于DMFIA、IDMFIA(improved algorithm of DMFIA)和BDRFI(algorithm for mining frequent itemsets based on decreasing dimensionality reduction of frequent itemsets)算法的,说明FP-EMFIA算法在候选项目集维数较大时有相对优势。
