In this paper, we propose an efficient algorithm, called FFP-Growth (shortfor fast FP-Growth) , to mine frequent itemsets. Similar to FP-Growth, FFP-Growth searches theFP-tree in the bottom-up order, but need not cons...In this paper, we propose an efficient algorithm, called FFP-Growth (shortfor fast FP-Growth) , to mine frequent itemsets. Similar to FP-Growth, FFP-Growth searches theFP-tree in the bottom-up order, but need not construct conditional pattern bases and sub-FP-trees,thus, saving a substantial amount of time and space, and the FP-tree created by it is much smallerthan that created by TD-FP-Growth, hence improving efficiency. At the same time, FFP-Growth can beeasily extended for reducing the search space as TD-FP-Growth (M) and TD-FP-Growth (C). Experimentalresults show that the algorithm of this paper is effective and efficient.展开更多
The Hausdorff dimensions of some refined irregular sets associated with β-expansions are determined for any β > 1. More precisely, Hausdorff dimensions of the sets {x ∈ [0, 1) :lim inf(n→∞) S_n(x, β)/n= α_1,...The Hausdorff dimensions of some refined irregular sets associated with β-expansions are determined for any β > 1. More precisely, Hausdorff dimensions of the sets {x ∈ [0, 1) :lim inf(n→∞) S_n(x, β)/n= α_1, lim sup (n→∞) S_n(x, β)/n= α_2}, α_1, α_2≥0 are obtained completely, where S_n(x, β) =sum ε_k(x, β) from k=1 to n denotes the sum of the first n digits of the β-expansion of x. As an application, we present another concise proof of that the set of points x ∈ [0, 1) satisfying lim_(n→∞) S_n(x,β)/n does not exist is of full Hausdorff dimension.展开更多
文摘In this paper, we propose an efficient algorithm, called FFP-Growth (shortfor fast FP-Growth) , to mine frequent itemsets. Similar to FP-Growth, FFP-Growth searches theFP-tree in the bottom-up order, but need not construct conditional pattern bases and sub-FP-trees,thus, saving a substantial amount of time and space, and the FP-tree created by it is much smallerthan that created by TD-FP-Growth, hence improving efficiency. At the same time, FFP-Growth can beeasily extended for reducing the search space as TD-FP-Growth (M) and TD-FP-Growth (C). Experimentalresults show that the algorithm of this paper is effective and efficient.
基金National Natural Science Foundation of China (Grant Nos. 11301473, 11411130372, 11201155 and 11371148)the Natural Science Foundation of Fujian Province (Grant No. 2014J05008)+2 种基金the Education Committee of Fujian Province (Grant No. JA13203)the Program for New Century Excellent Talents in Minnan Normal University (Grant No. MX13002)the Science and Technology Development Fund of Macao (Grant No. 069/2011/A)
文摘The Hausdorff dimensions of some refined irregular sets associated with β-expansions are determined for any β > 1. More precisely, Hausdorff dimensions of the sets {x ∈ [0, 1) :lim inf(n→∞) S_n(x, β)/n= α_1, lim sup (n→∞) S_n(x, β)/n= α_2}, α_1, α_2≥0 are obtained completely, where S_n(x, β) =sum ε_k(x, β) from k=1 to n denotes the sum of the first n digits of the β-expansion of x. As an application, we present another concise proof of that the set of points x ∈ [0, 1) satisfying lim_(n→∞) S_n(x,β)/n does not exist is of full Hausdorff dimension.
