A FAST ALGORITHM FOR COMPUTING SAMPLE ENTROPY

2011 ◽  
Vol 03 (01n02) ◽  
pp. 167-186 ◽  
Author(s):  
YING JIANG ◽  
DONG MAO ◽  
YUESHENG XU
Keyword(s):  
Time Series ◽  
Data Structure ◽  
Fast Algorithm ◽  
Time Complexity ◽  
Computing Time ◽  
Sample Entropy ◽  
Computational Costs ◽  
Tree Data ◽  
Input Time ◽  
Tree Data Structure

Sample entropy is a widely used tool for quantifying complexity of a biological system. Computing sample entropy directly using its definition requires large computational costs. We propose a fast algorithm based on a k-d tree data structure for computing sample entropy. We prove that the time complexity of the proposed algorithm is [Formula: see text] and its space complexity is O(N log N), where N is the length of the input time series and m is the length of its pattern templates. We present a numerical experiment that demonstrates significant improvement of the proposed algorithm in computing time.

A Scalable Algorithm for Constructing Frequent Pattern Tree

2014 ◽  
Vol 10 (1) ◽  
pp. 42-56 ◽  
Author(s):  
Zailani Abdullah ◽  
Tutut Herawan ◽  
A. Noraziah ◽  
Mustafa Mat Deris
Keyword(s):  
Data Structure ◽  
Frequent Pattern ◽  
Frequent Patterns ◽  
Scalable Algorithm ◽  
Tree Construction ◽  
Frequent Pattern Tree ◽  
Support Threshold ◽  
Benchmark Datasets ◽  
Tree Data ◽  
Tree Data Structure

Frequent Pattern Tree (FP-Tree) is a compact data structure of representing frequent itemsets. The construction of FP-Tree is very important prior to frequent patterns mining. However, there have been too limited efforts specifically focused on constructing FP-Tree data structure beyond from its original database. In typical FP-Tree construction, besides the prior knowledge on support threshold, it also requires two database scans; first to build and sort the frequent patterns and second to build its prefix paths. Thus, twice database scanning is a key and major limitation in completing the construction of FP-Tree. Therefore, this paper suggests scalable Trie Transformation Technique Algorithm (T3A) to convert our predefined tree data structure, Disorder Support Trie Itemset (DOSTrieIT) into FP-Tree. Experiment results through two UCI benchmark datasets show that the proposed T3A generates FP-Tree up to 3 magnitudes faster than that the benchmarked FP-Growth.

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