# Performance Evaluation of Sequential Rule Mining Algorithms
## 1 Introduction  
There is a fundamental issue in extracting useful information from the temporal relations in large sequence datasets. It helps a user to acquire useful knowledge for making a prediction. Many methods are emerging for finding the temporal relations in datasets. One of the foremost popular methods is mining sequential patterns to discover, as often as possible, patterns in sequence datasets [1, 2]. Mining sequential patterns rely on one measure called support measure. The support measure means the number of presence items in a dataset. It can be misleading and inadequate for making a prediction. Mining sequential rules is an extension of sequential patterns mining that addresses the previous problem by considering additional measures [3, 4]. Mining sequential rules take another measure besides the support into consideration, called the confidence measure, which means that the probability of executing the next pattern is calculated. There are many challenges for mining sequential rules, such as classifying similar rules differently. Additionally, some rules have been discovered that lose their importance when appearing separately. Therefore, particular rules are losing their use in predicting. All previous reasons impact the generation of a large number of redundant rules that affect the efficiency of the mining process. Numerous analysts have proposed upgraded methods of sequential rule mining (SRM) to decrease redundant rules andprogress the proficiency of these algorithms. SRM is divided into two categories: partially ordered and standard sequential rules. The proposed enhanced algorithms concentrate on two directions:  
The first type is a common type for mining the sequential rules named standard. It helps to enhance efficiency through the process of mining. The mining process consists of two procedures; the first is mining sequential patterns that appear frequently. The second is producing sequential rules that rely on the first procedure. Therefore, numerous researchers give consideration to the first procedure to enhance the performance through disposing of grouping that does not affect the ultimate result. Mining closed sequential patterns is an example of the previous idea. It helps to produce rules based on more compact data. In this study, we make a reference to this type with the non-redundant dynamic bit-vector algorithm. The second type is the newest type for mining the sequential rules named partially ordered rules. It helps to enhance efficiency by extending the mining of sequential rules algorithms by adding constraints or by finding a specified number of the most visit rules in a database. In the partially ordered mining, there is no arrangement between items in the prior and posterior sides. The pattern growth approach is applied to discover all rules incrementally. There are improved algorithms that acknowledge an extra constraint to enhance the overall performance. The TRuleGrowth algorithm adds a window size parameter. It makes a difference to decrease the number of rules produced, as it diminishes the runtime, and diminished disk space is a prerequisite to store generating rules, so that users are able to analyze the rules in an easy manner. Additionally, we have another approach to produce non-redundant rules. We find the most frequent rules (the top-k) that achieved the minConf threshold. Therefore, we have only two parameters, K and minConf. Like the TNS algorithm, we did not take the minSup into consideration due to the difficulty of determining the valid values that suit each dataset's features. In this paper, we present a broad consider of two sorts of SRM: partially ordered and standard sequential rules. We study three algorithms named TRuleGrowth, TNS, and non-redundant with a dynamic bit-vector algorithm. All these algorithms generate non-redundant rules and we compare the results of their implementation to decide the most reasonable areas for each of them. We assess the final results according to these criteria: runtime, number of produced rules, and memory utilization.