# Incremental Algorithm for Association Rule Mining under Dynamic Threshold
## 1 Introduction  
This study addresses association rule mining (ARM), which refers to a widely known data mining technique. Data mining extracts useful patterns that are hidden in a huge database. The reckoned forms for the knowledge are a frequent pattern (frequent itemset) and a rule set. Nevertheless, acquiring hidden knowledge from a massive database is a complicated process [1]. Some of the proposed data mining strategies and techniques are ARM [2; 3; 4; 5; 6; 7; 8], classification rules [9; 10], clustering rules [8], and sequential patterns [11; 12]. The ARM, in particular, unravels correlations between various attributes (items) in transaction databases [2; 5; 6; 8; 13]. Applications of ARM include the market basket and a great deal of issues that demand discovery of hidden knowledge, such as protein sequences [14], medical diagnosis [14], energy [3; 15; 16], smart homes [11], and other vast industrial fields [17]. The Apriori algorithm has been acknowledged as an icon implementation for the ARMtechnique [11]. The Apriori algorithm generates a frequent itemset that is determined by testing the candidate itemsets. When an itemset within the candidate itemset has weight exceeding the minimum support threshold, it is considered as a frequent itemset. After generating all frequent itemsets, the association rules are retrieved from the gathered frequent itemsets. Since rules have confidence and a user defines the minimum confidence threshold, any rule with confidence exceeding its minimum level is considered as a strong rule set. Data mining is a highly attractive field and has become an even more popular topic amongst researchers since the introduction of ARM in the work carried out by [PERSON] (see [2; 13]). The data mining processes have been continually improved and developed by a substantial number of studies. In fact, a significant correlation has been established between ARM and other fields [6; 8], namely machine learning [18], association rule discovery, clustering rules [19; 20], classification rules [6; 19; 21], associative techniques [19], sequential patterns [21], and decision trees [22]. Amidst these, looking for common itemsets within a massive database has become a rather common method in data mining, where the preponderance of data mining techniques is associated with discovering frequent patterns, which serve as the main output for ARM. These techniques arrange the frequent itemsets and rules in a timely manner. Data mining has been implemented in the high business domain to increase its value, such as Internet of things and sensors [3]. One popular area in the domain of ARM refers to data stream and control of sensors [3]. The relationship between data mining and other artificial intelligence involving machines and network sensors is extendable, along with increasing opportunities [23]. Data representation and coverage may be insufficient when the mined knowledge is limited. Hence, the discovered knowledge typically encloses a set of rules. One feature of the discovered knowledge is that it should retain its validity when the database experiences nil change. However, the question that arises is: 'How does one extend the validity of knowledge with less processing time?' Precisely, knowledge represents the present state of the processed data with limited change in the data, inclusive of added, updated, or deleted transactions. The two commonly used approaches to maintain the legitimacy of knowledge are:  
1. Rediscovery of knowledge from scratch upon changed state of the database. 2. Consideration of the impact of change on the database in terms of knowledge. Upon database manipulation (adding, deleting, or updating transactions), the changes should be reflected in the elicited knowledge. While Apriori is the most common approach for ARM, other prominent algorithms do exist, such as Eclat [24], DHP [7], AprioriTID [25], McEclat [26], and MsApriori [5], which enhance collection of rare frequent items. Generally, the ARM process line mainly refers to the following two processes [13]:  
1.