# Mining Top-\(k\) High Average-Utility Sequential Patterns for Resource Transformation
###### Abstract
This frequent-oriented framework fails to consider the intrinsic value of individual items and does not capture the uniqueness of patterns. As is well known, the main task of retail business is to make more profits than sales. To overcome this problem, the relative importance of items was considered [12,13]. By incorporating the concept of utility, high-utility pattern mining (HUPM) [14] was introduced within a utility-oriented framework [15,16]. HUPM focuses on discovering patterns with high utility values in non-binary databases [17,18]. The utility value of an item is determined by multiplying its internal utility (which represents its quantity) by its external utility (which represents its unique value). Sequential patterns based on pattern frequency do not always correspond to the purpose of analysis, such as selling quantity and profit. Therefore, the SPM methods do not always provide sufficient information to support the decisions of stakeholders. The obvious contrast is between luxury goods and everyday supplies. Since each item in the sequential database is accompanied by a timestamp, traditional high-utility itemset mining (HUIM)methods are unable to effectively address this aspect. To tackle this issue, HUSPM [19, 20] has been developed in the field of knowledge discovery in databases. It could be applied to various scenarios [21]. In HUSPMA, a quantitative sequence database has been defined to represent the relative importance of patterns. In the context of retail business, the number of intelligent appliances or batteries purchased by a customer in a single visit is considered to be internal utility, reflecting the number of item occurrences. The unit profit of intelligent appliances or batteries is generally defined as external utility, indicating the relative importance of the item. The main task of HUSPM is to discover high-utility sequential patterns (HUSPs), which are subsequences with high utility values. Researchers have proposed many efficient algorithms for mining HUSPs [22, 23], such as designing efficient pruning strategies and incorporating novel data structures. Notably, compared to SPM and HUIM, HUSPM takes into account the chronological ordering of items and their associated utility values [24]. Although HUSPM can overcome some disadvantages of SPM and HUIM, there are still some typical challenging problems in HUSPM. The utility of a combined pattern is determined by the sum of the utilities of subpatterns constituting this combined pattern. Therefore, as the number of combined subpatterns increases, the length of the pattern also increases, leading to a higher utility value. This implies that a longer pattern has an advantage over a shorter one in terms of being a high-utility pattern. As the pattern length increases and the number of subpatterns grows, the association rules between these patterns become more difficult to comprehend [25]. Therefore, [PERSON] et al. proposed the average-utility measurement, which offers a more comprehensive assessment of itemset utility [26]. The high average-utility itemset (HAUI) mining approach [27, 28] is designed to extract patterns with high average-utility value by considering both the utility of the pattern and its length [28, 29]. In this way, it is more objective to assess the utility of the pattern. A high average-utility pattern indicates that each item comprising the pattern has a high utility value. Consequently, patterns with long lengths and high utilities may not always qualify as high average-utility patterns. There is another limitation in HAUI and HUSP mining algorithms. In most cases, it is challenging to specify an appropriate value for the minimum utility threshold that ensures sufficient but not excessive itemset mining, particularly when they are unfamiliar with the features of the database.