# Mining Top-\(k\) High Average-Utility Sequential Patterns for Resource Transformation
###### Abstract
For instance, when designing a general model or analyzing a new database, users are often unaware of the distribution of utilities and the total number of sequences, so they must try different threshold parameters and execute the algorithm multiple times until they obtain a desirable result. If the threshold is specified too low, many HUSPs with redundant and unimportant information may be discovered. Conversely, if the threshold value is set too high, the number of captured HUSPs may not provide sufficient information. Additionally, fine-tuning the threshold extraction process is time-consuming. However, in many practical applications, stakeholders are more interested in identifying the top profitable patterns rather than hundreds of thousands of results. The top-\(k\) HUSPM was proposed to handle this problem [30], which was desired to specify the number of patterns instead of the minimum utility threshold. It draws inspiration from the top-\(k\) HUIM [31]and top-\(k\) SPM [32]. The objective of the top-\(k\) HUSPM is to select patterns with the top-\(k\) highest utilities from a sequential database. Some preliminary studies [33] were conducted to capture top-\(k\) HAUI in the transaction database. However, research in this area is still in its early stages, and these strategies are not applicable to sequential databases. The approach proposed by [PERSON] et al. was limited to specific cases where each item can occur only once [34]. [PERSON] et al. [35] proposed the algorithm EHAUSM to identify HAUSP. However, there is a gap between the over-estimation of utility, which is calculated by the total sequence utility or the maximum item utility, and the actual utility, with the former being consistently higher. Furthermore, the proposed upper bounds, which are similar to those in HAUPM, require a set number of items with the highest utility in the rest of the sequence through multiple sorting. To address these challenges and to improve performance and scalability, we formulate the problem of top-\(k\) HAUSPM and propose a novel algorithm named TKAUS. The main contributions could be summarized as follows:  
* By considering the HUSPM and the HAUIM, the concept of TKAUS is addressed, and the problem of top-\(k\) HAUSPM is formulated. To quickly increase the minimum average-utility threshold, we investigate the sequence average-utility-raising (SAUR) strategy. * Based on the widely accepted definition of high average utility, a novel algorithm with utility upper bounds and corresponding pruning strategies is designed for mining HAUSP. The proposed approach not only takes into account the actual utility of prefixes but also avoids extra sorting processing. * Comprehensive experiments demonstrate that the proposed algorithm TKAUS performs excellently for top-\(k\) HAUSPM, particularly in terms of execution time, unpromising candidate filtering, memory usage, and scalability. The remainder of this paper is organized as follows. Section 2 briefly reviews various related work. In Section 3, we provide definitions and formulate the top-\(k\) HAUSPM problem. Section 4 presents our proposed TKAUS algorithm, including data structures and several strategies. Section 5 presents experimental results and evaluates the performance of our proposed algorithm. Finally, in Section 6, we provide a summary and discuss future work.