# Mining Top-\(k\) High Average-Utility Sequential Patterns for Resource Transformation
## 4 Proposed TKAUS Algorithm
### Proposed TKAUS Algorithm
Moreover, note that when \(k=500\) on the Sign dataset, the search space of the top-\(k\) EHAUSM algorithm is far beyond the other two algorithms. Therefore, we do not show more experiments. The proposed algorithm will generate more candidates than TKUS with increasing parameter \(k\) in Figure 2c,d. The average length of the sequence and the maximal length of the sequence have great effects on HAUSPM. In addition, that is why the results of runtime have similar trends. ### Memory Overhead Evaluation

We can see from Figure 4 that TKAUS generally outperforms top-\(k\) EHAUSM and TKUS in terms of memory usage. Figure 3d,e clearly illustrates that both EHAUSM and

Figure 3: Number of candidates and threshold of top-\(k\) HAUSPs in different datasets. TKUS have more candidates than top-\(k\) EHAUSM in some cases. Although the gap is still obvious, the process of sorting brings more memory consumption in top-\(k\) EHAUSM. The more candidates are generated, the more sorting operations are needed. In TKUS, the threshold is the sum of utilities. It is harder to avoid generating the candidate, which consists of some low-utility items. This is different from top-\(k\) EHAUSM or TKAUS, and it will incur a high memory usage. Because of that, both EHAUSM and TKUS have good performance by adopting efficient strategies, but TKAUS has greater improvement. Likewise, the memory consumption becomes larger when the parameter \(k\) increases. ### Scalability Evaluation

The scalability of TKAUS is evaluated in this part. The series of datasets with varying sizes is built by combining the duplication of dataset Scalability_10k repeatedly. The experimental results, including execution time, memory consumption, and the number of candidates with \(k=500\), are depicted in Figure 5. The runtime increases linearly as the database size grows. The increase in memory consumption is likewise linear. The number of candidates keeps a constant value. It means that variations in dataset size did not cause significant volatility or anomalies in algorithm efficiency based on the experimental results. This supports the idea that the proposed method can provide relatively stable performance

Figure 4: Memory usage for various \(k\) in different dataset. when processing datasets of diverse magnitudes. According to the experiments, the proposed TKAUS shows a better scalability performance. ### Limitations

The experimental results presented in the preceding sections highlight the varying degrees of efficiency advantages exhibited by the proposed algorithm across datasets with diverse features. Although both the proposed method and the compared algorithms are capable of handling datasets of the same type, the efficiency advantages may differ when applied to datasets with different characteristics, e.g., the dataset Sign and Yoochoose. The efficiency of the algorithm is significantly influenced by the specific characteristics of the datasets. Although the experimental section includes discussions of six commonly used datasets with diverse features, it is important to acknowledge that the quantity and characteristics of the experimental datasets do not encompass the entire spectrum. Furthermore, the experimentation parameter \(k\) has limited values, allowing for only a partial representation of trends. The proposed algorithm is motivated by fundamental aspects of the research problem and identified optimization potential in existing algorithms. However, it demonstrates notable advantages in terms of algorithm efficiency. The computation of average-utility upper bounds remains somewhat complex. This complexity leaves room for further research to propose even more superior algorithms in this regard. In addition, as research on SPM and the transformation of typified resources within DIKWP structures progresses, it is expected that additional relevant factors will be identified and considered. This will necessitate further studies to enhance and potentially adjust existing algorithms accordingly.