## 5 Conclusions  
The multiplication of SpMV is ranked among the most significant and extensively utilized scientific kernels that arise in various scientific problems, such as computer graphics or computer vision, problems in robotics, 3D and 2D problems, acoustic problems, research in the surgical field, thermodynamics problems, medical care, and tissues. Several engineering, economic, social, and scientific projects require solutions to sparse linear equation  
Figure 17: Performance gain random forest with important features (**A**) and execution time comparison (**B**) with important features (test Set).  
systems. Some common exemplary applications are thermodynamics problems, computer graphics, robotics, life sciences, research, smart phones, computer work, transportation, social media analytics, and autonomous vehicles. Therefore, SpMV is considered to be the most vital and time-taking kernel for iterative solutions of sparse linear equation systems. The performance of SpMV calculation is affected by a series of factors. Among these categories, some common factors are matrix properties, storage format, and operation of hardware and software platforms. Improvement in the application performance is always a challenge when dealing with multicore architectures because of the diversity and heterogeneity of these architectures. Over the years, numerous sparse matrix storage formats have been proposed and are highly dependent on the structure of the matrix. BCSR is considered to be the most promising one because it reduces the indexing structure to store sparse matrices.  
In this paper, we proposed a machine learning-based performance optimization of SpMV on the underlying shared memory architecture. We exploited the structure of matrices by extracting relevant features and predicting the optimal block size for SpMV computation. To achieve this, we utilized nearly 700 real-world matrices associated with 43 application domains. We used five different base and ensemble machine learning methods, including gradient boosting, decision tree, random forest, ridge regressor, and AdaBoost. DT showed the lowest MAE, while RF showed the lowest RME among all feature sets. Our proposed tool, AAQAL, achieved an ideally attainable performance of almost 93.5%. The difference between the random selection of block sizes and our proposed tool is approximately 40% against the ideally achievable performance. The manual process on hit and trial basis for the optimal block size is time consuming and error prone.  
In the future, we will enhance the proposed approach by incorporating different learning models, adding more features with low computation complexity and increasing the dataset size, both in terms of size and dimensionality. The proposed methodology requires some modifications to cater more complex scenarios, i.e., variable size blocking, decomposition method (to avoid padding), etc. Currently we are working on improving the proposed methodology to minimize format conversion and features extraction cost by incorporating features that requires low preprocessing. We are also planning to extend our proposed methodology to a distributed memory environment with hybrid MPI/OpenMP programming models.  
Funding acquisition, A.M.A.; Investigation, K.A.A.; Methodology, M.A.; Project administration, M.U.A.; Resources, N.A.S.; Supervision, S.U.; Visualization, A.A.B. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia, under Grant No. (RG-11-611-43).  
Not applicable.  
This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia, under Grant No. (RG-11-611-43). The authors therefore, gratefully acknowledge DSR technical and financial support. We would like to thanks also the all the helping bodies from Leads, GCWUS, and Grand Asian University for assisting us to carry out this research work.  
The authors declare no conflict of interest.