## 8 Conclusions  
This study indicates that PCA can be used to reduce dimensionality by improving the accuracy of image classification with statistically weighted dimension features. The class weight that is used to provide variational information about the dataset's attributes is established using the statistically weighted dimensions. This idea, based on the distribution scheme by standard deviation for three types, is proposed in this study. These types include (1) collection-class (overview class) (**SDW**), (2) inter-class (between classes) (**ICSW**), and (3) intra-class (within a class) (**ACSW**). Three algorithms of image classification, (1) logistic regression, (2) KNN, and (3) SVM (RBF) are investigated on three datasets; MNIST, E-MNIST, and F-MNIST. The results fully indicate that our scheme (SWD-PCA) outperforms the conventional BASE-LINE algorithm by **ICSW** on the promoting side (+) and **ACSW** and **SDW** on the demoting side (-). As a result of the experiment, it is possible to conclude that the statistically weighted algorithm should be employed to improve the performance of the classification technique on exponent ranges from \(-1\) to \(+1\). Finally, it can be concluded that, as compared with the conventional BASE-LINE image classification algorithm, the classification with statistically weighted dimensions and dimensionality reduction improves logistic regression, KNN, and SVM (RBF) with the enhanced accuracy rate of 0.48%, 1.48%, and 0.57%, respectively, by using PCA to reduce the number of components or dimensionality by more than 50%. It is imperative to point out that the proposed technique is applied to three different types of datasets and obtains the most accurate results. In the future, we intend to apply this methodology to diverse standard datasets, including text, signal, and medical datasets, to examine its efficacy and efficiency. It is also important to investigate the efficacy and efficiency of this strategy when dimensionality reduction such as factor analysis (FA), independent component analysis (ICA), linear discriminant analysis (LDA), and t-distributed stochastic neighbor embedding (t-SNE) are employed. We also intend to compare the effectiveness of our technique to that of other statistically weighted methods and examine how distribution might enhance their performance.  
**Author Contributions:** Conceptualization, U.B.; methodology, U.B.; software, validation, U.B.; formal analysis, U.B. and M.U.J.; investigation, resource, and data cu ration, U.B. and M.U.J.; writing--original draft preparation, U.B.; writing--review and editing, U.B. and M.U.J.; funding acquisition, U.B. All authors have read and agreed to the published version of the manuscript.  
This research is financially supported under the Faculty of Science and Arts, Burapha University, Chanthaburi Campus, Thailand Research Fund.  
The study did not require ethical approval because it did not involve human or animals, and the trial dataset is already legally accessible to the public.  
Not applicable.  
The research datasets used in this study are available for MNIST at [[https://www.kaggle.com/datasets/oddrationale/mnist-in-csv](https://www.kaggle.com/datasets/oddrationale/mnist-in-csv)]([https://www.kaggle.com/datasets/oddrationale/mnist-in-csv](https://www.kaggle.com/datasets/oddrationale/mnist-in-csv)), E-MNIST at [[https://github.com/aurelienduarte/emnist/tree/master/gzip](https://github.com/aurelienduarte/emnist/tree/master/gzip)]([https://github.com/aurelienduarte/emnist/tree/master/gzip](https://github.com/aurelienduarte/emnist/tree/master/gzip)), and F-MNIST at [[https://www.kaggle.com/datasets/zalando-research/fashionmnist](https://www.kaggle.com/datasets/zalando-research/fashionmnist)]([https://www.kaggle.com/datasets/zalando-research/fashionmnist](https://www.kaggle.com/datasets/zalando-research/fashionmnist)) (accessed on 25 November 2022).  
The authors declare no conflict of interest.