## 5 Conclusions and Future Works  
This paper presented a novel NBC training method for the mixed-attribute data classification problem without continuous attribute discretization and complex Bayesian network structure learning. The original mixed attributes were transformed into a series of continuous attributes with minimum dependence using an autoencoder neural network. To obtain optimal network weights, an effective objective function was designed, and corresponding weight updating rules were derived. The experimental results finally demonstrated improved classification performance for the novel Bayes model in comparison with eight state-of-the-art Bayesian algorithms. The technical advantages of MAF-NBC are four-fold:  
* Preserving the information. The autoencoder neural network transforms mixed attributes into independent encoded attributes, which can also be decoded to restore the original mixed attributes. Thus, useful information from the original data set is conserved as much as possible. * Simple model structure. MAF-NBC effectively handles the attribute dependence problem between discrete attributes and continuous attributes by transforming original attributes into encoded attributes. The simple structure of the NBC was not modified by providing a data transformation-oriented preprocessing strategy. * Stable training process. The efficient weight updating strategy guarantees the convergence of the autoencoder neural network and thus provided stable data transformation results. In addition, the quasi-normal distribution of independent encoded attributes provided accurate calculations for the joint conditional probability in the NBC. * Low computation complexity. A single hidden-layer encoder neural network was used to fuse the original mixed attributes. Training to find optimal network weights has a low computational complexity. As mentioned in Section 3, a shallow learning mechanism was able to satisfy the demand of NBC construction. Hence, it is unenc  
Figure 5: CD diagrams corresponding to comparisons in Tables 2 and 3. (**a**) CD diagram of training accuracies. (**b**) CD diagram of testing accuracies. essary to explore the availability of deep learning for data transformation-oriented NBC training. In future studies, we plan (1) to implement MAF-NBC in a distributed environment so that it can be used to deal with large-scale mixed-attribute data-classification problems and (2) to utilize the autoencoder neural network to transform mixed attributes into dependent continuous attributes to construct a non-naive Bayesian classifier [29] based on the joint probability density function estimation technique. Data curation, formal analysis, and writing--original draft preparation, G.O. ; methodology, writing--original draft preparation and review and editing, Y.H. ; investigation and writing--review and editing, P.F.-V.; supervision, J.Z.H. All authors have read and agreed to the published version of the manuscript. This research was funded by the Scientific Research Foundation of National Natural Science Foundation of China (61972261) and Basic Research Foundations of Shenzhen (JCYJ20210324093609026 and JCYJ20200813091134001). None. None. The data are available in BaiduPan [[https://pan.baidu.com/s/1741](https://pan.baidu.com/s/1741)]([https://pan.baidu.com/s/1741](https://pan.baidu.com/s/1741)) 72F-IIP6 IW_ut7 IRTqA (accessed on 14 October 2022) with extraction code _fcju_ or GitHub platform [[https://github.com/ouguiliang110/DataSet_of_MAF-NBC](https://github.com/ouguiliang110/DataSet_of_MAF-NBC)]([https://github.com/ouguiliang110/DataSet_of_MAF-NBC](https://github.com/ouguiliang110/DataSet_of_MAF-NBC)) (accessed on 14 October 2022). The authors would like to thank the editors and anonymous reviewers who carefully read the paper and provided valuable suggestions that considerably improved the paper.