最佳化理論經常被使用於電機領域相關研究，舉凡機器人步態平衡、機械手臂路徑規劃與避障等控制問題，從而得到靈感可將最佳化理論結合機器學習方法用於解決迴歸分析之研究議題。本論文提出機器學習演算法與最佳化演算法之混合模型，透過粒子群演算法(Particle Swarm Optimization)混合七種機器學習演算法的預測結果，最佳化整體預測效能。七種迴歸模型包含支持向量迴歸 (Support Vector Regression)、隨機森林 (Random Forest)、決策樹 (Decision Tree)、線性迴歸 (Linear Regression)、自適應增強 (Adaptive Boosting)、K-近鄰演算法 (K-Nearest Neighbor)以及多層感知器 (Multilayer Perceptron)，本論文以UCI (University of California Irvine)機器學習資料庫中波士頓房地產中位數價格預測資料作為複迴歸分析的資料來源。由於房地產資料普遍存在特徵維度過高的問題，考慮所有特徵的情況下，使用粒子群演算法調整不同機器學習迴歸模型預測結果的權重以及偏差值的權重，以平衡預測數據。實驗結果顯示，與單一機器學習演算法相比較，本論文所提方法能提升預測準確度，並證明其可行性與有效性。

Optimization theory can merge machine learning algorithms to solve the research problems of regression analysis was inspired by optimization theory has been widely used in the field of electrical engineering, such as gait balance for biped robots, obstacles avoidance and path planning. This thesis proposes a hybrid model combining machine learning algorithms with the Particle Swarm Optimization (PSO) algorithm. Applying PSO to optimize the prediction results of different machine learning algorithms can improve the overall prediction performance. First, seven different machine learning models, including Support Vector Regression (SVR), Random Forest (RF), Decision Tree (DT), Linear Regression (LR), Adaptive Boosting (AdaBoost), K-Nearest Neighbor (KNN), and Multilayer Perceptron (MLP), are adopted to run multiple regression analysis on real estate price dataset. Due to high-dimensional regression problem in the real estate price prediction field, PSO is utilized to adjust the weights of the prediction results of different machine learning algorithms and the weight of the deviation values under the condition of considering all the features to balance the prediction data. Finally, the experimental results show that compared with a single machine learning algorithm, the proposed hybrid model in this thesis can improve the accuracy of real estate price prediction and prove its feasibility and effectiveness.

[1] M. Kearns, “Thoughts on hypothesis boosting,” Unpublished manuscript (Machine Learning Class Project), Dec. 1988, https://www.cis.upenn.edu/~mkearns/papers/boostnote.pdf
[2] Y. Freund and R. E. Schapire, “A desicion-theoretic generalization of on-line learning and an application to boosting,” Journal of Computer and System Sciences, vol. 55, no. 1, pp. 119-139, August 1997.
[3] [online] Available: https://www.kaggle.com/c/otto-group-product-classification-challenge/discussion/14335
[4] J. Manasa, R. Gupta and N. S. Narahari, "Machine Learning based Predicting House Prices using Regression Techniques," in 2020 2nd International Conference on Innovative Mechanisms for Industry Applications (ICIMIA), pp. 624-630, 2020.
[5] M. F. Mukhlishin, R. Saputra, and A. Wibowo, “Predicting house sale price using fuzzy logic, Artificial Neural Network and K-Nearest Neighbor,” in Proc. 2017 1st International Conference on Informatics and Computational Sciences (ICICoS), pp. 172-176, Nov. 2017.
[6] N. Pow, E. Janulewicz, and L. Liu, “Applied Machine Learning Project 4 Prediction of real estate property prices in Montréal,” 2014, http://rl.cs.mcgill.ca/comp598/fall2014/comp598_submission_99.pdf
[7] M. Ahtesham, N. Z. Bawany, and K. Fatima, “House Price Prediction using Machine Learning Algorithm - The Case of Karachi City, Pakistan,” in Proc. 2020 21st International Arab Conference on Information Technology (ACIT), Nov. 2020.
[8] V. S. Rana, J. Mondal, A. Sharma, and I. Kashyap, “House Price Prediction Using Optimal Regression Techniques,” in Proc. 2020 2nd International Conference on Advances in Computing, Communication Control and Networking (ICACCCN), Dec. 2020.
[9] J. Mu, F. Wu, and A. Zhang, “Housing Value Forecasting Based on Machine Learning Methods,” Aug. 2014. https://doi.org/10.1155/2014/648047.
[10] P.-Y. Wang, C.-T. Chen, J.-W. Su, T.-Y. Wang, and S.-H. Huang, “Deep Learning Model for House Price Prediction Using Heterogeneous Data Analysis Along With Joint Self-Attention Mechanism,” Eng. Appl. Artif. Intell., vol. 9, pp. 55244-55259, April 2021.
[11] I. M. El-Hasnony, S. I. Barakat, M. Elhoseny and R. R. Mostafa “Improved Feature Selection Model for Big Data Analytics,” in IEEE Acess, vol. 8, no. 1, pp. 66989-67004, April. 2020.
[12] S. Gu, R. Cheng and Y. Jin, “Feature selection for high-dimensional classification using a competitive swarm optimizer”, Soft Comput., vol. 22, no. 3, pp. 811-822, Feb. 2016.
[13] B. Wei, W. Zhang, X. Xia, Y. Zhang, F. Yu and Z. Zhu, “Efficient Feature Selection Algorithm Based on Particle Swarm Optimization With Learning Memory,” in IEEE Access, vol. 7, pp. 166066-166078, 2019.
[14] Y. Ding, K. Zhou and W. Bi, “Feature selection based on hybridization of genetic algorithm and competitive swarm optimizer”, Soft Comput., pp. 1-10, Feb. 2020.
[15] R. Bello, Y. Gomez, A. Nowe and M. M. Garcia, “Two-step particle swarm optimization to solve the feature selection problem”, in 2007 7th International Conference on Intelligent Systems Design and Applications, pp. 691-696, Oct. 2007.
[16] B. Xue, M. Zhang and W. N. Browne, “Particle swarm optimization for feature selection in classification: A multi-objective approach”, IEEE transactions on cybernetics, vol. 43, no. 6, pp. 1656-1671, 2013.
[17] Y. Xu, C. Wu, K. Zheng, Xu Wang, X. Niu, T. Lu, “Computing Adaptive Feature Weights with PSO to Improve Android Malware Detection”, Security and Communication Networks, vol. 2017, Article ID 3284080, 14 pages, 2017.
[18] G. M. Nayeem, M. Fan and Y. Akhter, “A Time-Varying Adaptive Inertia Weight based Modified PSO Algorithm for UAV Path Planning,” in 2021 2nd International Conference on Robotics, Electrical and Signal Processing Techniques (ICREST), pp. 573-576, 2021.
[19] [online] Available: https://www.kaggle.com/c/house-prices-advanced-regression-techniques.
[20] V. Roman, “Machine learning project: Predicting Boston house prices with regression,” in towards data science, Jan. 2019, https://towardsdatascience.com/machine-learning-project-predicting-boston-house-prices-with-regression-b4e47493633d
[21] V. Vapnik, “The Nature of Statistical Learning Theory,” Springer-Verlag New York, DOI: 10.1007/978-1-4757-3264-1, 2020.
[22] V. Vapnik, S. E. Golowich, and A. Smola, “Support Vector Method for Function Approximation, Regression Estimation, and Signal Processing,” in Proceedings of the 9th International Conference on Neural Information Processing Systems,, pp. 281-287, Dec. 1996.
[23] A. J. Smola and B. Schölkopf, “A tutorial on support vector regression,” Statistics and Computing, vol. 14, pp. 199-222, 2004.
[24] L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stone, “Classification and regression Trees,” Wadsworth, Calif., 1984. ISBN 978-0-412-04841-8.
[25] L. Breiman, “Random Forests,” Machine Learning in Springer, vol. 45, pp. 5-32, 2001.
[26] Y. Freund and R. E. Schapire, “Game theory, on-line prediction and boosting,” in Proceedings of the Ninth Annual Conference on Computational Learning Theory, pp. 325-332, 1996.
[27] G. Menardi, N. Torelli, “Evaluating enterprise risk of default using boosting procedures,” in researchgate, 2008, https://www.researchgate.net/publication/242244746
[28] E. Fix and J .L. Hodges Jr, “Discriminatory Analysis. Nonparametric Discrimination: Consistency Properties,” USAF School of Aviation Medicine, Randolph Field, Texas., Feb. 1951.
[29] T. Cover and P. Hart, “Nearest neighbor pattern classification,” IEEE Transactions on Information Theory, vol. 13, no. 1, pp. 21-27, Jan. 1967.
[30] N. S. Altman, “An introduction to kernel and nearest-neighbor nonparametric regression,” The American Statistician, pp. 175-185, 1992.
[31] J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of ICNN'95 - International Conference on Neural Networks., pp. 1942-1948, 1995.
[32] J. Kennedy and R. Eberhart, “A new optimizer using particle swarm theory,” MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science, pp. 39-43, Oct. 1995.