基於多群機器學習的多目標複數神經模糊預測方法

A Novel Complex-Valued Neuro-Fuzzy Predictive Approach to Multiple Targets with Multi-Swarm Machine Learning

本研究提出一個基於複數的神經模糊推理系統（Complex Number based Neuro Fuzzy Inference System，CNNFIS），模型採用模糊If-Then規則的神經網絡框架，以球型複數模糊集（Sphere Complex Fuzzy Sets，SCFSs）為前鑑部，後鑑部使用線性函數。我們提出多群粒子群演算法（Multi-Swarm Particle Swarm Optimization，MSPSO），將參數空間劃分為多個子空間，使各群體專注搜索特定子空間以增進最佳解，並結合遞迴最小平方估計法，利用混合式學習更有效地訓練模型。透過基於熵的特徵選取方法，我們選出高資訊量的特徵。基於減法分群法，我們提出複數數據的減法分群法，將輸入空間劃分為多個部分，符合條件的輸入空間於CNNFIS建模，並應用投影矩陣於SCFS，計算複數隸屬度，靈活調整模型輸出數量。我們以單目標、雙目標和四目標的實驗評估該方法的效能，並與其他方法比較。

This study presents a novel concept for a model operating on complex data called a complex number based neuro-fuzzy inference system (CNNFIS). With the neural framework of fuzzy if-then rules, utilizes sphere complex fuzzy sets (SCFSs) for the premise parts and linear functions for the consequent parts. We propose a novel multi-swarm particle swarm optimization (MSPSO). Each swarm can focus on searching for a specific sub-space by dividing the whole parameter space into several sub-spaces. This optimization method can increase the chance of finding the best solution, and combined with the recursive least squares estimation algorithm (RLSE), we adopt a hybrid parameter learning to train the model more efficiently. We also use the method of entropy-based feature selection, by which high-information features are selected for the model. Moreover, based on the method of subtractive clustering, we propose the algorithm of subtractive clustering for complex-valued data (SCC) for dividing the input space into parts, and then the input-space parts qualified are used for CNNFIS modeling and apply the projection matrix to the calculation of SCFS to form complex membership used in the model to flexibly adjust the number of model outputs. Finally, we evaluate the performance of the method and compare it with other methods through single-, dual- and four-target experiments.