| 摘要: | 本研究提出一種新的時間序列預測方法，採用多目標複數神經模糊結合多群機器學習技術。傳統的時間序列預測中，通常只考慮單一目標，忽略了多個目標之間的關聯性。因此，本研究提出一個僅使用複數數據的模型概念，稱為基於複數的神經模糊推理系統（Complex number based neuro-fuzzy inference system; CNNFIS）。該模型採用模糊If-Then規則的神經網絡框架，將球型複數模糊集（Sphere Complex Fuzzy Sets; SCFSs）作為模型前鑑部，後鑑部使用線性函數。在模型中，數據和參數都表示為複數數據，以避免維度過高的問題。這種方法可以降低模型的複雜性，進而減少過度擬合的可能性。本研究也提出新的多群粒子群最佳化（Multi-swarm particle swarm optimization; MSPSO）機器學習方法，將整個參數空間劃分為多個子空間，每個群體可以專注於搜索特定的子空間，而不是搜索整個空間。將多群粒子群最佳化演算法結合遞迴最小平方估計法（Recursive least squares estimator; RLSE)，採用混合式參數學習的分而治之方法來更有效地訓練模型。另外，使用基於熵的特徵選取方法進行數據的前處理，透過影響資訊和選取增益的概念為模型選擇重要和高資訊量的特徵作為模型的輸入。此外，基於減法分群法（Subtractive clustering; SC）的基礎上，提出複數數據的減法分群法（Subtractive clustering for complex-valued data; SCC），將輸入空間劃分為多個部分，將符合條件的輸入空間用於CNNFIS建模，並應用投影矩陣於SCFS的計算，形成模型中使用的複數隸屬度，以靈活調整模型輸出數量。本研究使用數個金融時間序列數據集進行三個實驗，包括單目標、雙目標和四目標預測，來評估該方法的效能，並將其效能與其他方法進行了比較。;This study proposes a new time series forecasting method using multi-target complex neuro-fuzzy combined with multi-swarm machine learning techniques. In traditional time series forecasting, usually, only a single target is considered, and the correlation between multiple targets is ignored. Therefore, this study introduces a model concept that exclusively utilizes complex data, termed the complex number-based neuro-fuzzy inference system (CNNFIS). The model adopts a neural network framework with fuzzy If-Then rules, utilizing sphere complex fuzzy sets (SCFSs) as the premise part and linear functions as the consequent part. In this model, both data and parameters are represented as complex data to avoid the issue of high dimensionality. This approach reduces model complexity, thus decreasing the possibility of overfitting. Additionally, this study proposes a novel multi-swarm particle swarm optimization (MSPSO) machine learning method, which divides the entire parameter space into multiple subspaces, allowing each swarm to focus on searching specific subspaces rather than the entire space. By combining the MSPSO algorithm with the recursive least squares estimator (RLSE) and employing a divide-and-conquer approach with hybrid parameter learning, the model training process becomes more efficient. Moreover, a feature selection method based on entropy is employed for data preprocessing, selecting important and highly informative features for model input based on the concepts of influence information and selection gain. Furthermore, building upon the subtractive clustering (SC) method, a subtractive clustering for complex-valued data (SCC) approach is proposed, which partitions the input space into multiple regions and utilizes the selected input space that meets certain conditions for CNNFIS modeling. The projection matrix is applied to calculate SCFSs, forming complex membership degrees used in the model, allowing for flexible adjustment of the model′s output quantity. Several financial time series datasets are employed in three experiments, including single, dual, and four-target predictions, to evaluate the performance of the proposed method, which is compared to other existing approaches. |
