模糊認知圖學(xué)習算法及應用綜述
doi: 10.16383/j.aas.c230120
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北京交通大學(xué)計算機科學(xué)與技術(shù)學(xué)院 北京 100044
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交通數據分析與挖掘北京市重點(diǎn)實(shí)驗室 北京 100044
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智慧高鐵系統前沿科學(xué)中心 北京 100044
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中國科學(xué)技術(shù)大學(xué)自動(dòng)化系 合肥 230027
基金項目: 中央高?；究蒲袠I(yè)務(wù)費專(zhuān)項資金(2022YJS121), 國家自然科學(xué)基金(51827813), 國家自然科學(xué)基金委員會(huì )?中國國家鐵路集團有限公司鐵路基礎研究聯(lián)合基金(U2268206), 科技部重點(diǎn)研發(fā)計劃項目(2022YFB2603302)資助
A Review of Fuzzy Cognitive Map Learning Algorithms and Applications
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School of Computer Science and Technology, Beijing Jiaotong University, Beijing 100044
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Beijing Key Laboratory of Traffic Data Analysis and Mining, Beijing 100044
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Frontiers Science Center for Smart High-Speed Railway System, Beijing 100044
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Department of Automation, University of Science and Technology of China, Hefei 230027
Funds: Support by Fundamental Research Funds for the Central Universities (2022YJS121), National Natural Science Foundation of China (51827813), National Natural Science Foundation of China-China National Railway Group Corporation Joint Fund for Railway Infrastructure Research (U2268206), and National Key Research and Development Program of China (2022YFB2603302)
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摘要: 模糊認知圖(Fuzzy cognitive map, FCM)是建立在認知圖和模糊集理論上的一類(lèi)代表性的軟計算理論, 兼具神經(jīng)網(wǎng)絡(luò )和模糊決策兩者的優(yōu)勢, 已成功地應用于復雜系統建模和時(shí)間序列分析等眾多領(lǐng)域. 學(xué)習權重矩陣是基于模糊認知圖建模的首要任務(wù), 是模糊認知圖研究領(lǐng)域的焦點(diǎn). 針對這一核心問(wèn)題, 首先, 全面綜述模糊認知圖的基本理論框架, 系統地總結近年來(lái)模糊認知圖的拓展模型. 其次, 歸納、總結和分析模糊認知圖學(xué)習算法的最新研究進(jìn)展, 對學(xué)習算法進(jìn)行重新定義和劃分, 深度闡述各類(lèi)學(xué)習算法的時(shí)間復雜度和優(yōu)缺點(diǎn). 然后, 對比分析各類(lèi)學(xué)習算法在不同科學(xué)領(lǐng)域的應用特點(diǎn)以及現有的模糊認知圖建模軟件工具. 最后, 討論學(xué)習算法未來(lái)潛在的研究方向和發(fā)展趨勢.Abstract: Fuzzy cognitive maps (FCM) are a representative soft computing theory based on cognitive maps and fuzzy set theory. They combine the advantages of both neural networks and fuzzy decision-making and have been successfully applied in many fields, including complex system modeling and time series analysis. Learning the weight matrix is the primary task of modeling based on fuzzy cognitive maps and is the focus of research in this field. To address this core issue, we first comprehensively review the basic theoretical framework of fuzzy cognitive maps and systematically summarize the extended models developed in recent years. Next, the most recent advancements in fuzzy cognitive map learning algorithms are reviewed, analyzed, and summarized. The algorithms are redefined and categorized, with a detailed exploration of their time complexity, strengths, and weaknesses. Additionally, the application properties of various learning algorithms in various scientific domains are also compared and analyzed in this research, along with the software tools that are now available for creating fuzzy cognitive maps. Finally, potential research directions and development trends for learning algorithms are discussed.
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圖 4 專(zhuān)家知識驅動(dòng)的學(xué)習算法的基本流程
Fig. 4 The basic process of expert knowledge-driven learning algorithms
圖 6 半自動(dòng)學(xué)習算法的基本流程
Fig. 6 The basic process of semi-automatic learning algorithms
表 1 拓展認知圖模型對比
Table 1 Comparison of extension cognitive map models
類(lèi)別 名稱(chēng) 特點(diǎn) 優(yōu)點(diǎn) 缺點(diǎn) 應用領(lǐng)域 基于不同
模糊理論
的拓展
認知圖RBFCM[28] 引入模糊進(jìn)位累加器計算因果權重 涵蓋多種概念關(guān)系并具有
多功能性和簡(jiǎn)單性建模要求高 決策支持 FGCM[29] 引入灰色數衡量因果強度 建模概念之間的不確定信息 推理復雜 可靠性工程 IFCM[30] 利用直覺(jué)模糊集建模因果關(guān)系 衡量了因果關(guān)系中的不確定性 推理復雜 時(shí)間序列預測 IVFCM[31] 利用區間值描述因果關(guān)系的強度 考慮了非結構化環(huán)境相關(guān)的不確定性 依賴(lài)專(zhuān)家知識 決策支持, 時(shí)間序列
預測模型ECM[32] 在因果推理中融入了證據理論 既能表示不確定性又能進(jìn)行知識融合 依賴(lài)專(zhuān)家知識,
推理復雜決策支持 RCN[33] 利用粗糙集表示因果關(guān)系 解決了不確定情況下的決策問(wèn)題 依賴(lài)專(zhuān)家知識 決策支持軟件,
可靠性評估FRCN[34] 利用模糊粗糙結構構建神經(jīng)網(wǎng)絡(luò ) 建模了因果關(guān)系的不確定性 推理復雜 決策支持 zT2FSs-FCM[35] 引入二型模糊集建模節點(diǎn)間的
因果權重捕獲了概念間的不確定性關(guān)系 推理復雜 系統評估 面向動(dòng)態(tài)
系統建模
的拓展
認知圖DCN[37] 考慮了因果關(guān)系的時(shí)變性 結構上具有更高的可擴展性和靈活性 依賴(lài)拉普拉斯框架,
建模復雜度高決策支持 DRFCM[39] 推理過(guò)程中引入非線(xiàn)性動(dòng)態(tài)函數 能夠捕獲動(dòng)態(tài)因果關(guān)系,
具有自適應性建模要求高 風(fēng)險評估, 決策支持 FTCM[40] 考慮了因果關(guān)系強度和時(shí)間滯后性 能夠隨時(shí)間推移分析系統的動(dòng)態(tài)行為 建模復雜 時(shí)間序列預測 E-FCM[41] 采用檢查機制模擬動(dòng)態(tài)因果關(guān)系 能夠自我進(jìn)化適應不斷發(fā)展的行為 計算耗時(shí) 動(dòng)態(tài)場(chǎng)景建模 HFCM[42] 考慮了復雜系統建模過(guò)程中的
多階動(dòng)態(tài)性準確地描述了系統行為 隨著(zhù)階數增加,
計算復雜度增加時(shí)間序列預測 TAFCM[43] 引入了定時(shí)自動(dòng)機理論建模
系統的時(shí)間粒度推理過(guò)程具有動(dòng)態(tài)性和自適應性 建模要求高 人類(lèi)情緒建模 DFCM[44] 嵌入在深度神經(jīng)網(wǎng)絡(luò )的框架中 構建可解釋預測器, 挖掘隱藏的
因果關(guān)系訓練耗時(shí), 容易面臨
“數據饑餓”問(wèn)題時(shí)間序列預測 AFCM[45] 構建基于趨勢的信息粒引入
自適應更新機制自適應權重長(cháng)期預測 計算耗時(shí) 時(shí)間序列預測 
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表 2 基于學(xué)習范式的模糊認知圖學(xué)習算法分類(lèi)
Table 2 Classification of fuzzy cognitive map learning algorithms based on the learning paradigm
類(lèi)別 學(xué)習方法 時(shí)間復雜度 優(yōu)點(diǎn) 缺點(diǎn) 作者 發(fā)表年份 專(zhuān)家知識
驅動(dòng)的方法DHL[47] ${\rm{O}}(N^2)$ 簡(jiǎn)單, 易操作 只考慮了當前的一對概念 Dickerson等 1994 BDA[48] ${\rm{O}}(N^2)$ 考慮多個(gè)概念的影響 只適用于二進(jìn)制計算 Huerga 2002 AHL[49] ${\rm{O}}(N^2)$ 考慮了所有概念的影響 訓練耗時(shí) Papageorgiou等 2004 NHL[50] ${\rm{O}}(N^2)$ 保留了原始的圖結構, 具有合理的物理解釋性 依賴(lài)專(zhuān)家標準 Papageorgiou等 2003 INHL[51] ${\rm{O}}(N^2)$ 避免陷入局部最小值 需要先驗知識 Li等 2004 DDNHL[52] ${\rm{O}}(N^2)$ 數據驅動(dòng) 依賴(lài)專(zhuān)家知識 Stach 等 2008 帶終端約束的
NHL算法[53]${\rm{O}}(N^2)$ 提高結果的可行性 需要先驗知識 陳寧等 2016 FBN[54] ${\rm{O}}(N^2)$ 利用模糊因果規則推理 性能受激活參數的影響 Carvalho等 2007 基于bagging增強的NHL算法[55] ${\rm{O}}(N^2)$ 泛化性能較好 依賴(lài)專(zhuān)家知識 Papageorgiou等 2012 自動(dòng)學(xué)習
算法GA[56] ${\rm{O}}(N^2)$ 數據驅動(dòng) 受限于二進(jìn)制編碼 Mateou等 2005 RCGA[57] ${\rm{O}}(N^2)$ 數據驅動(dòng), 實(shí)數編碼 參數尋優(yōu)耗時(shí) Stach 等 2005 PSO[58?59] ${\rm{O}}(N!)$ 數據驅動(dòng), 元啟發(fā)式算法 依賴(lài)專(zhuān)家知識 Parsopoulos 等Oikonomou 等 2003
2013SOMA[60] ${\rm{O}}(N^2)$ 數據驅動(dòng) 計算耗時(shí) Va??ák 2010 ACO[61] ${\rm{O}}(N^2)$ 概率型算法魯棒性強 計算耗時(shí), 容易早熟收斂 Chen等 2012 ABC[62] ${\rm{O}}(N^2)$ 數據驅動(dòng) 參數尋優(yōu)耗時(shí) Yesil等 2013 ICA[63] ${\rm{O}}(N^3)$ 數據驅動(dòng) 計算復雜, 耗時(shí) Ahmadi 等 2015 DE[64] ${\rm{O}}(N^2)$ 容易理解, 計算簡(jiǎn)單 易局部收斂 Juszczuk等 2009 SA[65?66] ${\rm{O}}(N^2)$ 計算簡(jiǎn)單 參數尋優(yōu)耗時(shí) Ghazanfari 等
Alizadeh等2007
2009BB-BC[67] ${\rm{O}}(N^2)$ 算法簡(jiǎn)單, 泛化能力較好 不適用于解決高維問(wèn)題 Yesil等 2010 CA[68] ${\rm{O}}(N^2)$ 全局搜索與局部搜索結合 參數尋優(yōu)耗時(shí), 對問(wèn)題的依賴(lài)性強 Ahmadi等 2014 基于互信息的
模因算法[70]${\rm{O}}(N^2)$ 適用于大規模圖學(xué)習 無(wú)法在搜索過(guò)程中
關(guān)注圖的稀疏性Zou等 2018 MARO[71] ${\rm{O}}(N^2)$ 只需調用一次目標
函數, 無(wú)需設置參數計算復雜, 易陷入局部最優(yōu) Salmeron等 2019 分解RCGA[72?73] ${\rm{O}}(N^2)$ 分解并行計算 計算復雜 Chen等, Stach等 2015, 2010 D&C RCGA[74] ${\rm{O}}(N^2)$ 可并行計算并具有可擴展性 隨著(zhù)圖的大小和處理器數量增加, 算法性能下降 Stach等 2007 dMAGA[75] ${\rm{O}}(N^2)$ 適用于大規模圖學(xué)習
具有魯棒性受 FCM 節點(diǎn)的取值范圍限制, 需在算法執行前進(jìn)行數據歸一化 Liu等 2015 MA-NN[76] ${\rm{O}}(N^2)$ 分布式計算框架適用于
大規模網(wǎng)絡(luò )重建受FCM節點(diǎn)的取值范圍限制, 需在算法執行前進(jìn)行數據歸一化 Chi等 2019 MOEA[77, 79?80] ${\rm{O}}(N^2)$ 多目標進(jìn)化考慮了圖的稀疏性 不適用于大規模圖學(xué)習 Liu等, Poczeta 等,
Chi等2019, 2018, 2016 IMFPSO[78] ${\rm{O}}(N!)$ 優(yōu)化過(guò)程考慮了知識遷移 算法易早熟, 過(guò)早收斂 Liang等 2022 SRCGA[15] ${\rm{O}}(N^2)$ 考慮了圖的稀疏性 不適用于處理大規模數據 Stach等 2012 MMMA[17] ${\rm{O}}(N^2)$ 多圖優(yōu)化知識轉移 有可能發(fā)生負信息遷移, 導致收斂速度緩慢 Shen等 2020 CS[81] ${\rm{O}}(N^3)$ 適用于大規模稀疏圖學(xué)習 參數尋優(yōu)耗時(shí) Wu等 2017 內點(diǎn)法[82] ${\rm{O}}(N^4)$ 精度高, 可擴展性好 對初值敏感, 難以處理
不等式約束問(wèn)題Lu等 2020 約束優(yōu)化[83] ${\rm{O}}(N^3)$ 考慮了矩陣分布具有抗噪能力 僅適用于有監督學(xué)習 Feng等 2021 近似梯度下降[84] ${\rm{O}}(N^3)$ 適用于解決大規模數據問(wèn)題 對初始點(diǎn)敏感, 可能
陷入局部最優(yōu)Ding等 2021 Moore-Penrose逆[85] ${\rm{O}}(N^3)$ 參數較少 計算復雜 Vanhoenshoven等 2020 Lasso回歸[86] ${\rm{O}}(N^3)$ 考慮了圖的稀疏性, 適用于
大規模圖學(xué)習可能出現過(guò)擬合 Wu等 2016 嶺回歸[87] ${\rm{O}}(N^3)$ 泛化性能較好, 適用于
大規模圖學(xué)習對特征的縮放敏感 Yang等 2018 彈性網(wǎng)絡(luò )回歸[88] ${\rm{O}}(N^3)$ 增加了L1 和L2 正則化, 適用于大規模圖學(xué)習 參數調節困難 Shen等 2020 支持向量回歸[89] ${\rm{O}}(N^4)$ 適用于高維非線(xiàn)性數據 對缺失數據敏感 Gao等 2020 貝葉斯嶺回歸[90] ${\rm{O}}(N^4)$ 簡(jiǎn)單、模型適應性較強 對模型的假設較多依賴(lài)先驗分布 Liu等 2020 FTRL[91] ${\rm{O}}(N^3)$ 在線(xiàn)學(xué)習 計算、推理過(guò)程復雜 Wu 等 2021 半自動(dòng)學(xué)習算法 DE+NHL[92] ${\rm{O}}(N^2)$ 進(jìn)化過(guò)程中保留了圖的物理意義 依賴(lài)專(zhuān)家知識 Papageorgiou等 2005 RCGA+NHL[93] ${\rm{O}}(N^2)$ 利用了遺傳算法的全局優(yōu)化能力 受限于專(zhuān)家經(jīng)驗 Zhu等 2008 PSO+NHL[94] ${\rm{O}}(N!)$ 避免人為因素產(chǎn)生的訓練誤差 受限于專(zhuān)家經(jīng)驗 Yazdi等 2008 EGDA+NHL[95] ${\rm{O}}(N^2)$ 全局搜索, 參數少 受限于專(zhuān)家經(jīng)驗 Ren 2012 DDNHL+GA[96] ${\rm{O}}(N^3)$ 數據驅動(dòng)分類(lèi)推理能力強 受限于專(zhuān)家經(jīng)驗 Natarajan等 2016 RCGA+DE+
梯度下降[97]${\rm{O}}(N^2)$ 全局搜索 參數尋優(yōu)耗時(shí) Madeiro 等 2012 注: 時(shí)間復雜度為該算法更新一次FCM權重矩陣所需時(shí)間開(kāi)銷(xiāo), 未考慮數據量大小及最大迭代次數. N表示節點(diǎn)個(gè)數.
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表 3 大規模模糊認知圖學(xué)習算法分類(lèi)
Table 3 Large-scale fuzzy cognitive map learning algorithm classification
類(lèi)別 方法 轉換函數 最大FCM規模 發(fā)表年份 基于暴力求解的方法 D&C RCGA[73] sigmoid 40 2010 并行RCGA[74] sigmoid 80 2007 dMAGA[75] sigmoid 200 2015 MA-NN[76] sigmoid 100 2019 MOEA[80] sigmoid 40 2015 SRCGA[15] sigmoid 40 2012 基于維度縮減的方法 MIMA[70] sigmoid 500 2018 文獻[100] sigmoid/tanh 25 2015 文獻[101] sigmoid 10 2018 基于分解的方法 CS[81] sigmoid 1 000 2017 MMMA[17] sigmoid/tanh 600 2020 內點(diǎn)法[82] sigmoid/tanh 200 2020 約束優(yōu)化[83] sigmoid/tanh 200 2021 近似梯度下降[84] sigmoid 200 2021 Lasso回歸[86] sigmoid 500 2016 彈性網(wǎng)絡(luò )回歸[88] sigmoid 200 2020 HTMA-DRA[99] sigmoid 200 2022 dMAGA-FCM$_D$[102] sigmoid 500 2017 NMMMAGA[103] sigmoid 200 2019 Parallel FCM[104] sigmoid 1 000 2023
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表 4 模糊認知圖學(xué)習算法的應用文獻總結
Table 4 Literature review on the application of fuzzy cognitive map learning algorithms
類(lèi)別 應用領(lǐng)域 文獻 專(zhuān)家知識驅動(dòng)的方法 模式分類(lèi) [55] 前列腺癌診斷 [105] 公司信用風(fēng)險評估 [106] 自閉癥預測 [107] 結構損傷檢測 [108] 帕金森病預測 [110] 事故成因預測 [111] 裂紋嚴重程度分級 [112] 乳腺癌風(fēng)險評估 [113] 自動(dòng)學(xué)習算法 基因調控網(wǎng)絡(luò )重建 [17, 75–77, 82, 84, 86] 多變量時(shí)間序列預測 [44?45, 78, 85, 116–119] 單變量時(shí)間序列預測 [83, 87, 89?91, 120?127, 140–143] 情景意識評估 [114] 病情趨勢預測 [134] 前列腺癌預測 [135] 日需水量預測 [136] 電器能耗預測 [137] RFID物流操作評估 [138] 分類(lèi) [5, 128–133, 140] 半自動(dòng)學(xué)習算法 醫學(xué)診斷 [139] 甘蔗產(chǎn)量預測 [96] 決策支持 [92] 化學(xué)控制 [94] 太陽(yáng)能發(fā)電 [97]
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表 5 模糊認知圖建模工具對比
Table 5 Comparison of fuzzy cognitive map modeling tools
工具名稱(chēng) 受眾定位 適用場(chǎng)景 應用形式 學(xué)習算法數量 圖形頁(yè)面 年份 FCM Modeler[144] 學(xué)術(shù)研究 靜態(tài)建模, 群體決策 Java Applet 1 √ 1997 FCMappers.net[145] 學(xué)術(shù)研究 網(wǎng)絡(luò )分析, 系統建模 網(wǎng)站 — — 2009 FCM Tool[146] 商業(yè)產(chǎn)品, 學(xué)術(shù)研究 決策支持, 系統建模 軟件 1 √ 2011 FCM Designer[147] 學(xué)術(shù)研究 系統建模 Java Applet — √ 2010 FCM Designer Version 2.0[148] 學(xué)術(shù)研究 醫學(xué)診斷, 推薦系統建模 Java Applet — √ 2016 Mental Modeler[149] 商業(yè)產(chǎn)品, 學(xué)術(shù)研究 群體決策, 系統建模 Web 頁(yè)面 — √ 2013 JFCM[150] 教學(xué)工具, 學(xué)術(shù)研究 系統建模 Java開(kāi)源庫 — — 2014 ISEMK[152] 商業(yè)產(chǎn)品, 學(xué)術(shù)研究 決策支持, 時(shí)間序列預測 — 6 √ 2015 FCM Expert[154] 學(xué)術(shù)研究 決策支持, 系統建模 Java軟件 4 √ 2017 FCMpy[158] 學(xué)術(shù)研究 系統建模 開(kāi)源Python模塊 5 √ 2022 注: “—”表示“無(wú)”或者未查詢(xún)到.
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