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                    基于核自適應濾波器的時間序列在線預測研究綜述

                    韓敏 馬俊珠 任偉杰 鐘凱

                    韓敏, 馬俊珠, 任偉杰, 鐘凱. 基于核自適應濾波器的時間序列在線預測研究綜述. 自動化學報, 2019, 45(x): 1?17 doi: 10.16383/j.aas.c190051
                    引用本文: 韓敏, 馬俊珠, 任偉杰, 鐘凱. 基于核自適應濾波器的時間序列在線預測研究綜述. 自動化學報, 2019, 45(x): 1?17 doi: 10.16383/j.aas.c190051
                    Han Min, Ma Jun-Zhu, Ren Wei-Jie, Zhong Kai. A survey of time series online prediction based on kernel adaptive filters. Acta Automatica Sinica, 2019, 45(x): 1?17 doi: 10.16383/j.aas.c190051
                    Citation: Han Min, Ma Jun-Zhu, Ren Wei-Jie, Zhong Kai. A survey of time series online prediction based on kernel adaptive filters. Acta Automatica Sinica, 2019, 45(x): 1?17 doi: 10.16383/j.aas.c190051

                    基于核自適應濾波器的時間序列在線預測研究綜述

                    doi: 10.16383/j.aas.c190051
                    基金項目: 國家自然科學基金(61773087)資助
                    詳細信息
                      作者簡介:

                      韓敏:大連理工大學電子信息與電氣工程學部教授. 主要研究方向為模式識別, 復雜系統建模及時間序列預測. 本文通信作者.E-mail: minhan@dlut.edu.cn

                      馬俊珠:大連理工大學電子信息與電氣工程學部碩士研究生. 主要研究方向為時間序列在線建模, 預測.E-mail: majunzhu@mail.dlut.edu.cn

                      任偉杰:大連理工大學電子信息與電氣工程學部博士研究生. 主要研究方向為時間序列分析和特征選擇.E-mail: renweijie@mail.dlut.edu.cn

                      鐘凱:大連理工大學電子信息與電氣工程學部博士研究生. 主要研究方向為工業過程監控, 故障診斷.E-mail: zhongkai0402@mail. dlut.edu.cn

                    A Survey of Time Series Online Prediction based on Kernel Adaptive Filters

                    Funds: Supported by National Natural Science Foundation of China (61773087)
                    • 摘要: 核自適應濾波器是時間序列在線預測的重點研究領域之一, 本文對核自適應濾波器的最新進展及未來研究方向進行了分析和總結. 基于核自適應濾波器的時間序列在線預測方法, 能較好的解決預測、跟蹤問題. 本文首先概述了三類核自適應濾波器的基本模型, 包括核最小均方算法, 核遞歸最小二乘算法和核仿射投影算法. 在此基礎上, 從核自適應濾波器在線預測的內容和機理入手, 綜述基于核自適應濾波器的時間序列在線預測方法. 最后, 本文將介紹這一領域潛在的研究方向和發展趨勢, 并展望未來的挑戰.
                    • 圖  1  從輸入空間到特征空間的非線性映射f(·)

                      Fig.  1  Nonlinear mapping f(·) from input space to feature space

                      圖  2  KAF方法分類框圖

                      Fig.  2  Classification diagram of the KAF method

                      表  1  不同KAF方法的時間序列在線預測特性對比結果

                      Table  1  Comparison of online prediction characteristics of time series of different KAF methods

                      算法類型 預測效率 預測精度 收斂速度 特點
                      KLMS[19] 較高 較低 較慢 泛化能力和正則化特性
                      KRLS[20] 較低 較高 較快 白化處理, 收斂速度較快
                      KAPA[21] 考慮多個樣本, 降低梯度噪聲
                      下載: 導出CSV

                      表  2  每次迭代過程涉及的計算復雜度比較

                      Table  2  Comparison of computational complexity involved in each iteration

                      核自適應濾
                      波器類型
                      在線稀
                      疏類型
                      計算復雜度
                      KLMS[19] VQ 更新$ {\alpha} \left( i \right) $ $ {\rm O}\left( {{L^2}} \right) $
                      在線VQ ${\rm O}\left( {{L}} \right)$
                      SF 更新$ {\omega} \left( i \right) $ ${\rm O}\left( {{L}} \right)$
                      更新$ {e}\left( i \right) $ ${\rm O}\left( {{L}} \right)$
                      KRLS[20] VQ 更新$ {\alpha} \left( i \right) $ $ {\rm O}\left( {{L}} \right) $
                      在線VQ ${\rm O}\left( {{L}} \right)$
                      更新$ {P}\left( i \right) $ ${\rm O}\left( {{L^2}} \right)$
                      ALD 更新$ {\alpha} \left( i \right) $ ${\rm O}\left( {{L^2}} \right)$(${\rm O}\left( {{L^2}} \right)$
                      假如字典改變)
                      更新ALD ${\rm O}\left( {{L^2}} \right)$
                      更新${P}\left( i \right)$ ${\rm O}\left( {{L^2}} \right)$
                      SW 更新$ {\alpha} \left( i \right) $ ${\rm O}\left( {{K^2}} \right)$(${\rm O}\left( {{K}} \right)$
                      假如字典改變)
                      更新${P}\left( i \right)$ ${\rm O}\left( {{K^2}} \right)$
                      更新${D}\left( i \right)$ ${\rm O}\left( {{K^2}} \right)$
                      FB 更新$ {\alpha} \left( i \right) $ ${\rm O}\left( {{K^2}} \right)$(${\rm O}\left( {{K}} \right)$
                      假如字典改變)
                      更新${P}\left( i \right)$ ${\rm O}\left( {{K^2}} \right)$
                      更新$ {{\hat K}_n}\left( i \right) $ ${\rm O}\left( {{K^2}} \right)$
                      MF 更新$ {\alpha} \left( i \right) $ ${\rm O}\left( {{L}} \right)$
                      更新$ {e}\left( i \right) $ ${\rm O}\left( {{L}} \right)$
                      更新${D}\left( i \right)$ ${\rm O}\left( {{L^2}} \right)$
                      CC 更新$ {\alpha} \left( i \right) $ ${\rm O}\left( {{K^2}} \right)$(${\rm O}\left( {{K}} \right)$
                      假如字典改變)
                      更新$ {e}\left( i \right) $ ${\rm O}\left( {{K^2}} \right)$
                      更新${D}\left( i \right)$ ${\rm O}\left( {{K^2}} \right)$
                      KAPA[21] VQ 更新$ {\alpha} \left( i \right) $ $ {\rm O}\left( {{L}} \right) $
                      在線VQ ${\rm O}\left( {{L}} \right)$
                      更新${P}\left( i \right)$ ${\rm O}\left( {{L^2}} \right)$
                      HC 更新$ {e}\left( i \right) $ ${\rm O}\left( {{L}} \right)$
                      更新$ {\bf{\zeta }}\left( i \right) $ ${\rm O}\left( {{L}} \right)$
                      下載: 導出CSV
                      360彩票
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                    • 收稿日期:  2019-01-21
                    • 錄用日期:  2019-09-24
                    • 網絡出版日期:  2020-01-02

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