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目录
📋1 概述
📝2 运行结果
📃3 参考文献
📋4 Matlab代码实现
📋1 概述
[1]Waleed Fakhr, "Sparse Locally Linear and Neighbor Embedding for Nonlinear Time Series Prediction", ICCES 2015, December 2015.
“本文提出了一种基于字典的L1范数稀疏编码，用于时间序列预测，不需要训练阶段，参数调整最少，适用于非平稳和在线预测应用。预测过程被表述为基础追求 L1 范数问题，其中为每个测试向量估计一组稀疏权重。尝试了约束稀疏编码公式，包括稀疏局部线性嵌入和稀疏最近邻嵌入。16个时间序列数据集用于测试离线时间序列预测方法，其中训练数据是固定的。所提出的方法还与Bagging树（BT），最小二乘支持向量回归（LSSVM）和正则化自回归模型进行了比较。所提出的稀疏编码预测显示出比使用10倍交叉验证的LSSVM更好的性能，并且比正则化AR和Bagging树的性能明显更好。平均而言，在LSSVM训练时可以完成几千个稀疏编码预测。
📝2 运行结果
部分代码：
if(nnnn==1) %Mackey-Glass data
load MGData;
a = MGData;
time = a(:, 1);
x_t = a(:, 2);
trn_data = zeros(500, 5);
chk_data = zeros(500, 5);
% prepare training data
trn_data(:, 1) = x_t(101:600);
trn_data(:, 2) = x_t(107:606);
trn_data(:, 3) = x_t(113:612);
trn_data(:, 4) = x_t(119:618);
trn_data(:, 5) = x_t(125:624);
% prepare checking data
chk_data(:, 1) = x_t(601:1100);
chk_data(:, 2) = x_t(607:1106);
chk_data(:, 3) = x_t(613:1112);
chk_data(:, 4) = x_t(619:1118);
chk_data(:, 5) = x_t(625:1124);
Train=trn_data;
Test=chk_data;
K=4;
delta=2;
eps=0.001;
C='Mackey Glass Data';elseif(nnnn==2)
load Henon1 %Henon chaotic map data
x_t=Henon1;
sz=length(x_t);
time = 1:sz;
Train = x_t(1:1004);
Test = x_t(1005:1259);
%here we add the WGN with standard deviation of 0.05
nnn = 0.05*randn(1004,1);
Train = Train + nnn;
K=4;
delta=2;
eps=0.001;
C = 'Henon Chaotic Map Data'elseif(nnnn==3) %Lorenz chaotic map data
load Lorenz1
x_t=Lorenz1;
sz=length(x_t);
time = 1:sz;
Train = x_t(1:1004);
Test = x_t(1005:1259);
nnn = 0.05*randn(1004,1);
Train = Train + nnn;
K=4;
delta=2;
eps=0.001;
C = 'Lorenz Chaotic Map Data';elseif(nnnn==4)
load Rossler1 %Rossler
x_t=Rossler1;
sz=length(x_t);
time = 1:sz;
Train = x_t(1:1004);
Test = x_t(1005:1259);
%here we add the WGN with standard deviation of 0.05
nnn = 0.05*randn(1004,1);
Train = Train + nnn;
K=4;
delta=2;
eps=0.001;
C = 'Rossler Chaotic Map Data';elseif(nnnn==5)
load Nord1 %NordPool
x_t=Nord1;
sz=length(x_t);
time = 1:sz;
Train = x_t(1:880);
Test = x_t(881:988);
K=9; %as recommended by reference
delta=2;
eps=0.001;
C= 'Nord Pool Exchange Electricity Prices Data';
📃3 参考文献
[1]Waleed Fakhr, "Sparse Locally Linear and Neighbor Embedding for Nonlinear Time Series Prediction", ICCES 2015, December 2015.
