用于非线性时间序列预测的稀疏局部线性和邻域嵌入（Matlab代码实现）

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本文目录如下：

目录

1 概述

2 运行结果

3 参考文献

4 Matlab代码实现

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1 概述

“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：

clear all;
%Time series Prediction using Sparse coding with overcomplete dictionaries
%In each case, the test data prediction is plotted versus the real data
%and the sparsity of the solution is recorded.
%both L1-magic (if LASSO=0) and CVX libraries (if LASSO=1) must be included 
% in the Matlab path

%if normalize=1 use sqrt(x*x'), normalize=2 use st.dev., normalize=3 use 
%the L1 norm, or zero then no normalization.
normalize1=2;
normalize2=2;
eps=0.001;  %the error constraint 
thr=0.001;   %the pruning threshold
NN=20000;   %these are the max number of neighbors allowed
dthr=0.0;    %the distance threshold used to filter the dictionary. If it 
%is zero then no dictionary filtering is done
LASSO=1;   %0 for BP   and 1 for BPDN or LASSO using CVX

for kkk=1:16  %The 16 data sets used for evaluation
    nnnn=kkk;
     
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);

time = 1:sz;
Train = x_t(1:100);   
Test  = x_t(101:190);     
K=6;
eps=0.001;
C = 'USD-EURO Data'
elseif(nnnn==15)
load IkedaData1;   %Z-normalized   

if(nonorm==1)
    for i=1:L1-K
        dzz(i)=1;
    end
end

end

%Now we normalize the targets of the training data
for i=1:L1-K
if(normalize1==5)
    T(i) = (trg1(i)-dmm(i))/dvv(i);
else
T(i) = trg1(i)/dzz(i);
end
end
TR = T;

%%%%%%%%This is the dictionary filtering process (if we want to reduce the
%%%%%%%%number of similar atoms. It is controlled by the dthr value
%%%%%%%%specified by the user. I have not investigated this a lot
dictsize=size(DD);

    nn=dictsize(1);   %the large dimension
    mm=dictsize(2);   %the small dimension

    RR=randn(nn,mm);
    RR=orth(RR);

    tooclose=0;
    for io=1:nn  %over all the atoms
        xio = DD(io,1:mm);
        
        cnt=0;
        for jo= io+1 : nn
            dddd(jo) = dist(xio,DD(jo,1:mm)');
            if(dddd(jo) <= dthr) cnt=cnt+1;  %one or more atoms are too close
            end
            
        end
        
        if(io         mindist(io) = min(dist(xio,DD(io+1:nn,1:mm)'));  %the min distance for each atom with the next ones
        else
            mindist(io)=0;
        end
        
        if(cnt==0)   %no atoms are too close
            FF(io,1:mm) = DD(io,1:mm);
            FT(io) = TR(io);
        else   %some atoms are too close, so we remove this one and put a random atom
        FF(io,1:mm) = RR(io, 1:mm);
        FT(io) = 0;   %the target for the random atoms is zero
        
        tooclose=tooclose+1;
        end
        
    end
    
    %So, now the new dictionary is FF and the new targets is FT
    %(if no filtering happened then FF is the same as DD)

    TooClose(kkk) = tooclose;  %this will tell us how many atoms were replaced (removed)
    MinDist(kkk,1:nn)=mindist(1:nn);
    
%here we construct the test data
Test(1:(L2-K),1:K) = tst(1:(L2-K),1:K);
TT = trg2(1:(L2-K));

M=L2-K;

tic  %to get the test time
sprs=0;   %to accumulate the sparsity over test vectors

for i=1:M    %loop over M vectors from the test data

    disp('**************');
    disp(i);
    
    test(1:K) = Test(i,1:K);
    
    %here we normalize the test vector by its own dot product
    if(normalize2==1) normtest = sqrt(test*test');
    elseif(normalize2==2) normtest = sqrt(var(test));
    elseif(normalize2==3) normtest = norm(test,1);
    elseif(normalize2==0) normtest=1;
    end
    

3 参考文献

部分理论来源于网络，如有侵权请联系删除。

[1]Waleed Fakhr, "Sparse Locally Linear and Neighbor Embedding for Nonlinear Time Series Prediction", ICCES 2015, December 2015.

4 Matlab代码实现