【StatLearn】统计学习中knn算法实验（2）

接着统计学习中knn算法实验（1）的内容

Problem：

1. Explore the data before classification using summary statistics or visualization
2. Pre-process the data (such as denoising, normalization, feature selection, …)
3. Try other distance metrics or distance-based voting
4. Try other dimensionality reduction methods
5. How to set the k value, if not using cross validation? Verify your idea

问题：

1. 在对数据分类之前使用对数据进行可视化处理
2. 预处理数据（去噪，归一化，数据选择）
3. 在knn算法中使用不同的距离计算方法
4. 使用其他的降维算法
5. 如何在不使用交叉验证的情况下设置k值

使用Parallel coordinates plot做数据可视化，首先对数据进行归一化处理，数据的动态范围控制在[0,1]。注意归一化的处理针对的是每一个fearture。

通过对图的仔细观察，我们挑选出重叠度比较低的feature来进行fearture selection，feature selection实际上是对数据挑选出更易区分的类型作为下一步分类算法的数据。我们挑选出feature序号为（1）、（2）、（5）、（6）、（7）、（10）的feature。个人认为，feature selection是一种简单而粗暴的降维和去噪的操作，但是可能效果会很好。

根据上一步的操作，从Parallel coordinates上可以看出，序号为（1）、（2）、（5）、（6）、（7）、（10）这几个feature比较适合作为classify的feature。我们选取以上几个feature作knn，得到的结果如下：

当K=1 的时候，Accuracy达到了85.38%，并且相比于简单的使用knn或者PCA+knn的方式，Normalization、Featrure Selection的方法使得准确率大大提升。我们也可以使用不同的feature搭配，通过实验得到更好的结果。

MaxAccuracy= 0.8834 when k=17 （Normalization+FeartureSelection+KNN）

试验中，我们使用了两种不同的Feature Selection 策略，选用较少fearture的策略对分类的准确率还是有影响的，对于那些从平行坐标看出的不那么好的fearture，对分类还是有一定的帮助的。

在较小的k值下，Feature Selection的结果要比直接采用全部Feature的结果要好。这也体现了在相对纯净的数据下，较小的k值能够获得较好的结果，这和直观感觉出来的一致。

我们再尝试对数据进行进一步的预处理操作，比如denoising。

数据去噪的方法利用对Trainning数据进行一个去处最大最小边缘值的操作，我们认为，对于一个合适的feature，它的数据应该处于一个合理的范围中，过大或者过小的数据都将是异常的。

Denoising的代码如下：

function[DNData]=DataDenoising(InputData,KillRange)
DNData=InputData;
%MedianData=median(DNData);
for i=2:size(InputData,2)
   [temp,DNIndex]=sort(DNData(:,i));
   DNData=DNData(DNIndex(1+KillRange:end-KillRange),:);
end

采用LLE作为降维的手段，通过和以上的几种方案作对比，如下：

MaxAccuracy= 0.9376 when K=23 （LLE dimensionality reduction to 2）

关于LLE算法，参见这篇论文

• Nonlinear dimensionality reduction by locally linear embedding.Sam Roweis & Lawrence Saul.Science, v.290 no.5500 , Dec.22, 2000. pp.2323--2326.

以及项目主页：

http://www.cs.nyu.edu/~roweis/lle/

源代码：

StatLearnProj.m

clear;
data=load('wine.data.txt');
%calc 5-folder knn
Accuracy=[];
for i=1:5
    Test=data(i:5:end,:);
    TestData=Test(:,2:end);
    TestLabel=Test(:,1);
    Trainning=setdiff(data,Test,'rows');
    TrainningData=Trainning(:,2:end);
    TrainningLabel=Trainning(:,1);
    Accuracy=cat(1,Accuracy,CalcAccuracy(TestData,TestLabel,TrainningData,TrainningLabel));
end
AccuracyKNN=mean(Accuracy,1);

%calc PCA
Accuracy=[];
%PCA
[Coeff,Score,Latent]=princomp(data(:,2:end));
dataPCA=[data(:,1),Score(:,1:6)];
Latent
for i=1:5
    Test=dataPCA(i:5:end,:);
    TestData=Test(:,2:end);
    TestLabel=Test(:,1);
    Trainning=setdiff(dataPCA,Test,'rows');
    TrainningData=Trainning(:,2:end);
    TrainningLabel=Trainning(:,1);
    Accuracy=cat(1,Accuracy,CalcAccuracy(TestData,TestLabel,TrainningData,TrainningLabel));
end
AccuracyPCA=mean(Accuracy,1);
BarData=[AccuracyKNN;AccuracyPCA];
bar(1:2:51,BarData');

[D,I]=sort(AccuracyKNN,'descend');
D(1)
I(1)
[D,I]=sort(AccuracyPCA,'descend');
D(1)
I(1)

%pre-processing data
%Normalization
labs1={'1)Alcohol','(2)Malic acid','3)Ash','4)Alcalinity of ash'};
labs2={'5)Magnesium','6)Total phenols','7)Flavanoids','8)Nonflavanoid phenols'};
labs3={'9)Proanthocyanins','10)Color intensity','11)Hue','12)OD280/OD315','13)Proline'};
uniData=[];
for i=2:size(data,2)
    uniData=cat(2,uniData,(data(:,i)-min(data(:,i)))/(max(data(:,i))-min(data(:,i))));
end
figure();
parallelcoords(uniData(:,1:4),'group',data(:,1),'labels',labs1);
figure();
parallelcoords(uniData(:,5:8),'group',data(:,1),'labels',labs2);
figure();
parallelcoords(uniData(:,9:13),'group',data(:,1),'labels',labs3);

%denoising

%Normalization && Feature Selection
uniData=[data(:,1),uniData];
%Normalization all feature

for i=1:5
    Test=uniData(i:5:end,:);
    TestData=Test(:,2:end);
    TestLabel=Test(:,1);
    Trainning=setdiff(uniData,Test,'rows');
    TrainningData=Trainning(:,2:end);
    TrainningLabel=Trainning(:,1);
    Accuracy=cat(1,Accuracy,CalcAccuracy(TestData,TestLabel,TrainningData,TrainningLabel));
end
AccuracyNorm=mean(Accuracy,1);

%KNN PCA Normalization
BarData=[AccuracyKNN;AccuracyPCA;AccuracyNorm];
bar(1:2:51,BarData');

%Normalization& FS 1 2 5 6 7 10 we select 1 2 5 6 7 10 feature
FSData=uniData(:,[1 2 3 6 7 8 11]);
size(FSData)
for i=1:5
    Test=FSData(i:5:end,:);
    Trainning=setdiff(FSData,Test,'rows');
    TestData=Test(:,2:end);
    TestLabel=Test(:,1);
    TrainningData=Trainning(:,2:end);
    TrainningLabel=Trainning(:,1);
    Accuracy=cat(1,Accuracy,CalcAccuracy(TestData,TestLabel,TrainningData,TrainningLabel));
end
AccuracyNormFS1=mean(Accuracy,1);

%Normalization& FS 1 6 7
FSData=uniData(:,[1 2 7 8]);
for i=1:5
    Test=FSData(i:5:end,:);
    Trainning=setdiff(FSData,Test,'rows');
    TestData=Test(:,2:end);
    TestLabel=Test(:,1);
    TrainningData=Trainning(:,2:end);
    TrainningLabel=Trainning(:,1);
    Accuracy=cat(1,Accuracy,CalcAccuracy(TestData,TestLabel,TrainningData,TrainningLabel));
end
AccuracyNormFS2=mean(Accuracy,1);
figure();
BarData=[AccuracyNorm;AccuracyNormFS1;AccuracyNormFS2];
bar(1:2:51,BarData');

[D,I]=sort(AccuracyNorm,'descend');
D(1)
I(1)
[D,I]=sort(AccuracyNormFS1,'descend');
D(1)
I(1)
[D,I]=sort(AccuracyNormFS2,'descend');
D(1)
I(1)
%denoiding
%Normalization& FS 1 6 7
FSData=uniData(:,[1 2 7 8]);
for i=1:5
    Test=FSData(i:5:end,:);
    Trainning=setdiff(FSData,Test,'rows');
    Trainning=DataDenoising(Trainning,2);
    TestData=Test(:,2:end);
    TestLabel=Test(:,1);
    TrainningData=Trainning(:,2:end);
    TrainningLabel=Trainning(:,1);
    Accuracy=cat(1,Accuracy,CalcAccuracy(TestData,TestLabel,TrainningData,TrainningLabel));
end
AccuracyNormFSDN=mean(Accuracy,1);
figure();
hold on
plot(1:2:51,AccuracyNormFSDN);
plot(1:2:51,AccuracyNormFS2,'r');

%other distance metrics

Dist='cityblock';
for i=1:5
    Test=uniData(i:5:end,:);
    TestData=Test(:,2:end);
    TestLabel=Test(:,1);
    Trainning=setdiff(uniData,Test,'rows');
    TrainningData=Trainning(:,2:end);
    TrainningLabel=Trainning(:,1);
    Accuracy=cat(1,Accuracy,CalcAccuracyPlus(TestData,TestLabel,TrainningData,TrainningLabel,Dist));
end
AccuracyNormCity=mean(Accuracy,1);

BarData=[AccuracyNorm;AccuracyNormCity];
figure();
bar(1:2:51,BarData');

[D,I]=sort(AccuracyNormCity,'descend');
D(1)
I(1)

%denoising
FSData=uniData(:,[1 2 7 8]);
Dist='cityblock';
for i=1:5
    Test=FSData(i:5:end,:);
    TestData=Test(:,2:end);
    TestLabel=Test(:,1);
    Trainning=setdiff(FSData,Test,'rows');
    Trainning=DataDenoising(Trainning,3);
    TrainningData=Trainning(:,2:end);
    TrainningLabel=Trainning(:,1);
    Accuracy=cat(1,Accuracy,CalcAccuracyPlus(TestData,TestLabel,TrainningData,TrainningLabel,Dist));
end
AccuracyNormCityDN=mean(Accuracy,1);
figure();
hold on
plot(1:2:51,AccuracyNormCityDN);
plot(1:2:51,AccuracyNormCity,'r');

%call lle

data=load('wine.data.txt');
uniData=[];
for i=2:size(data,2)
    uniData=cat(2,uniData,(data(:,i)-min(data(:,i)))/(max(data(:,i))-min(data(:,i))));
end
uniData=[data(:,1),uniData];
LLEData=lle(uniData(:,2:end)',5,2);
%size(LLEData)
LLEData=LLEData';
LLEData=[data(:,1),LLEData];

Accuracy=[];
for i=1:5
    Test=LLEData(i:5:end,:);
    TestData=Test(:,2:end);
    TestLabel=Test(:,1);
    Trainning=setdiff(LLEData,Test,'rows');
    Trainning=DataDenoising(Trainning,2);
    TrainningData=Trainning(:,2:end);
    TrainningLabel=Trainning(:,1);
    Accuracy=cat(1,Accuracy,CalcAccuracyPlus(TestData,TestLabel,TrainningData,TrainningLabel,'cityblock'));
end
AccuracyLLE=mean(Accuracy,1);
[D,I]=sort(AccuracyLLE,'descend');
D(1)
I(1)

BarData=[AccuracyNorm;AccuracyNormFS2;AccuracyNormFSDN;AccuracyLLE];
figure();
bar(1:2:51,BarData');

save('ProcessingData.mat');

CalcAccuracy.m

function Accuracy=CalcAccuracy(TestData,TestLabel,TrainningData,TrainningLabel)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%calculate the accuracy of classify
%TestData:M*D matrix D stand for dimension,M is sample
%TrainningData:T*D matrix
%TestLabel:Label of TestData
%TrainningLabel:Label of Trainning Data
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
CompareResult=[];
for k=1:2:51
    ClassResult=knnclassify(TestData,TrainningData,TrainningLabel,k);
    CompareResult=cat(2,CompareResult,(ClassResult==TestLabel));
end
SumCompareResult=sum(CompareResult,1);
Accuracy=SumCompareResult/length(CompareResult(:,1));

CalcAccuracyPlus.m

function Accuracy=CalcAccuracyPlus(TestData,TestLabel,TrainningData,TrainningLabel,Dist)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%just as CalcAccuracy,but add distance metrics
%calculate the accuracy of classify
%TestData:M*D matrix D stand for dimension,M is sample
%TrainningData:T*D matrix
%TestLabel:Label of TestData
%TrainningLabel:Label of Trainning Data
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
CompareResult=[];
for k=1:2:51
    ClassResult=knnclassify(TestData,TrainningData,TrainningLabel,k,Dist);
    CompareResult=cat(2,CompareResult,(ClassResult==TestLabel));
end
SumCompareResult=sum(CompareResult,1);
Accuracy=SumCompareResult/length(CompareResult(:,1));