K-means算法和矢量量化
2024-10-11 19:33:43
语音信号的数字处理课程作业——矢量量化。这里采用了K-means算法，即假设量化种类是已知的，当然也可以采用LBG算法等，不过K-means比较简单。矢量是二维的，可以在平面上清楚的表示出来。
1. 算法描述
本次实验选择了K-means算法对数据进行矢量量化。算法主要包括以下几个步骤
- 初始化：载入训练数据，确定初始码本中心（4个）；
- 最近邻分类：对训练数据计算距离（此处采用欧式距离），按照距离最小分类；
- 码本更新：重新生成包腔对应的质心；
- 重复分类和码本更新步骤，知道达到最大迭代次数或满足一定停止准则；
- 利用上述步骤得到的码本对测试数据进行矢量量化，并求最小均方误差。
本实验准备使用MATLAB软件完成矢量量化任务，具体步骤实现如下
- 将training.dat和to_be_quantized.dat置于当前工作文件夹内，采用load命令载入training.dat 。
- 采用合适的规则选取初始的码本中心。如图 1所示。
图 1 码本中心选择
- 计算训练数据和每一码本中心之间的距离。
- 采用最近邻准则进行分类。
- 重新计算质心，计算公式如下所示。
- 重复3～5，直到满足最大迭代次数或是两次迭代结果没有发生改变时，此时结果为训练结果。
- 利用训练结果对to_be_quantized.dat进行矢量量化。
2. 代码
MATLAB代码如下
%% training
load('training.dat');
scatter(training(:,),training(:,));
%初始中心选取
x_max = max(training(:,));
x_min = min(training(:,));
y_max = max(training(:,));
y_min = min(training(:,));
z1 = [(*x_min+x_max)/ (*y_min+y_max)/];
z2 = [(*x_max+x_min)/ (*y_min+y_max)/];
z3 = [(*x_min+x_max)/ (*y_max+y_min)/];
z4 = [(*x_max+x_min)/ (*y_max+y_min)/];
z = [z1;z2;z3;z4];
hold on;
scatter(z(:,),z(:,));
legend('训练数据','码本');grid on;
hold off;
for k = :
%码本分类，欧式距离
distancetoz1 = (training - repmat(z1,size(training,),)).^;
distancetoz1 = sum(distancetoz1,);
distancetoz2 = (training - repmat(z2,size(training,),)).^;
distancetoz2 = sum(distancetoz2,);
distancetoz3 = (training - repmat(z3,size(training,),)).^;
distancetoz3 = sum(distancetoz3,);
distancetoz4 = (training - repmat(z4,size(training,),)).^;
distancetoz4 = sum(distancetoz4,);
distance = [distancetoz1 distancetoz2 distancetoz3 distancetoz4];
% 分类
if(classification == (distance == repmat(min(distance,[],),,)))
error = mean(min(distance,[],));
break; %如果两次迭代之间没有变化，结束迭代
end;
classification = (distance == repmat(min(distance,[],),,));
c1 = training(classification(:,),:);
c2 = training(classification(:,),:);
c3 = training(classification(:,),:);
c4 = training(classification(:,),:);
figure;scatter(c1(:,),c1(:,));hold on;scatter(c2(:,),c2(:,));
scatter(c3(:,),c3(:,));scatter(c4(:,),c4(:,));
legend('类型1','类型2','类型3','类型4');grid on;hold off;
% 码本更新
z1 = mean(c1);
z2 = mean(c2);
z3 = mean(c3);
z4 = mean(c4);
z = [z1;z2;z3;z4];
end
%% Test
load('to_be_quantized.dat')
distancetoz1 = (to_be_quantized - repmat(z1,size(to_be_quantized,),)).^;
distancetoz1 = sum(distancetoz1,);
distancetoz2 = (to_be_quantized - repmat(z2,size(to_be_quantized,),)).^;
distancetoz2 = sum(distancetoz2,);
distancetoz3 = (to_be_quantized - repmat(z3,size(to_be_quantized,),)).^;
distancetoz3 = sum(distancetoz3,);
distancetoz4 = (to_be_quantized - repmat(z4,size(to_be_quantized,),)).^;
distancetoz4 = sum(distancetoz4,);
distance = [distancetoz1 distancetoz2 distancetoz3 distancetoz4];
testerror = mean(min(distance,[],)); classification = (distance == repmat(min(distance,[],),,));
c1 = to_be_quantized(classification(:,),:);
c2 = to_be_quantized(classification(:,),:);
c3 = to_be_quantized(classification(:,),:);
c4 = to_be_quantized(classification(:,),:);
figure;scatter(c1(:,),c1(:,));hold on;scatter(c2(:,),c2(:,));
scatter(c3(:,),c3(:,));scatter(c4(:,),c4(:,));
legend('类型1','类型2','类型3','类型4');grid on;hold off;
3. 实验结果
图 2 训练码本分布
图 3第一次迭代结果 图 4第四次迭代结果
图 5第八次迭代结果 图 6第九次迭代结果
图 2展示了训练数据的分布，图 3～6是迭代过程中分类的变化情况，迭代完成后的码本为
- Z1 = [1.62060631541935 -0.108624145483871]
- Z2 = [7.96065094375000 -0.999061308437500]
- Z3 = [1.72161941468750 6.82121444062500]
- Z4 = [4.43652765757576 2.18874305151515]
4. 实验数据
training.dat
8.4416189e+000 -7.9885975e-001
1.1480908e+000 7.8735044e+000
7.7380144e+000 -1.2165061e+000
8.9727144e-001 7.3962468e+000
7.5343823e+000 -1.1424504e+000
-6.9234039e-001 -1.7096610e+000
7.6418740e+000 -1.3563792e+000
3.1091418e+000 6.3850541e+000
2.3482174e+000 4.7553506e-001
-1.3840364e+000 -2.5480394e+000
8.2008897e+000 -1.1448387e+000
-1.1392497e+000 -2.0809884e+000
3.7970116e+000 1.6906469e+000
3.4484200e+000 1.3980911e+000
2.5701485e+000 5.3755044e+000
8.3899076e+000 -6.6675309e-001
2.0146545e+000 5.6984592e+000
1.8853328e+000 5.2762628e-001
5.6781432e+000 3.2588691e+000
1.0102480e+000 5.8167707e+000
7.7302763e+000 -1.2030348e+000
4.2118845e+000 1.6527181e+000
4.3920049e-001 6.7168970e+000
8.1934984e-001 -5.1917945e-001
4.3708769e+000 2.1613573e+000
1.8569681e+000 4.8380565e+000
3.4732504e+000 1.7953635e+000
7.5822756e+000 -1.1521814e+000
2.6434078e+000 6.3295690e+000
1.9968582e+000 7.3529314e+000
4.0833513e+000 1.4936002e+000
3.6767894e+000 6.7446912e+000
1.3524515e+000 6.8177858e+000
3.9711504e+000 1.5452503e+000
1.5594711e+000 6.3885281e+000
3.4692089e+000 1.7118124e+000
5.2575491e+000 2.5601553e+000
7.8827882e+000 -6.8867840e-001
4.8176593e+000 2.1684005e+000
2.7402486e+000 8.3320174e+000
2.2549011e+000 3.9393641e-001
8.0840542e+000 -7.3155184e-001
8.8753667e-001 6.1607892e+000
1.8067727e+000 -2.1099454e-001
6.8650914e+000 4.4228389e+000
6.4174056e+000 3.7590081e+000
4.0933273e+000 1.3598676e+000
2.2882999e+000 5.1876795e-001
7.9225523e+000 -1.1725456e+000
4.3561335e+000 1.8976163e+000
8.3279098e+000 -1.0232899e+000
6.2551331e+000 3.3449949e+000
3.1276024e+000 7.8463356e-001
6.5241605e+000 3.4561490e+000
4.1588140e-001 6.4974858e+000
2.7379263e+000 6.4746080e+000
7.2185639e+000 -1.3525589e+000
7.5424890e+000 -1.5317814e+000
3.7468423e+000 1.6110753e+000
8.8708536e+000 -5.6439331e-001
7.6960713e+000 -1.1960633e+000
7.5979552e+000 -1.1469059e+000
2.8220978e+000 1.0360184e+000
3.8165165e+000 1.6082223e+000
6.6799248e-002 -1.2910367e+000
2.3054028e+000 2.8450986e-001
4.2788715e+000 5.1995858e+000
3.0006534e+000 9.1250414e-001
7.6051326e+000 -1.1005476e+000
2.5331653e+000 9.7428007e-001
1.0743104e+000 6.0859296e+000
6.7237149e-001 8.6117274e+000
2.4333003e+000 7.1421389e-001
1.7723473e+000 7.1841833e+000
3.5762796e+000 1.5348648e+000
2.7863558e+000 7.3565043e-001
8.0284284e+000 -7.9636983e-001
8.4672682e+000 -8.2062254e-001
2.3519727e+000 8.1632796e-001
7.4240720e+000 4.1800229e+000
1.9724319e+000 4.4328699e-001
7.7622621e+000 -1.3506605e+000
2.3793018e+000 -4.3107386e-001
3.2455220e+000 1.2697488e+000
1.3644859e+000 5.9712644e+000
5.4815655e+000 2.6608754e+000
-1.2002073e+000 -2.1765731e+000
-3.5558595e-001 6.4387512e+000
3.9418185e+000 1.9858047e+000
1.0533626e+000 -7.9068285e-001
1.9560213e+000 6.2001316e+000
7.5555203e+000 -1.2087337e+000
1.7851705e+000 7.0073148e+000
2.2736274e+000 7.9336349e-001
7.6615799e+000 -1.0445564e+000
2.7181608e+000 4.7615418e-001
1.8291149e+000 -6.7261971e-001
7.8640867e+000 -1.4296092e+000
2.6362814e+000 5.8303048e-001
3.7771102e+000 1.2928196e+000
7.5360359e+000 -9.7942712e-001
4.0257498e+000 1.2217666e+000
8.4500853e+000 -7.6599648e-001
3.0488646e+000 6.2159289e+000
2.0954150e+000 2.5848825e-001
1.6592148e+000 7.5650162e+000
3.5535363e+000 1.3326217e+000
4.3388636e+000 2.1235893e+000
3.1233524e+000 1.3971470e+000
7.6317385e+000 -1.0744610e+000
8.5028402e-001 -3.2822876e-001
8.6903131e+000 -2.6843242e-001
4.4418011e+000 2.5676053e+000
2.5119872e+000 -1.0521242e-001
1.9613752e+000 7.0072931e+000
3.2607143e+000 1.5432286e+000
3.2830401e+000 1.0228031e+000
8.0201528e+000 -7.0827461e-001
3.1597313e+000 7.6750043e+000
9.0059933e+000 -9.6130246e-001
1.1037820e+000 -1.2980812e-001
1.5334911e+000 7.4282719e+000
6.0948533e-001 6.3861341e+000
4.0065706e-001 -1.1015776e+000
2.3451558e+000 8.6384057e+000
1.4490876e+000 8.6646066e+000
8.0421821e+000 -8.1100509e-001
8.0175747e+000 -5.6119093e-001
to_be_quantized
3.7682247e+000 8.3609865e-001
2.6963398e+000 6.5766226e-001
3.3438207e+000 1.2495321e+000
1.3646195e+000 -6.3947640e-001
7.8227583e+000 -8.8616996e-001
1.3532508e+000 7.6607304e+000
2.2741739e+000 6.9387226e+000
3.5361382e+000 5.9729821e+000
8.0409138e+000 -1.1234886e+000
7.9630460e+000 -1.3032200e+000
2.3478158e+000 6.9759690e+000
3.2632942e+000 1.5675470e+000
1.5241488e+000 7.1053147e+000
5.7320838e+000 3.4042655e+000
2.3339411e+000 6.9428434e+000
6.5330392e+000 3.4415860e+000
3.1068803e+000 8.0080363e+000
7.4078126e+000 -1.3416027e+000
1.9925474e+000 -2.7782790e-001
5.0187915e+000 2.7058427e+000
2.6535497e-001 -1.2622069e+000
1.4960584e+000 6.3355004e+000
3.1933474e-001 7.1467466e+000
8.2821020e+000 -9.5178778e-001
2.5653586e+000 6.9836115e+000
3.6937139e+000 1.1535671e+000
8.5390043e+000 -5.0678923e-001
7.5436898e-001 -6.7669379e-001
2.1638213e+000 7.6142401e+000
4.8522826e+000 2.7079076e+000
5.4890641e+000 3.3875394e+000
4.2525899e+000 1.8861744e+000
8.4088615e+000 -1.1920963e+000
5.5396960e+000 2.9680110e+000
3.3334381e+000 1.4384861e+000
3.5212919e+000 1.0327602e+000
4.6303492e+000 2.1627805e+000
3.9385929e+000 1.0010804e+000
8.4553633e+000 -7.2297277e-001
1.8111095e+000 7.6132396e+000
1.1240984e+000 -2.7029879e-001
-3.3840083e-002 -1.5590834e+000
7.1674870e+000 -1.5449905e+000
8.5103026e+000 -9.8820393e-001
7.7529857e+000 -1.4787432e+000
1.8704913e+000 6.9370116e+000
6.0271939e+000 3.2118915e+000
2.8287461e+000 7.3399383e+000
4.1568876e+000 1.5631238e+000
8.2187067e-001 -5.8546437e-001
3.1084965e+000 5.3512449e+000
4.1581386e+000 2.1763345e+000
3.2267474e+000 1.4105815e+000
8.1564752e-001 7.2540175e+000
8.0241402e+000 -8.2411742e-001
6.2773554e+000 3.1729045e+000
8.5460058e+000 -1.0330056e+000
8.6215210e+000 -7.4057378e-001
7.4872291e+000 -1.0113921e+000
3.3155133e+000 9.7636038e-001
2.1051593e+000 3.4894654e-001
3.6776134e+000 1.5387928e+000
2.9009105e+000 5.6931589e+000
8.0567164e+000 -1.0000803e+000
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