相关向量机及其应用

1、相关向量机理论及其应用相关向量机理论及其应用1 1Presentation 2012 BJTUBEIJING JIAOTONG UNIVERSITYBEIJING JIAOTONG UNIVERSITY相关向量机理论及其应用相关向量机理论及其应用Relevance Vector Machine and its application姚畅姚畅北京交通大学北京交通大学2013-4-13相关向量机理论及其应用相关向量机理论及其应用2 2内容提要：内容提要：一、相关向量机一、相关向量机( (Relevance Vector Machine, RVM)理论理论二、二、基于基于RVM的交通标志识别研究进展

2、的交通标志识别研究进展三、待开展的工作三、待开展的工作相关向量机理论及其应用相关向量机理论及其应用3HOV车道车辆乘客检测HOV(High Occupancy Vehicle)： 即“高载客率汽车”，指载客数多的车辆HOV车道： 专门供HOV车辆行驶的车道 又称为合乘（carpool）车道 其标志为 (菱形)，也被称为“钻石车道” 3交通图像处理与分析相关向量机理论及其应用相关向量机理论及其应用4交通图像处理与分析交通图像处理与分析-交通标志检测与识别交通标志检测与识别光照不足、运动模糊、几何失真、遮挡光照不足、运动模糊、几何失真、遮挡 类别多，易混淆类别多，易混淆 内含文字、图标，影响识别效

3、果内含文字、图标，影响识别效果4相关向量机理论及其应用相关向量机理论及其应用5基于相关向量机的交通标志识别研究进展基于相关向量机的交通标志识别研究进展图像库的构建： 3131像素灰度图像相关向量机理论及其应用相关向量机理论及其应用6基于相关向量机的交通标志识别研究进展基于相关向量机的交通标志识别研究进展图像库的构建： 相关向量机理论及其应用相关向量机理论及其应用7基于相关向量机的交通标志识别研究进展基于相关向量机的交通标志识别研究进展图像库的构建： 样本统计共466个样本相关向量机理论及其应用相关向量机理论及其应用8基于相关向量机的交通标志识别研究进展基于相关向量机的交通标志识别研究进展图像库

4、的构建： 每个样本图像大小为3131像素,灰度图像,共466个样本相关向量机理论及其应用相关向量机理论及其应用9基于相关向量机的交通标志识别研究进展基于相关向量机的交通标志识别研究进展图像库的构建： 对466个样本进行随机排列,使得同类样本分散开相关向量机理论及其应用相关向量机理论及其应用10基于相关向量机的交通标志识别研究进展基于相关向量机的交通标志识别研究进展实验以靠右侧行驶指示标志作为识别目标（正样本），label=1；其余标志作为负样本，label=-1，采用相关向量机进行识别。以靠右侧行驶指示标志为例相关向量机理论及其应用相关向量机理论及其应用11基于相关向量机的交通标志识别研究进展

5、基于相关向量机的交通标志识别研究进展样本数据正态归一化( , )( , )F x yfN x ysf为均值，s为标准方差将正态归一化后的样本数据排列为1行961列的向量，作为特征向量。对整个图像库进行该操作，获得一个466961的数据矩阵。取其中一部分数据用于训练RVM，一部分数据用于测试。相关向量机理论及其应用相关向量机理论及其应用12基于相关向量机的交通标志识别研究进展基于相关向量机的交通标志识别研究进展一一 改变训练样本总数改变训练样本总数N1 训练样本总数N=100,测试样本总数Nt=366 maxIts=500,kernel=poly2,width=3020 L = -7.884 G

6、amma = 3.26 (nz = 43) 40 L = -7.877 Gamma = 3.14 (nz = 11) 60 L = -7.877 Gamma = 3.14 (nz = 8) 80 L = -7.877 Gamma = 3.14 (nz = 6) 100 L = -7.877 Gamma = 3.14 (nz = 5) 120 L = -7.877 Gamma = 3.14 (nz = 5) 140 L = -7.877 Gamma = 3.14 (nz = 5) Terminating: max log(alpha) change is 1.15463e-014 ( L = -

7、7.877 Gamma = 3.14 (nz = 4) non-zero parameters:4 RVM CLASSIFICATION test error: 1.91%Time=0.6354s00110001111相关向量错误识别的样本相关向量机理论及其应用相关向量机理论及其应用13基于相关向量机的交通标志识别研究进展基于相关向量机的交通标志识别研究进展一一 改变训练样本总数改变训练样本总数N2 训练样本总数N=200,测试样本总数Nt=266 maxIts=500,kernel=poly2,width=30相关向量错误识别的样本 20 L = -9.677 Gamma = 3.99 (n

8、z = 52) 40 L = -9.293 Gamma = 3.63 (nz = 16) 60 L = -9.218 Gamma = 3.56 (nz = 10) 80 L = -9.205 Gamma = 3.54 (nz = 7) 100 L = -9.199 Gamma = 3.53 (nz = 6) 120 L = -9.196 Gamma = 3.53 (nz = 5) Terminating: max log(alpha) change is 0.00135018 ( L = -9.196 Gamma = 3.53 (nz = 5) non-zero parameters:5 RV

9、M CLASSIFICATION test error: 1.13%Time=0.7237s00110111相关向量机理论及其应用相关向量机理论及其应用14基于相关向量机的交通标志识别研究进展基于相关向量机的交通标志识别研究进展一一 改变训练样本总数改变训练样本总数N3 训练样本总数N=300,测试样本总数Nt=166 maxIts=500,kernel=poly2,width=30相关向量20 L = -11.276 Gamma = 4.43 (nz = 90) 40 L = -10.784 Gamma = 3.90 (nz = 29) 60 L = -10.790 Gamma = 4.05

10、 (nz = 16) 80 L = -10.784 Gamma = 4.04 (nz = 12) 100 L = -10.784 Gamma = 4.04 (nz = 10) 120 L = -10.784 Gamma = 4.04 (nz = 7) 140 L = -10.784 Gamma = 4.04 (nz = 6) 160 L = -10.784 Gamma = 4.04 (nz = 6) 180 L = -10.784 Gamma = 4.04 (nz = 6) 200 L = -10.784 Gamma = 4.04 (nz = 6) 220 L = -10.784 Gamma

11、= 4.04 (nz = 6) 240 L = -10.784 Gamma = 4.04 (nz = 6) Terminating: max log(alpha) change is 0.00487965 ( L = -10.784 Gamma = 4.04 (nz = 6) non-zero parameters: 6 RVM CLASSIFICATION test error: 0.00%Time=1.5190s110000相关向量机理论及其应用相关向量机理论及其应用15基于相关向量机的交通标志识别研究进展基于相关向量机的交通标志识别研究进展一一 改变训练样本总数改变训练样本总数N4 训练

12、样本总数N=400,测试样本总数Nt=66 maxIts=500,kernel=poly2,width=30相关向量20 L = -11.372 Gamma = 4.44 (nz = 120) 40 L = -10.791 Gamma = 3.98 (nz = 29) 60 L = -10.799 Gamma = 3.98 (nz = 14) 80 L = -10.799 Gamma = 3.99 (nz = 10) 100 L = -10.798 Gamma = 3.99 (nz = 9) 120 L = -10.796 Gamma = 3.99 (nz = 9) 140 L = -10.7

13、94 Gamma = 3.99 (nz = 8) 160 L = -10.791 Gamma = 3.99 (nz = 8) 180 L = -10.786 Gamma = 3.99 (nz = 7) 200 L = -10.779 Gamma = 3.98 (nz = 7) 220 L = -10.767 Gamma = 3.98 (nz = 7) 240 L = -10.751 Gamma = 3.96 (nz = 7) 260 L = -10.735 Gamma = 3.95 (nz = 7) 280 L = -10.726 Gamma = 3.95 (nz = 7) 300 L = -

14、10.723 Gamma = 3.94 (nz = 7) 320 L = -10.721 Gamma = 3.94 (nz = 7) 340 L = -10.721 Gamma = 3.94 (nz = 7) 360 L = -10.721 Gamma = 3.94 (nz = 7) 380 L = -10.721 Gamma = 3.94 (nz = 7) 400 L = -10.721 Gamma = 3.94 (nz = 7) 420 L = -10.721 Gamma = 3.94 (nz = 7) 440 L = -10.721 Gamma = 3.94 (nz = 7) 460 L

15、 = -10.721 Gamma = 3.94 (nz = 7) 480 L = -10.721 Gamma = 3.94 (nz = 7) 500 L = -10.721 Gamma = 3.94 (nz = 7) Terminating due to max iterations (did not converge) non-zero parameters:7 RVM CLASSIFICATION test error: 0.00%Time=2.5508s0110110相关向量机理论及其应用相关向量机理论及其应用16基于相关向量机的交通标志识别研究进展基于相关向量机的交通标志识别研究进展一

16、一 改变训练样本总数改变训练样本总数NN100200300400RVs4567Error rate1.91%1.13%00Time (s)0.63540.72371.51902.5508相关向量机理论及其应用相关向量机理论及其应用17基于相关向量机的交通标志识别研究进展基于相关向量机的交通标志识别研究进展二二 改变width训练样本数N=230，测试样本数Nt=233maxIts=500,kernel=poly2width510152025303540455060T e s t error1.69492.11861.69491.271200001.27121.69491.6949Time(s)

17、1.43010.83051.25720.97811.43250.88721.09541.06711.15311.27401.1636Width 取 30为最佳值相关向量机理论及其应用相关向量机理论及其应用18基于相关向量机的交通标志识别研究进展基于相关向量机的交通标志识别研究进展三三 改变核函数类型kernelN=230，maxIts=500, width=301 kernel=poly120 L = -11.546 Gamma = 3.98 (nz = 91) 40 L = -11.408 Gamma = 3.95 (nz = 34) 60 L = -11.407 Gamma = 3.95

18、(nz = 18) 80 L = -11.407 Gamma = 3.95 (nz = 16) 100 L = -11.407 Gamma = 3.95 (nz = 10) 120 L = -11.407 Gamma = 3.95 (nz = 9) 140 L = -11.407 Gamma = 3.95 (nz = 7) 160 L = -11.407 Gamma = 3.95 (nz = 7) 180 L = -11.407 Gamma = 3.95 (nz = 7) 200 L = -11.407 Gamma = 3.95 (nz = 7) 220 L = -11.407 Gamma =

19、 3.95 (nz = 6) 240 L = -11.407 Gamma = 3.95 (nz = 6) 260 L = -11.407 Gamma = 3.95 (nz = 6) Terminating: max log(alpha) change is 0.00127245 ( L = -11.407 Gamma = 3.95 (nz = 6) non-zero parameters: 6 RVM CLASSIFICATION test error: 0.42%Time=1.0940s1010010相关向量错误识别的样本相关向量机理论及其应用相关向量机理论及其应用19基于相关向量机的交通标

20、志识别研究进展基于相关向量机的交通标志识别研究进展三三 改变核函数类型kernelN=230，maxIts=500, width=302 kernel=poly2相关向量20 L = -10.947 Gamma = 4.15 (nz = 78) 40 L = -10.662 Gamma = 4.01 (nz = 25) 60 L = -10.379 Gamma = 3.75 (nz = 13) 80 L = -10.376 Gamma = 3.74 (nz = 10) 100 L = -10.376 Gamma = 3.74 (nz = 7) 120 L = -10.376 Gamma = 3

21、.74 (nz = 6) 140 L = -10.376 Gamma = 3.74 (nz = 6) 160 L = -10.376 Gamma = 3.74 (nz = 6) Terminating: max log(alpha) change is 7.44294e-013 ( L = -10.376 Gamma = 3.74 (nz = 5) non-zero parameters:5 RVM CLASSIFICATION test error: 0.00%Time=1.035901010相关向量机理论及其应用相关向量机理论及其应用20基于相关向量机的交通标志识别研究进展基于相关向量机的

22、交通标志识别研究进展三三 改变核函数类型kernelN=230，maxIts=500, width=303 kernel=poly3相关向量20 L = -10.552 Gamma = 4.09 (nz = 84) 40 L = -9.812 Gamma = 3.48 (nz = 17) 60 L = -9.803 Gamma = 3.47 (nz = 10) 80 L = -9.803 Gamma = 3.47 (nz = 6) 100 L = -9.803 Gamma = 3.47 (nz = 5) 120 L = -9.803 Gamma = 3.47 (nz = 5) 140 L =

23、-9.803 Gamma = 3.47 (nz = 5) 160 L = -9.803 Gamma = 3.47 (nz = 5) 180 L = -9.803 Gamma = 3.47 (nz = 5) Terminating: max log(alpha) change is 3.01981e-014 ( L = -9.803 Gamma = 3.47 (nz = 4) non-zero parameters:4 RVM CLASSIFICATION test error: 0.00%Time=1.02460110相关向量机理论及其应用相关向量机理论及其应用21基于相关向量机的交通标志识别

24、研究进展基于相关向量机的交通标志识别研究进展三三 改变核函数类型kernelN=230，maxIts=500, width=304 kernel=poly4相关向量20 L = -11.923 Gamma = 4.88 (nz = 64) 40 L = -12.090 Gamma = 4.91 (nz = 21) 60 L = -12.093 Gamma = 4.92 (nz = 14) 80 L = -12.094 Gamma = 4.92 (nz = 11) 100 L = -12.096 Gamma = 4.92 (nz = 9) 120 L = -12.103 Gamma = 4.94

25、 (nz = 9) 140 L = -12.127 Gamma = 5.01 (nz = 9) 160 L = -12.114 Gamma = 5.19 (nz = 9) 180 L = -11.890 Gamma = 5.04 (nz = 8) 200 L = -10.374 Gamma = 4.04 (nz = 8) 220 L = -10.223 Gamma = 3.75 (nz = 6) 240 L = -10.211 Gamma = 3.74 (nz = 6) 260 L = -10.208 Gamma = 3.75 (nz = 6) 280 L = -10.207 Gamma =

26、3.75 (nz = 6) 300 L = -10.207 Gamma = 3.75 (nz = 6) 320 L = -10.207 Gamma = 3.75 (nz = 6) 340 L = -10.207 Gamma = 3.75 (nz = 6) 360 L = -10.207 Gamma = 3.75 (nz = 6) 380 L = -10.207 Gamma = 3.75 (nz = 6) 400 L = -10.207 Gamma = 3.75 (nz = 6) 420 L = -10.207 Gamma = 3.75 (nz = 6) 440 L = -10.207 Gamm

27、a = 3.75 (nz = 6) 460 L = -10.207 Gamma = 3.75 (nz = 6) 480 L = -10.207 Gamma = 3.75 (nz = 6) 500 L = -10.207 Gamma = 3.75 (nz = 6) Terminating due to max iterations (did not converge) non-zero parameters:6 RVM CLASSIFICATION test error: 0.42%Time=1.3293s0110000错误识别的样本相关向量机理论及其应用相关向量机理论及其应用22基于相关向量机

28、的交通标志识别研究进展基于相关向量机的交通标志识别研究进展三三 改变核函数类型kernelN=230，maxIts=500, width=305 kernel=gauss相关向量20 L = -11.913 Gamma = 4.18 (nz = 111) 40 L = -11.777 Gamma = 4.06 (nz = 34) 60 L = -11.738 Gamma = 4.03 (nz = 21) 80 L = -11.729 Gamma = 4.02 (nz = 14) 100 L = -11.725 Gamma = 4.02 (nz = 13) 120 L = -11.723 Gam

29、ma = 4.01 (nz = 11) 140 L = -11.722 Gamma = 4.01 (nz = 10) 160 L = -11.721 Gamma = 4.01 (nz = 10) 180 L = -11.722 Gamma = 4.01 (nz = 10) 200 L = -11.724 Gamma = 4.02 (nz = 10) 220 L = -11.731 Gamma = 4.03 (nz = 10) 240 L = -11.755 Gamma = 4.08 (nz = 8) 260 L = -11.759 Gamma = 4.12 (nz = 7) 280 L = -

30、11.629 Gamma = 3.99 (nz = 7) 300 L = -11.627 Gamma = 3.99 (nz = 7) 320 L = -11.627 Gamma = 3.99 (nz = 6) Terminating: max log(alpha) change is 9.98597e-011 ( L = -11.627 Gamma = 3.99 (nz = 5) non-zero parameters: 5 RVM CLASSIFICATION test error: 0.00%01100相关向量机理论及其应用相关向量机理论及其应用23基于相关向量机的交通标志识别研究进展基于

31、相关向量机的交通标志识别研究进展三三 改变核函数类型kernelKernelpoly1poly2poly3poly4gaussRVs65465Error rate0.42%000.42%0Time(s)1.09401.03591.02461.32931.1511相关向量机理论及其应用相关向量机理论及其应用24基于相关向量机的交通标志识别研究进展基于相关向量机的交通标志识别研究进展四四 改变图像库样本尺寸大小1 每个样本图像大小为每个样本图像大小为2121像素像素440 L = -12.686 Gamma = 3.98 (nz = 12) 460 L = -12.686 Gamma = 3.98

32、 (nz = 12) 480 L = -12.686 Gamma = 3.98 (nz = 12) 500 L = -12.686 Gamma = 3.98 (nz = 12) Terminating due to max iterations (did not converge) non-zero parameters: 12 RVM CLASSIFICATION test error: 0.42%Time: 1.8121s1001001010000Kernel=gaussKernel=poly2 260 L = -13.264 Gamma = 4.35 (nz = 8) 280 L = -

33、13.265 Gamma = 4.36 (nz = 8) 300 L = -13.266 Gamma = 4.37 (nz = 8) 320 L = -13.266 Gamma = 4.38 (nz = 7) Terminating: max log(alpha) change is 0.00738987 ( L = -13.266 Gamma = 4.38 (nz = 7) non-zero parameters: 7 RVM CLASSIFICATION test error: 0.00%Time: 1.1240s0111000相关向量错误识别的样本相关向量相关向量机理论及其应用相关向量机

34、理论及其应用25基于相关向量机的交通标志识别研究进展基于相关向量机的交通标志识别研究进展四四 改变图像库样本尺寸大小1 每个样本图像大小为每个样本图像大小为4141像素像素Kernel=gaussKernel=poly2相关向量相关向量120 L = -11.192 Gamma = 4.03 (nz = 6) 140 L = -11.041 Gamma = 3.85 (nz = 6) 160 L = -11.039 Gamma = 3.85 (nz = 6) 180 L = -11.039 Gamma = 3.85 (nz = 6) Terminating: max log(alpha) change is 8.58932e-010 ( L = -11.039 Gamma = 3.85 (nz = 5) non-zero parameters: 5 RVM CLASSIFICATION test error: 0.00%Time: 1.0335s01010 440 L = -10.651 Gamma = 3.91 (nz = 6) 460 L =