基于Matlab实现空间数据的主成分局部均值聚类

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⛄ 内容介绍

从理论,设计程序和代码实现等方面,说明如何通过数据挖掘中K-均值聚类算法,利用Matlab的灵活编程功能进行探索性和优化性综合实验.以实验教学实践说明,为将创新思维和动手能力培养贯穿于实验教学的始终,利用Matlab仿真K-均值聚类具有较好的实际意义.

⛄ 部分代码

close all

disp(' ')

disp('This DEMO simulates 2D-3D spatial data {Xi,Yi,Zi} and computes their')

disp('principal curves and surfaces by means of local clustering techniques.')

disp('These methods are based on iterative projections of local simple means')

disp('made by the principal components (PC) of the local covariance matrices.')

disp('The archive contains 5 programs:')

disp('1) PCLM_estimate: computes principal curves in 2D an surfaces in 3D,')

disp('2) PCLM_select_n: identifies the optimal size "n" of means and cov,')

disp('3) PCLM_select_k: identifies the optimal number "k" of iterations,')

disp('4) PCLM_slice_3d: estimates 3d surfaces by layers of 2d curves,')

disp('5) PCLM_adaptive: as in 1) but with k-varying coefficient n.')

disp(' ')

disp('Press enter to continue ...')

disp(' ')

disp('Data generation:') 

disp('882 points of two intesecting planes are simulated and randomized')

disp('Wait while computing ... ')

rng('default')

[x y] = meshgrid(-10:1:10);

Z1 = 1*x + 50*y + 500; figure; subplot(221); surf(x,y,Z1/100)

Z2 = 1*x - 50*y + 500; hold on; surf(x,y,Z2/100); axis tight

title('Ground surfaces')

n=length(x(:)); a=1;

xx=x(:)+randn(n,1)*a; 

yy=y(:)+randn(n,1)*a; 

z1=Z1(:)/100+randn(n,1)*a; 

z2=Z2(:)/100+randn(n,1)*a;

subplot(222)

plot3(yy,z1,xx,'.b'); grid; hold on

plot3(yy,z2,xx,'.r'); box; axis tight

xlabel('x'); ylabel('y'); zlabel('z')

title('Randomized points')

XYZ=[[yy z1 xx]; [yy z2 xx]];

disp(' ')

disp('Press enter to continue ...')

disp(' ')

disp('2D fitting of data with heuristic selection of coefficients:')

disp('YY = PCLM_estimate( [XYZ ones(n*2,1)], 2,1,2, 40,1,6, 1);')

      YY = PCLM_estimate( [XYZ ones(n*2,1)], 2,1,2, 40,1,6, 1);

disp(' ')

disp('Press enter to continue ...')

disp(' ')

disp('3D fitting of data with 2D selection of nearest neighbors:')

disp('YY = PCLM_estimate( [XYZ ones(n*2,1)], 3,1,2, 40,1,6, 1);')

      YY = PCLM_estimate( [XYZ ones(n*2,1)], 3,1,2, 40,1,6, 1);

disp(' ')

disp('Press enter to continue ...')

disp(' ')

disp('Tentative selection of the optimal number "n" of neighbors in 2D')

disp('PCLM_select_n( [XYZ ones(n*2,1)], 2,1,2,  1,6,  15,90,6, 1 );')

      PCLM_select_n( [XYZ ones(n*2,1)], 2,1,2,  1,6,  15,90,6, 1 );

disp(' ')

disp('Press enter to continue ...')

disp(' ')

disp('Tentative selection of the optimal number "k" of iterations in 2D')

disp('PCLM_select_k( [XYZ ones(n*2,1)], 2,1,2, 40,1,9, 1 );')

      PCLM_select_k( [XYZ ones(n*2,1)], 2,1,2, 40,1,9, 1 );

disp(' ')

disp('Press enter to continue ...')

disp('Finally, run a sliced 3D fitting with 2D sequential curves ...')

disp('PCLM_slice_3d( [XYZ ones(n*2,1)], 20,1,6, 3,50,4 );')

      PCLM_slice_3d( [XYZ ones(n*2,1)], 20,1,6, 3,50,4 );

disp(' ')

disp('Press enter to continue ...')

disp(' ')

disp('Also, run the adaptive version of the basic code ...')

disp('with proportional distance weighting of the local statistics')

disp('and decreasing value of the sample size during the iterations')

disp('PCLM_adaptive( [XYZ ones(n*2,1)], 2,1,2,  100,1,10,  2,-9, 1 );')

      PCLM_adaptive( [XYZ ones(n*2,1)], 2,1,2,  100,1,10,  2,-9, 1 );

disp(' ')

disp('bye :-)')

⛄ 运行结果

⛄ 参考文献

[1]陈璐, 汪亚明, 韩永华. 基于子空间K均值聚类的概率配准算法[J]. 软件导刊, 2021.

⛄ 完整代码

❤️部分理论引用网络文献，若有侵权联系博主删除

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