Added SMEM GMM examples

examples/undocumented/python_modular/graphical/smem_1d_gmm.py

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+from pylab import figure,show,connect,hist,plot,legend
+from numpy import array, append, arange, empty
+from shogun.Distribution import Gaussian, GMM
+from shogun.Features import RealFeatures
+import util
+
+util.set_title('SMEM for 1d GMM example')
+
+max_iter=100
+max_cand=5
+min_cov=1e-9
+max_em_iter=1000
+min_change=1e-9
+
+real_gmm=GMM(3)
+
+real_gmm.set_nth_mean(array([-2.0]), 0)
+real_gmm.set_nth_mean(array([0.0]), 1)
+real_gmm.set_nth_mean(array([2.0]), 2)
+
+real_gmm.set_nth_cov(array([[0.3]]), 0)
+real_gmm.set_nth_cov(array([[0.1]]), 1)
+real_gmm.set_nth_cov(array([[0.2]]), 2)
+
+real_gmm.set_coef(array([0.3, 0.5, 0.2]))
+
+generated=array([real_gmm.sample()])
+for i in range(199):
+    generated=append(generated, array([real_gmm.sample()]), axis=1)
+
+feat_train=RealFeatures(generated)
+est_smem_gmm=GMM(3)
+est_smem_gmm.train(feat_train)
+print est_smem_gmm.train_smem(max_iter, max_cand, min_cov, max_em_iter, min_change)
+est_em_gmm=GMM(3)
+est_em_gmm.train(feat_train)
+print est_em_gmm.train_em(min_cov, max_em_iter, min_change)
+
+min_gen=min(min(generated))
+max_gen=max(max(generated))
+plot_real=empty(0)
+plot_est_smem=empty(0)
+plot_est_em=empty(0)
+for i in arange(min_gen, max_gen, 0.001):
+    plot_real=append(plot_real, array([real_gmm.cluster(array([i]))[3]]))
+    plot_est_smem=append(plot_est_smem, array([est_smem_gmm.cluster(array([i]))[3]]))
+    plot_est_em=append(plot_est_em, array([est_em_gmm.cluster(array([i]))[3]]))
+real_plot=plot(arange(min_gen, max_gen, 0.001), plot_real, "b")
+est_em_plot=plot(arange(min_gen, max_gen, 0.001), plot_est_em, "g")
+est_smem_plot=plot(arange(min_gen, max_gen, 0.001), plot_est_smem, "r")
+real_hist=hist(generated.transpose(), bins=50, normed=True, fc="gray")
+legend(("Real GMM", "Estimated EM GMM", "Estimated SMEM GMM"))
+connect('key_press_event', util.quit)
+show()

examples/undocumented/python_modular/graphical/smem_2d_gmm.py

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+from pylab import figure,scatter,contour,show,legend,connect
+from numpy import array, append, arange, reshape, empty
+from shogun.Distribution import Gaussian, GMM
+from shogun.Features import RealFeatures
+import util
+
+util.set_title('SMEM for 2d GMM example')
+
+max_iter=100
+max_cand=5
+min_cov=1e-9
+max_em_iter=1000
+min_change=1e-9
+cov_type=0
+
+real_gmm=GMM(3)
+
+real_gmm.set_nth_mean(array([2.0, 2.0]), 0)
+real_gmm.set_nth_mean(array([-2.0, -2.0]), 1)
+real_gmm.set_nth_mean(array([2.0, -2.0]), 2)
+
+real_gmm.set_nth_cov(array([[1.0, 0.2],[0.2, 0.5]]), 0)
+real_gmm.set_nth_cov(array([[0.2, 0.1],[0.1, 0.5]]), 1)
+real_gmm.set_nth_cov(array([[0.3, -0.2],[-0.2, 0.8]]), 2)
+
+real_gmm.set_coef(array([0.3, 0.4, 0.3]))
+
+generated=array([real_gmm.sample()])
+for i in range(199):
+    generated=append(generated, array([real_gmm.sample()]), axis=0)
+
+generated=generated.transpose()
+feat_train=RealFeatures(generated)
+est_smem_gmm=GMM(3, cov_type)
+est_smem_gmm.train(feat_train)
+print est_smem_gmm.train_smem(max_iter, max_cand, min_cov, max_em_iter, min_change)
+est_em_gmm=GMM(3, cov_type)
+est_em_gmm.train(feat_train)
+print est_em_gmm.train_em(min_cov, max_em_iter, min_change)
+
+min_x_gen=min(min(generated[[0]]))-0.1
+max_x_gen=max(max(generated[[0]]))+0.1
+min_y_gen=min(min(generated[[1]]))-0.1
+max_y_gen=max(max(generated[[1]]))+0.1
+
+plot_real=empty(0)
+plot_est_smem=empty(0)
+plot_est_em=empty(0)
+
+for i in arange(min_x_gen, max_x_gen, 0.05):
+    for j in arange(min_y_gen, max_y_gen, 0.05):
+        plot_real=append(plot_real, array([real_gmm.cluster(array([i, j]))[3]]))
+        plot_est_smem=append(plot_est_smem, array([est_smem_gmm.cluster(array([i, j]))[3]]))
+        plot_est_em=append(plot_est_em, array([est_em_gmm.cluster(array([i, j]))[3]]))
+
+plot_real=reshape(plot_real, (arange(min_x_gen, max_x_gen, 0.05).shape[0], arange(min_y_gen, max_y_gen, 0.05).shape[0]))
+plot_est_smem=reshape(plot_est_smem, (arange(min_x_gen, max_x_gen, 0.05).shape[0], arange(min_y_gen, max_y_gen, 0.05).shape[0]))
+plot_est_em=reshape(plot_est_em, (arange(min_x_gen, max_x_gen, 0.05).shape[0], arange(min_y_gen, max_y_gen, 0.05).shape[0]))
+
+real_plot=contour(arange(min_x_gen, max_x_gen, 0.05), arange(min_y_gen, max_y_gen, 0.05), plot_real.transpose(), colors="b")
+est_smem_plot=contour(arange(min_x_gen, max_x_gen, 0.05), arange(min_y_gen, max_y_gen, 0.05), plot_est_smem.transpose(), 3, colors="r")
+est_em_plot=contour(arange(min_x_gen, max_x_gen, 0.05), arange(min_y_gen, max_y_gen, 0.05), plot_est_em.transpose(), colors="g")
+real_scatter=scatter(generated[[0]], generated[[1]], c="gray")
+legend((real_plot.collections[0], est_em_plot.collections[0], est_smem_plot.collections[0]), ("Real GMM", "Estimated EM GMM", "Estimated SMEM GMM"))
+
+connect('key_press_event', util.quit)
+show()