%load_ext watermark

%watermark -u -v -d -p matplotlib,numpy

%matplotlib inline

frommatplotlibimportpyplotaspltimportnumpyasnp# Generating a Gaussion dataset:# creating random vectors from the multivariate normal distribution# given mean and covariancemu_vec1=np.array([0,0])cov_mat1=np.array([[2,0],[0,2]])x1_samples=np.random.multivariate_normal(mu_vec1,cov_mat1,100)x2_samples=np.random.multivariate_normal(mu_vec1+0.2,cov_mat1+0.2,100)x3_samples=np.random.multivariate_normal(mu_vec1+0.4,cov_mat1+0.4,100)# x1_samples.shape -> (100, 2), 100 rows, 2 columnsplt.figure(figsize=(8,6))plt.scatter(x1_samples[:,0],x1_samples[:,1],marker='x',color='blue',alpha=0.7,label='x1 samples')plt.scatter(x2_samples[:,0],x1_samples[:,1],marker='o',color='green',alpha=0.7,label='x2 samples')plt.scatter(x3_samples[:,0],x1_samples[:,1],marker='^',color='red',alpha=0.7,label='x3 samples')plt.title('Basic scatter plot')plt.ylabel('variable X')plt.xlabel('Variable Y')plt.legend(loc='upper right')plt.show()

importmatplotlib.pyplotaspltx_coords=[0.13,0.22,0.39,0.59,0.68,0.74,0.93]y_coords=[0.75,0.34,0.44,0.52,0.80,0.25,0.55]fig=plt.figure(figsize=(8,5))plt.scatter(x_coords,y_coords,marker='s',s=50)forx,yinzip(x_coords,y_coords):plt.annotate('(%s,%s)'%(x,y),xy=(x,y),xytext=(0,-10),textcoords='offset points',ha='center',va='top')plt.xlim([0,1])plt.ylim([0,1])plt.show()

# 2-category classification with random 2D-sample data# from a multivariate normal distributionimportnumpyasnpfrommatplotlibimportpyplotaspltdefdecision_boundary(x_1):""" Calculates the x_2 value for plotting the decision boundary."""return4-np.sqrt(-x_1**2+4*x_1+6+np.log(16))# Generating a Gaussion dataset:# creating random vectors from the multivariate normal distribution# given mean and covariancemu_vec1=np.array([0,0])cov_mat1=np.array([[2,0],[0,2]])x1_samples=np.random.multivariate_normal(mu_vec1,cov_mat1,100)mu_vec1=mu_vec1.reshape(1,2).T# to 1-col vectormu_vec2=np.array([1,2])cov_mat2=np.array([[1,0],[0,1]])x2_samples=np.random.multivariate_normal(mu_vec2,cov_mat2,100)mu_vec2=mu_vec2.reshape(1,2).T# to 1-col vector# Main scatter plot and plot annotationf,ax=plt.subplots(figsize=(7,7))ax.scatter(x1_samples[:,0],x1_samples[:,1],marker='o',color='green',s=40,alpha=0.5)ax.scatter(x2_samples[:,0],x2_samples[:,1],marker='^',color='blue',s=40,alpha=0.5)plt.legend(['Class1 (w1)','Class2 (w2)'],loc='upper right')plt.title('Densities of 2 classes with 25 bivariate random patterns each')plt.ylabel('x2')plt.xlabel('x1')ftext='p(x|w1) ~ N(mu1=(0,0)^t, cov1=I)\np(x|w2) ~ N(mu2=(1,1)^t, cov2=I)'plt.figtext(.15,.8,ftext,fontsize=11,ha='left')# Adding decision boundary to plotx_1=np.arange(-5,5,0.1)bound=decision_boundary(x_1)plt.plot(x_1,bound,'r--',lw=3)x_vec=np.linspace(*ax.get_xlim())x_1=np.arange(0,100,0.05)plt.show()

importnumpyasnpimportmatplotlib.pyplotaspltfig=plt.figure(figsize=(8,6))# Generating a Gaussion dataset:# creating random vectors from the multivariate normal distribution# given mean and covariancemu_vec1=np.array([0,0])cov_mat1=np.array([[1,0],[0,1]])X=np.random.multivariate_normal(mu_vec1,cov_mat1,500)R=X**2R_sum=R.sum(axis=1)plt.scatter(X[:,0],X[:,1],color='gray',marker='o',s=32.*R_sum,edgecolor='black',alpha=0.5)plt.show()