Plotting a decision boundary python ( give a good idea of how contourf matplotlib function works ) -

this can considered duplicate of thread, it's meant granular level explanation intended question.

in machine learning algorithms (let's consider perceptron), having set of data points, spans 2 features. input features of form

## assume classifier has been trained simplicity x = [[a1,b1] , [a2,b2] , .... , [an,bn]]  x1_min, x1_max = x[:, 0].min() - 1, x[:, 0].max() + 1 x2_min, x2_max = x[:, 1].min() - 1, x[:, 1].max() + 1 xx1, xx2 = np.meshgrid(np.arange(x1_min, x1_max, resolution),                    np.arange(x2_min, x2_max, resolution))  z = classifier.net_input(np.array([xx1.ravel(), xx2.ravel()]).t)  ### here z set of prediction has values +1 or -1 , data points in x z = z.reshape(xx1.shape).  # plot class samples  idx, cl in enumerate(np.unique(y)):      plt.scatter(x=x[y == cl, 0], y=x[y == cl, 1],             alpha=0.8, c=cmap(idx),             marker=markers[idx], label=cl) plt.show() 

as of fine. real problem following function or how works, when passing data points xx1 , xx2 along predicted value z (which nothing bunch of +1 , -1). not familiar contours. can 1 explain how getting decision boundary through contourf function?

plt.contourf(xx1, xx2, z, alpha=0.4, cmap=cmap) 

this generated decision boundary separating 2 classes. can explain happening inside countourf function or how derive decision boundary xx1, xx2 , z (bunch of +1 , -1)?

in

xx1, xx2 = np.meshgrid(np.arange(x1_min, x1_max, resolution),                        np.arange(x2_min, x2_max, resolution)) 

you create grid spans range of data , has given resolution. grid has no connection actual data points, grid laid on input space.

then, in

z = classifier.net_input(np.array([xx1.ravel(), xx2.ravel()]).t) z = z.reshape(xx1.shape) 

you let classifier compute output each point of grid. gives +1 or -1 each point on grid , reshapes output array matches shape of gird.

finally, there contourf function. here documentation. contourf takes 3-d surface specified grid (i.e. bunch of x-y points along z-value of these points) , plots surface displaying contours. contour line surface has same value. since z array contains +1s , -1s, real contour @ points "between" +1s , -1s, i.e. decision boundary.

in nutshell, decision boundary extracted finely sampling feature space , plotting output value each sample. boundary comes out implicitly output values vary across feature space.