Multilayer perceptron neural network¶
A multilayer perceptron neural network consists of several layers of nodes, interconnected through weighted acyclic arcs from each preceding layer to the following, without lateral or feedback connections. Each node calculates a transformed weighted linear combination of its inputs (output activations from the preceding layer), with one of the weights acting as a trainable bias connected to a constant input. The transformation, called activation function, is a bounded non-decreasing (non-linear) function, such as the sigmoid functions (ranges from 0 to 1). Another popular activation function is hyperbolic tangent which is actually equivalent to the sigmoid function in shape but ranges from -1 to 1. More specialized activation functions include radial basis functions which are used in RBF networks.
from miml import datasets from miml.classification import MLPClassifer fn = os.path.join(datasets.get_data_home(), 'classification', 'toy', 'toy-test.txt') df = DataFrame.read_table(fn, header=None, names=['x1','x2'], format='%2f', index_col=0) X = df.values y = array(df.index.data) model = MLPClassifer() model.fit(X, y) # Plot the decision boundary. For that, we will assign a color to each # point in the mesh [x_min, x_max]x[y_min, y_max]. x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1 y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1 n = 50 # size in the mesh xx, yy = np.meshgrid(np.linspace(x_min, x_max, n), np.linspace(y_min, y_max, n)) data = np.vstack((xx.flatten(), yy.flatten())).T Z = model.predict(data) # Put the result into a color plot Z = Z.reshape(xx.shape) #Plot # Create color maps cmap_light = ['#FFAAAA', '#AAAAFF'] cmap_bold = ['#FF0000', '#0000FF'] imshow(xx[0,:], yy[:,0], Z, colors=cmap_light) # Plot also the training points ls = plt.scatter(X[:, 0], X[:, 1], c=y, edgecolor=None, s=3, levels=[0,1], colors=cmap_bold) plt.contour(xx[0,:], yy[:,0], Z, [0.5], color='k', smooth=False) plt.xlim(xx.min(), xx.max()) plt.ylim(yy.min(), yy.max()) plt.title("Neural network classifer example")