Ridge: Effect of parameters

                                     Ridge-Effect of parameters on output 

Ridge technique is tested here to see their accuracy in terms of output.

Python program:

>>> import numpy as np

>>> import matplotlib.pyplot as plt

>>> from matplotlib.colors import ListedColormap

>>> from sklearn import neighbors, datasets

>>> n_neighbors = 24

>>> iris = datasets.load_iris()

>>> x = iris.data[:, :2]

>>> y = iris.target

>>> h = .02

>>> cmap_bold = ListedColormap(['firebrick', 'lime', 'blue'])

>>> cmap_light = ListedColormap(['pink', 'lightgreen', 'paleturquoise'])

//Plotting the analysis//

>>> from sklearn import linear_model
>>> clf = linear_model.Ridge()
>>> clf.fit(x, y)
Ridge(alpha=1.0, copy_X=True, fit_intercept=True, max_iter=None,
   normalize=False, random_state=None, solver='auto', tol=0.001)

a) Effect of alpha:

>>> for alpha in [1, 2, 5, 25, 100, 500, 1000]:
...     clf = linear_model.Ridge(alpha=alpha)
...     clf.fit(x, y)
...     x_min, x_max = x[:, 0].min() -1, x[:, 0].max() +1
...     y_min, y_max = x[:, 1].min() -1, x[:, 1].max() +1
...     xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
...     z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
...     z = z.reshape(xx.shape)
...     plt.figure()
...     plt.pcolormesh(xx, yy, z, cmap=cmap_light)
...     plt.scatter(x[:, 0], x[:, 1], c=y, cmap=cmap_bold, edgecolor='k', s=24)
...     plt.xlim(xx.min(), xx.max())
...     plt.ylim(yy.min(), yy.max())
...     plt.title("Linear Regression (alpha='%s')" %(alpha))
...

b) Effect of maximum iterations (max_iter):

>>> for max_iter in [1, 2, 5, 25, 100, 500, 1000]:
...     clf = linear_model.Ridge(max_iter=max_iter)
...     clf.fit(x, y)
...     x_min, x_max = x[:, 0].min() -1, x[:, 0].max() +1
...     y_min, y_max = x[:, 1].min() -1, x[:, 1].max() +1
...     xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
...     z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
...     z = z.reshape(xx.shape)
...     plt.figure()
...     plt.pcolormesh(xx, yy, z, cmap=cmap_light)
...     plt.scatter(x[:, 0], x[:, 1], c=y, cmap=cmap_bold, edgecolor='k', s=24)
...     plt.xlim(xx.min(), xx.max())
...     plt.ylim(yy.min(), yy.max())
...     plt.title("Ridge (max_iter='%s')" %(max_iter))
...

c) Effect of tolerances (tol):

>>> for tol in [0.001, 0.01, 0.05, 0.1, 0.2, 0.5, 1]:
...     clf = linear_model.Ridge(tol=tol)
...     clf.fit(x, y)
...     x_min, x_max = x[:, 0].min() -1, x[:, 0].max() +1
...     y_min, y_max = x[:, 1].min() -1, x[:, 1].max() +1
...     xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
...     z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
...     z = z.reshape(xx.shape)
...     plt.figure()
...     plt.pcolormesh(xx, yy, z, cmap=cmap_light)
...     plt.scatter(x[:, 0], x[:, 1], c=y, cmap=cmap_bold, edgecolor='k', s=24)
...     plt.xlim(xx.min(), xx.max())
...     plt.ylim(yy.min(), yy.max())
...     plt.title("Ridge (tol='%s')" %(tol))
...