A lesser-known, step-like function approximation method. Note that the default assumes an incremental (positive) approximation and in order to approx the cosine you need to set this to False.
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 |
import numpy as np import matplotlib.pyplot as plt from matplotlib.collections import LineCollection %matplotlib inline from sklearn.linear_model import LinearRegression from sklearn.isotonic import IsotonicRegression from sklearn.utils import check_random_state n = 100 x = np.arange(n) rs = check_random_state(0) # log1p = log(1 + x) y = rs.randint(-1, 1, size=(n,)) + 50. * np.cos(np.arange(n)/n) ir = IsotonicRegression(increasing = False) y_ = ir.fit_transform(x, y) lr = LinearRegression() # x needs to be 2d for LinearRegression, the newaxis simply increases the array dimension lr.fit(x[:, np.newaxis], y) segments = [[[i, y[i]], [i, y_[i]]] for i in range(n)] lc = LineCollection(segments, zorder=0) lc.set_array(np.ones(len(y))) lc.set_linewidths(np.full(n, 0.5)) fig = plt.figure() plt.plot(x, y, 'r.', markersize=12) plt.plot(x, y_, 'g.-', markersize=12) plt.plot(x, lr.predict(x[:, np.newaxis]), 'b-') plt.gca().add_collection(lc) plt.legend(('Data', 'Isotonic Fit', 'Linear Fit'), loc='lower right') plt.title('Isotonic regression') plt.show() |
