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Linearly penalized segmentation (Pelt)#

Description#

The method is implemented in Pelt.

Because the enumeration of all possible partitions impossible, the algorithm relies on a pruning rule. Many indexes are discarded, greatly reducing the computational cost while retaining the ability to find the optimal segmentation. The implementation follows [Killick2012]. In addition, under certain conditions on the change point repartition, the avarage computational complexity is of the order of \(\mathcal{O}(CKn)\), where \(K\) is the number of change points to detect, \(n\) the number of samples and \(C\) the complexity of calling the considered cost function on one sub-signal. Consequently, piecewise constant models (model=l2) are significantly faster than linear or autoregressive models.

To reduce the computational cost, you can consider only a subsample of possible change point indexes, by changing the min_size and jump arguments when instantiating Pelt:

  • min_size controls the minimum distance between change points; for instance, if min_size=10, all change points will be at least 10 samples apart.
  • jump controls the grid of possible change points; for instance, if jump=k, only changes at k, 2*k, 3*k,... are considered.

Usage#

import numpy as np
import matplotlib.pylab as plt
import ruptures as rpt

# creation of data
n, dim = 500, 3
n_bkps, sigma = 3, 1
signal, b = rpt.pw_constant(n, dim, n_bkps, noise_std=sigma)

# change point detection
model = "l1"  # "l2", "rbf"
algo = rpt.Pelt(model=model, min_size=3, jump=5).fit(signal)
my_bkps = algo.predict(pen=3)

# show results
fig, (ax,) = rpt.display(signal, bkps, my_bkps, figsize=(10, 6))
plt.show()

References#

[Killick2012] Killick, R., Fearnhead, P., & Eckley, I. (2012). Optimal detection of changepoints with a linear computational cost. Journal of the American Statistical Association, 107(500), 1590–1598.