Measuring the similarity between two irregular plots

Question

I have two irregular lines as a list of [x,y] coordinates, which has peaks and troughs. The length of the list might vary slightly(unequal). I want to measure their similarity such that to check occurence of the peaks and troughs (of similar depth or height) are coming at proper interval and give a similarity measure. I want to do this in Python. Is there any inbuilt function to do this?

Answer 1

I don't know of any builtin functions in Python to do this.

I can give you a list of possible functions in the Python ecosystem you can use. This is in no way a complete list of functions, and there are probably quite a few methods out there that I am not aware of.

If the data is ordered, but you don't know which data point is the first and which data point is last:

1. Use the directed Hausdorff distance

If the data is ordered, and you know the first and last points are correct:

1. Discrete Fréchet distance ^*
2. Dynamic Time Warping (DTW) ^*
3. Partial Curve Mapping (PCM) ^**
4. A Curve-Length distance metric (uses arc length distance from beginning to end) ^**
5. Area between two curves ^**

^* Generally mathematical method used in a variety of machine learning tasks

^** Methods I've used to identify unique material hysteresis responses

First let's assume we have two of the exact same random X Y data. Note that all of these methods will return a zero. You can install the similaritymeasures from pip if you do not have it.

import numpy as np
from scipy.spatial.distance import directed_hausdorff
import similaritymeasures
import matplotlib.pyplot as plt

# Generate random experimental data
np.random.seed(121)
x = np.random.random(100)
y = np.random.random(100)
P = np.array([x, y]).T

# Generate an exact copy of P, Q, which we will use to compare
Q = P.copy()

dh, ind1, ind2 = directed_hausdorff(P, Q)
df = similaritymeasures.frechet_dist(P, Q)
dtw, d = similaritymeasures.dtw(P, Q)
pcm = similaritymeasures.pcm(P, Q)
area = similaritymeasures.area_between_two_curves(P, Q)
cl = similaritymeasures.curve_length_measure(P, Q)

# all methods will return 0.0 when P and Q are the same
print(dh, df, dtw, pcm, cl, area)

The printed output is 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 This is because the curves P and Q are exactly the same!

Now let's assume P and Q are different.

# Generate random experimental data
np.random.seed(121)
x = np.random.random(100)
y = np.random.random(100)
P = np.array([x, y]).T

# Generate random Q
x = np.random.random(100)
y = np.random.random(100)
Q = np.array([x, y]).T

dh, ind1, ind2 = directed_hausdorff(P, Q)
df = similaritymeasures.frechet_dist(P, Q)
dtw, d = similaritymeasures.dtw(P, Q)
pcm = similaritymeasures.pcm(P, Q)
area = similaritymeasures.area_between_two_curves(P, Q)
cl = similaritymeasures.curve_length_measure(P, Q)

# all methods will return 0.0 when P and Q are the same
print(dh, df, dtw, pcm, cl, area)

The printed output is 0.107, 0.743, 37.69, 21.5, 6.86, 11.8 which quantify how different P is from Q according to each method.

You now have many methods to compare the two curves. I would start with DTW, since this has been used in many time series applications which look like the data you have uploaded.

We can visualize what P and Q look like with the following code.

plt.figure()
plt.plot(P[:, 0], P[:, 1])
plt.plot(Q[:, 0], Q[:, 1])
plt.show()