Curve Similarity MeasureMENT�

Curves are: - discretized by inidviudal data points - ordered from a beginning to an ending

Curve similarity measurement based on it's length.

Curve similarity measurement based on it's area covered.

This means when two curves would appear directly on top of each other. Our measures of similarity would return a zero distance between two curves that were on top of each other.

installing similaritymeasures library

!pip install similaritymeasures

importing required libraries

import numpy as np
import similaritymeasures
import matplotlib.pyplot as plt

1. Curve similarity measurement based on it's length�

First Example

Creating curve in the X-Y plane

# first curve having 5 points on the X-Y axis
fx1 = np.zeros((5, 2))
fx1[:, 0] = [1, 2, 3, 4, 5]
fx1[:, 1] = [1, 2, 3, 4, 5]

#second curve having 4 points on the X-Y axis
gx1 = np.zeros((4, 2))
gx1[:, 0] = [1, 2, 3, 4]
gx1[:, 1] = [1, 2, 3, 4]

fig, axs = plt.subplots(nrows=1, ncols=2, figsize=(12,4))

axs[0].plot(fx1[:, 0], fx1[:, 1],  marker='o', linewidth=2)
axs[1].plot(gx1[:, 0], gx1[:, 1], color='red',  marker='o', linewidth=2)

[<matplotlib.lines.Line2D at 0x27dcd5ea0c8>]

# quantify the difference between the two curves using
# Curve Length based similarity measure
curve_length = similaritymeasures.curve_length_measure(fx1, gx1)

# print the results
print("difference between first curve length and second curve length  is {}".format(curve_length))

difference between first curve length and second curve length  is 0.57047924843273

plt.plot(fx1[:, 0], fx1[:, 1], marker='o', linewidth=2)
plt.plot(gx1[:, 0], gx1[:, 1], marker='o', linewidth=2)

[<matplotlib.lines.Line2D at 0x27dcd84c7c8>]

Second Example

# first curve having 5 points on the X-Y axis
fx2 = np.zeros((5, 2))
fx2[:, 0] = [1, 2, 3, 4, 5]
fx2[:, 1] = [1, 2, 3, 4, 5]

#second curve having 4 points on the X-Y axis
gx2 = np.zeros((4, 2))
gx2[:, 0] = [2, 4, 6, 8]
gx2[:, 1] = [3, 6, 9, 12]

fig, axs = plt.subplots(nrows=1, ncols=2, figsize=(12,4))

axs[0].plot(fx2[:, 0], fx2[:, 1],  marker='o', linewidth=2)
axs[1].plot(gx2[:, 0], gx2[:, 1], color='red',  marker='o', linewidth=2)

[<matplotlib.lines.Line2D at 0x27dcd93dec8>]

# quantify the difference between the two curves using
# Curve Length based similarity measure
curve_length = similaritymeasures.curve_length_measure(fx2, gx2)

# print the results
print("difference between first curve length and second curve length is {}".format(curve_length))

difference between first curve length and second curve length is 2.3644443270061015

plt.plot(fx2[:, 0], fx2[:, 1], marker='o', linewidth=2)
plt.plot(gx2[:, 0], gx2[:, 1], marker='o', linewidth=2)

[<matplotlib.lines.Line2D at 0x27dcd9aae48>]

1. Curve similarity measurement based on it's area covered�

applying similarity measures over first curves i.e over fx1 and gx1

# quantify the difference between the two curves using
# area between two curves
area = similaritymeasures.area_between_two_curves(fx1, gx1)

# print the results
print("difference between the two curve areas {}".format(area))

difference between the two curve areas 0.0

plt.plot(fx1[:, 0], fx1[:, 1], marker='o', linewidth=2)
plt.plot(gx1[:, 0], gx1[:, 1], marker='o', linewidth=2)

[<matplotlib.lines.Line2D at 0x27dcda20b88>]

applying similarity measures over second curves i.e over fx2 and gx2

# quantify the difference between the two curves using
# Curve Length based similarity measure
area = similaritymeasures.area_between_two_curves(fx2, gx2)

# print the results
print("difference between the two curve areas {}".format(area))

difference between the two curve areas 9.5

plt.plot(fx2[:, 0], fx2[:, 1], marker='o', linewidth=2)
plt.plot(gx2[:, 0], gx2[:, 1], marker='o', linewidth=2)

[<matplotlib.lines.Line2D at 0x27dcda7e208>]

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