Performance

Lets compare the methods and tune the parameters and find out how the peak detection is with and without noisy data.

Comparison peak detection in one-dimensional data

Small dataset

For the first scenario we will create a dataset containing some small peaks and some larger ones. We will detect peaks using the topology and peakdetect method with and without interpolation.

# Import library
from findpeaks import findpeaks
# peakdetect
fp_peakdetect = findpeaks(method='peakdetect', interpolate=None, lookahead=1)
# peakdetect with interpolation
fp_peakdetect_int = findpeaks(method='peakdetect', interpolate=10, lookahead=1)
# topology
fp_topology = findpeaks(method='topology', interpolate=None)
# topology with interpolation
fp_topology_int = findpeaks(method='topology', interpolate=10)

# Example 1d-vector
X = [1,1,1.1,1,0.9,1,1,1.1,1,0.9,1,1.1,1,1,0.9,1,1,1.1,1,1,1,1,1.1,0.9,1,1.1,1,1,0.9,1,1.1,1,1,1.1,1,0.8,0.9,1,1.2,0.9,1,1,1.1,1.2,1,1.5,1,3,2,5,3,2,1,1,1,0.9,1,1,3,2.6,4,3,3.2,2,1,1,0.8,4,4,2,2.5,1,1,1]

# Fit the methods on the 1d-vector
results_1 = fp_peakdetect.fit(X)
results_2 = fp_peakdetect_int.fit(X)
results_3 = fp_topology.fit(X)
results_4 = fp_topology_int.fit(X)

# Plot
fp_peakdetect.plot()
fp_peakdetect_int.plot()
fp_topology.plot()
fp_topology_int.plot()

A visual look of the results for the peakdetect with and without interpolation. Note that the interpolated results are readily mapped back to the original plot.

Peakdetect results without interpolation (left) and with (right)

fig8

fig9

The differences become clear with and without the use of interpolation

Topology results without interpolation (left) and with (right)

fig10

fig11

The four approaches results in various diffent peaks and valleys. A simple comparison, by means of a confusion matrix shows that the interpolation results in the detection of similar peaks and valleys.

Peaks detected between peakdetect vs topology using interpolation show only 4 differences in detection of peaks.

      True  False
True  [45,  1]
False [ 3, 25]

A comparison between peakdetect vs topology without interpolation show 20 differences in detection of peaks.

      True  False
True  [48,  13]
False [ 7,  6 ]

Large dataset

For this scenario we create a large dataset to detect peaks using peakdetect and topology.

# Import library
from findpeaks import findpeaks
# Initialize peakdetect
fp1 = findpeaks(method='peakdetect', lookahead=200)
# Initialize topology
fp2 = findpeaks(method='topology')

# Example 1d-vector
i = 10000
xs = np.linspace(0,3.7*np.pi,i)
X = (0.3*np.sin(xs) + np.sin(1.3 * xs) + 0.9 * np.sin(4.2 * xs) + 0.06 * np.random.randn(i))

# Fit using peakdetect
results_1 = fp1.fit(X)
# Fit using topology
results_2 = fp2.fit(X)

# Plot peakdetect
fp1.plot()
# Plot topology
fp2.plot()
fp2.plot_persistence()

The topology methods detects thousands of local minima and maxima whereas the peakdetect approach finds the correct ones.

Peakdetect on a large noisy dataset

fig3

The homology-persistence plots can help to filter the thousands of hits that are mostly alongside the diagonal and therefore not of interest. Only a few points seems to be of interest; numbers one to eight. With this knowledge we can set the limit paramater and remove the false positive peaks.

Topology on a large noisy dataset

fig12

Redo the analysis but now with the limit parameter. Note that your should investigate first what your limit is.

# Checkout the limit by looking at the top 10
limit_min = fp2.results['persistence'][0:8]['score'].min()

from findpeaks import findpeaks
# Initialize topology
fp2 = findpeaks(method='topology', limit=limit_min)
# Fit using topology
results_2 = fp2.fit(X)
# Plot topology
fp2.plot()
fp2.plot_persistence()
Topology with limit parameter set to 1

fig13