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    <p>@Zhenya's answer of manually setting knots in between datapoints was too rough to deliver good results in noisy data without being selective about how this technique is applied. However, inspired by his/her suggestion, I have had success with <a href="http://scikit-learn.sourceforge.net/dev/modules/generated/sklearn.cluster.MeanShift.html#sklearn.cluster.MeanShift" rel="nofollow noreferrer">Mean-Shift clustering</a> from the scikit-learn package. It performs auto-determination of the cluster count and seems to do a fairly good smoothing job (very smooth in fact).</p> <pre><code># Imports import numpy import pylab import scipy import sklearn.cluster # Set up original data - note that it's monotonically increasing by X value! data = {} data['original'] = {} data['original']['x'] = [0, 5024.2059124920379, 7933.1645067836089, 7990.4664106277542, 9879.9717114947653, 13738.60563208926, 15113.277958924193] data['original']['y'] = [0.0, 3072.5653360000988, 5477.2689107965398, 5851.6866463790966, 6056.3852496014106, 7895.2332350173638, 9154.2956175610598] # Cluster data, sort it and and save inputNumpy = numpy.array([[data['original']['x'][i], data['original']['y'][i]] for i in range(0, len(data['original']['x']))]) meanShift = sklearn.cluster.MeanShift() meanShift.fit(inputNumpy) clusteredData = [[pair[0], pair[1]] for pair in meanShift.cluster_centers_] clusteredData.sort(lambda pair1, pair2: cmp(pair1[0],pair2[0])) data['clustered'] = {} data['clustered']['x'] = [pair[0] for pair in clusteredData] data['clustered']['y'] = [pair[1] for pair in clusteredData] # Build a spline using the clustered data and predict mySpline = scipy.interpolate.UnivariateSpline(x=data['clustered']['x'], y=data['clustered']['y'], k=1) xi = range(0, round(max(data['original']['x']), -3) + 3000, 20) yi = mySpline(xi) # Plot the datapoints pylab.plot(data['clustered']['x'], data['clustered']['y'], "D", label="Datapoints (%s)" % 'clustered') pylab.plot(xi, yi, label="Predicted (%s)" % 'clustered') pylab.plot(data['original']['x'], data['original']['y'], "o", label="Datapoints (%s)" % 'original') # Show the plot pylab.grid(True) pylab.xticks(rotation=45) pylab.legend( loc="lower right" ) pylab.show() </code></pre> <p><img src="https://i.stack.imgur.com/KxIW9.png" alt="enter image description here"></p>
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    1. COWould you mind posting your code then? I guess it'd be beneficial to the community as this subject pops up quite often in different contexts?
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    2. CO@Zhenya: Will do, I need to pull it out of a couple classes / functions into a self-contained example. I'll post it in my answer in the next day or so.
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