Clustering Algorithms - Mean Shift Algorithm

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Introduction to Mean-Shift Algorithm

As discussed earlier, it is another powerful clustering algorithm used in unsupervised learning. Unlike K-means clustering, it does not make any assumptions; hence it is a non-parametric algorithm.

Mean-shift algorithm basically assigns the datapoints to the clusters iteratively by shifting points towards the highest density of datapoints i.e. cluster centroid.

The difference between K-Means algorithm and Mean-Shift is that later one does not need to specify the number of clusters in advance because the number of clusters will be determined by the algorithm w.r.t data.

Working of Mean-Shift Algorithm

We can understand the working of Mean-Shift clustering algorithm with the help of following steps −

• Step 1 − First, start with the data points assigned to a cluster of their own.

• Step 2 − Next, this algorithm will compute the centroids.

• Step 3 − In this step, location of new centroids will be updated.

• Step 4 − Now, the process will be iterated and moved to the higher density region.

• Step 5 − At last, it will be stopped once the centroids reach at position from where it cannot move further.

Implementation in Python

It is a simple example to understand how Mean-Shift algorithm works. In this example, we are going to first generate 2D dataset containing 4 different blobs and after that will apply Mean-Shift algorithm to see the result.

%matplotlib inline
import numpy as np
from sklearn.cluster import MeanShift
import matplotlib.pyplot as plt
from matplotlib import style
style.use("ggplot")
from sklearn.datasets.samples_generator import make_blobs
centers = [[3,3,3],[4,5,5],[3,10,10]]
X, _ = make_blobs(n_samples = 700, centers = centers, cluster_std = 0.5)
plt.scatter(X[:,0],X[:,1])
plt.show()

ms = MeanShift()
ms.fit(X)
labels = ms.labels_
cluster_centers = ms.cluster_centers_
print(cluster_centers)
n_clusters_ = len(np.unique(labels))
print("Estimated clusters:", n_clusters_)
colors = 10*['r.','g.','b.','c.','k.','y.','m.']
for i in range(len(X)):
    plt.plot(X[i][0], X[i][1], colors[labels[i]], markersize = 3)
plt.scatter(cluster_centers[:,0],cluster_centers[:,1],
    marker=".",color='k', s=20, linewidths = 5, zorder=10)
plt.show()

Output

[[ 2.98462798 9.9733794 10.02629344]
[ 3.94758484 4.99122771 4.99349433]
[ 3.00788996 3.03851268 2.99183033]]
Estimated clusters: 3

Advantages and Disadvantages

Advantages

The following are some advantages of Mean-Shift clustering algorithm −

• It does not need to make any model assumption as like in K-means or Gaussian mixture.

• It can also model the complex clusters which have nonconvex shape.

• It only needs one parameter named bandwidth which automatically determines the number of clusters.

• There is no issue of local minima as like in K-means.

• No problem generated from outliers.

Disadvantages

The following are some disadvantages of Mean-Shift clustering algorithm −

Mean-shift algorithm does not work well in case of high dimension, where number of clusters changes abruptly.

• We do not have any direct control on the number of clusters but in some applications, we need a specific number of clusters.

• It cannot differentiate between meaningful and meaningless modes.