SciPy Cluster

Clustering is the procedure of dividing the datasets into groups consisting of similar data-points. For example, the Items are arranged in the shopping mall. Data Points are in the same group must be identical as possible and should be different from the other groups. There are two types of the cluster, which are:

• Central
• Hierarchy

The k- means clustering algorithm is a simple unsupervised algorithm that is used to predict groupings from within an unlabeled dataset. The prediction is based on the number of cluster centers present(k) and the nearest mean value (measured in Euclidian distance between observations).

K-means Algorithm

The steps are as follows, suppose we have an input x₁,x₂, x₃,....x_n, data and value K.

Step - 1:

Select K random points as a cluster center called centroid. Suppose these are c₁,c₂,...c_k, and it can be written as follows:

c1,c2,...ck

C is the set of all centroid.

Step-2:

Assign each input value xi to the nearest center by calculating its Euclidean (L2) distance between the point and each centroid.

Step-3:

In this step, we get the new centroid by calculating the average of all the points assigned to the cluster.

Step-4:

We repeat steps 2 and 3 until none of the clusters remains unstable.

K-means cluster and vector quantization (scipy.cluster.vq)

SciPy provides functions for K-means clustering, generating codebooks from k-means models, and quantizing vector by comparing them with centroid in a codebook.

K-Means Implementation in SciPy

Here, we will understand the implementation of K- means in SciPy

Import K-means

The following statement is used to implement the K-means algorithm:

Computing K-means with three Clusters

The K-means algorithm iterates again and again and adjusts the centroid until necessary progress cannot made change in distortion, since the last iteration is less than some threshold. Consider the following example:

Output:

[[1.97955982 1.78985952 1.51775359]
 [2.6926236  2.70116313 2.75279787]
 [0.84636826 0.93081751 1.0708057 ]]