How does the shape of clusters create a challenge when implementing a clustering algorithm? How would...
How does the shape of clusters create a challenge when implementing a clustering algorithm?
How would you pick k when using the k-Means algorithm? Explain your reasoning.
Homework Answers
Assuming the number of clusters k is predefined, and consequently, we get k clusters as an output, this may lead to addition of those data points that share no similarity with any cluster in a wrong cluster. These additional data points may change the shape of the cluster, which they are part of, leading to less accurate interpretation of the resulting clusters.
For example, in the graph below, for k=2, clearly 2 different clusters are formed, but there lies a point x almost equidistant from both the clusters. Whichever cluster x becomes a part of affects the shape of that cluster and also reduces the similarity among that cluster data points.
We can pick the most accurate k using elbow method. We plot the graph between the values of k and wcss (within cluster sum of squares, which is sum of squares of all centroids of each cluster for the k clusters). The value of k after which the wcss starts decreasing the most linearly is the optimal number of k. This is because minimising the wcss increases the distance between different clusters, leading to more similar data points being grouped together in each cluster.
For example, for the below elbow plot, k=y is the most optimal value for k.
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