K-Means vs Spectral Clustering

 Advantages 

1. Does not make strong assumptions on the statistics of the clusters — Clustering techniques like K-Means Clustering assume that the points assigned to a cluster are spherical about the cluster center. This is a strong assumption to make, and may not always be relevant. In such cases, spectral clustering helps create more accurate clusters.

2. Easy to implement and gives good clustering results. It can correctly cluster observations that actually belong to the same cluster but are farther off than observations in other clusters due to dimension reduction.

3. Reasonably fast for sparse data sets of several thousand elements.

Disadvantages

1. Use of K-Means clustering in the final step implies that the clusters are not always the same. They may vary depending on the choice of initial centroids.

2. Computationally expensive for large datasets — This is because eigenvalues and eigenvectors need to be computed and then we have to do clustering on these vectors. For large, dense datasets, this may increase time complexity quite a bit.

K-Means fails to cluster the below data points.