Spectral Clustering
Motivation
Clustering is a way to make sense of the data by grouping similar values into a group. There are many ways to achieve that and in this post we will be looking at one of the way based on spectral method. Spectral clustering provides a starting point to understand graphs with many nodes by clustering them into 2 or more clusters. This clustering technique can also be applied for analyzing general data. This technique is based on Linear algebra and Graph theory.
We will start with a very brief introduction of the prerequisite for the sake of completeness and one can skip the prerequisite topics if they already have the familiarity.
Prerequisite Topic
Eigen Vectors and Eigen Values
One way to interpret when we multiply a vector a matrix is that a matrix transforms the vector. For example: below is a vector \(\begin{pmatrix} 2\\1 \end{pmatrix}\)
we apply a transformation by multiplying the above vector to a matrix
\[\begin{pmatrix} -1 & 3 \\ 2 & -2 \end{pmatrix}\]The resultant vector \(\begin{pmatrix} 1\\2 \end{pmatrix}\) is in orange after transformation.
you can see how the vector changed its direction after the transformation. Now in case of Eigenvectors, which are special kinds of Continue reading
