Laplacian matrix to transform the data into a lower-dimensional space, capturing the critical connectivity patterns in the data. This transformation allows for the identification of complex, nonlinear clusters that K-Means might miss. Unlike K-Means, which operates directly in the original input space and assumes spherical clusters, spectral clustering leverages the graph structure to uncover clusters of arbitrary shape. By relying on a similarity matrix rather than distance measures, spectral clustering is particularly well-suited for data where distance-based methods are less effective.