spektrálisklaszterezés

Spektrálisklaszterezés, also known as spectral clustering, is a clustering technique that utilizes the eigenvalues (spectrum) of a similarity matrix to perform dimensionality reduction before clustering in fewer dimensions. It is particularly effective at identifying non-convex cluster shapes, unlike algorithms like k-means which assume spherical clusters.

The process begins by constructing a similarity graph where nodes represent data points and edges represent the similarity between them. This similarity is often quantified using a kernel function, such as the radial basis function (RBF). From this similarity matrix, a Laplacian matrix is derived. The eigenvalues and corresponding eigenvectors of this Laplacian matrix are then computed. The eigenvectors associated with the smallest eigenvalues are used to create a new, lower-dimensional representation of the data. Finally, a standard clustering algorithm, typically k-means, is applied to these transformed data points.

Spektrálisklaszterezés has found applications in various fields, including image segmentation, community detection in social networks, and document clustering. Its ability to uncover complex cluster structures makes it a powerful tool for exploratory data analysis when the underlying data distribution is not well-understood or does not conform to simple geometric assumptions. However, it can be computationally intensive for very large datasets due to the matrix decomposition step.