- Tytuł:
- Clustering based on eigenvectors of the adjacency matrix
- Autorzy:
-
Lucińska, M.
Wierzchoń, S. T. - Powiązania:
- https://bibliotekanauki.pl/articles/331178.pdf
- Data publikacji:
- 2018
- Wydawca:
- Uniwersytet Zielonogórski. Oficyna Wydawnicza
- Tematy:
-
spectral clustering
adjacency matrix eigenvalues
adjacency matrix eigenvectors
graph perturbation theory
eigengap heuristics
klastrowanie widmowe
macierz sąsiedztwa
teoria grafów - Opis:
- The paper presents a novel spectral algorithm EVSA (eigenvector structure analysis), which uses eigenvalues and eigenvectors of the adjacency matrix in order to discover clusters. Based on matrix perturbation theory and properties of graph spectra we show that the adjacency matrix can be more suitable for partitioning than other Laplacian matrices. The main problem concerning the use of the adjacency matrix is the selection of the appropriate eigenvectors. We thus propose an approach based on analysis of the adjacency matrix spectrum and eigenvector pairwise correlations. Formulated rules and heuristics allow choosing the right eigenvectors representing clusters, i.e., automatically establishing the number of groups. The algorithm requires only one parameter—the number of nearest neighbors. Unlike many other spectral methods, our solution does not need an additional clustering algorithm for final partitioning. We evaluate the proposed approach using real-world datasets of different sizes. Its performance is competitive to other both standard and new solutions, which require the number of clusters to be given as an input parameter.
- Źródło:
-
International Journal of Applied Mathematics and Computer Science; 2018, 28, 4; 771-786
1641-876X
2083-8492 - Pojawia się w:
- International Journal of Applied Mathematics and Computer Science
- Dostawca treści:
- Biblioteka Nauki
Artykuł