| Autor: |
Bolla Marianna, Winstein Vilas, You Tao, Seidl Frank, Abdelkhalek Fatma |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Special Matrices, Vol 10, Iss 1, Pp 394-416 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
2300-7451 |
| DOI: |
10.1515/spma-2022-0167 |
| Popis: |
We discuss spectral clustering from a variety of perspectives that include extending techniques to rectangular arrays, considering the problem of discrepancy minimization, and applying the methods to directed graphs. Near-optimal clusters can be obtained by singular value decomposition together with the weighted kk-means algorithm. In the case of rectangular arrays, this means enhancing the method of correspondence analysis with clustering, while in the case of edge-weighted graphs, a normalized Laplacian-based clustering. In the latter case, it is proved that a spectral gap between the (k−1)\left(k-1)st and kkth smallest positive eigenvalues of the normalized Laplacian matrix gives rise to a sudden decrease of the inner cluster variances when the number of clusters of the vertex representatives is 2k−1{2}^{k-1}, but only the first k−1k-1 eigenvectors are used in the representation. The ensemble of these eigenvectors constitute the so-called Fiedler-carpet. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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