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- W3139984185 abstract "The data clustering problem consists in dividing a data set into prescribed groups of homogeneous data. This is a NP-hard problem that can be relaxed in the spectral graph theory, where the optimal cuts of a graph are related to the eigenvalues of graph $1$-Laplacian. In this paper, we give a first step for proving that the $k$-th Cheeger constant is the minimum of the $1$-Laplacian Raylegh quotient among vectors that are pseudo-orthogonal to the vectors realizing the previous $k-1$ Cheeger constants. Moreover, we give new notations to punctually describe the paths, among critical eigenvectors of the graph $1$-Laplacian, realizing sets with prescribed genus. Eventually, we apply these results to give a method and a numerical algorithm, based on a generalized inverse power method, to compute the third Cheeger constant as the minimum of the $1$-Laplacian Raylegh quotient among vectors orthogonal to the first and the second eigenvector of graph $1$-Laplacian." @default.
- W3139984185 created "2021-04-13" @default.
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- W3139984185 date "2021-03-30" @default.
- W3139984185 modified "2023-10-11" @default.
- W3139984185 title "Optimizations of higher Cheeger constants on graphs and applications in data clustering" @default.
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