On the use of linear programming for unsupervised text classification
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
Spectral clustering by recursive partitioning
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Spectral clustering with limited independence
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Differentially private recommender systems: building privacy into the net
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Graph partitioning via adaptive spectral techniques
Combinatorics, Probability and Computing
Finding Planted Partitions in Random Graphs with General Degree Distributions
SIAM Journal on Discrete Mathematics
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We extend spectral methods to random graphs with skewed degree distributions through a degree based normalization closely connected to the normalized Laplacian. The normalization is based on intuition drawn from perturbation theory of random matrices, and has the effect of boosting the expectation of the random adjacency matrix without increasing the variances of its entries, leading to better perturbation bounds. The primary implication of this result lies in the realm of spectral analysis of random graphs with skewed degree distributions, such as the ubiquitous "power law graphs". Recently Mihail and Papadimitriou [22] argued that for randomly generated graphs satisfying a power law degree distribution, spectral analysis of the adjacency matrix will simply produce the neighborhoods of the high degree nodes as its eigenvectors, and thus miss any embedded structure. We present a generalization of their model, incorporating latent structure, and prove that after applying our transformation, spectral analysis succeeds in recovering the latent structure with high probability.