2021
DOI: 10.1214/20-aos2044
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Optimality of spectral clustering in the Gaussian mixture model

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Cited by 37 publications
(32 citation statements)
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“…Supplement A: Supplement to "Optimality of Spectral Clustering for Gaussian Mixture Model" (url to be specified). In the supplement [40], we first present some propositions that characterize the population quantities in Appendix A. Then in Appendix B, we give several auxiliary lemmas related to the noise matrix E. In Appendix C, we include proofs of Lemma 3.1, Lemma 3.2 and Lemma 3.4.…”
Section: Supplementary Materialsmentioning
confidence: 99%
“…Supplement A: Supplement to "Optimality of Spectral Clustering for Gaussian Mixture Model" (url to be specified). In the supplement [40], we first present some propositions that characterize the population quantities in Appendix A. Then in Appendix B, we give several auxiliary lemmas related to the noise matrix E. In Appendix C, we include proofs of Lemma 3.1, Lemma 3.2 and Lemma 3.4.…”
Section: Supplementary Materialsmentioning
confidence: 99%
“…To finish the proof, we first introduce an alternative algorithm which is simpler to analyze, which we refer to in the sequel as Algorithm (3). It turns out that there is a bijection φ : [k] → [k] such that c appx (i) = φ( c spec (i)) for each i ∈ [n] (for additional details, see Lemma 4.1 of [30]). Therefore, by definition of (•, •), we have that ( c spec , c ) = ( c appx , c ),…”
Section: A1 Auxillary Results For Theoremmentioning
confidence: 99%
“…Such eigengap assumptions are widely spread in the spectral clustering literature [LR15,VL07]. Assuming an eigengap condition, and combining the proof of Theorem 2.1 with the analysis of the k-means algorithm in [LZZ19], it is possible to extend the result of Theorem 2.1 to the k-cluster case. However, ultimately, this is not fully satisfactory as the performance of a good clustering algorithm should only depend on the distance between the clusters and eigenvalues should not matter.…”
Section: Extension To a General Number Of Clustersmentioning
confidence: 99%