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Low-Rank Riemannian Optimization for Graph-Based Clustering Applications

With the abundance of data, machine learning applications engaged increased attention in the last decade. An attractive approach to robustify the statistical analysis is to preprocess the data through clustering. This paper develops a low-complexity Riemannian optimization framework for solving optimization problems on the set of positive semidefinite stochastic matrices. The low-complexity feature of the proposed algorithms stems from the factorization of the optimization variable X=YYT and deriving conditions on the number of columns of Y under which the factorization yields a satisfactory solution. The paper further investigates the embedded and quotient geometries of the resulting Riemannian manifolds. In particular, the paper explicitly derives the tangent space, Riemannian gradients and Hessians, and a retraction operator allowing the design of efficient first and second-order optimization methods for the graph-based clustering applications of interest. The numerical results reveal that the resulting algorithms present a clear complexity advantage as compared with state-of-the-art euclidean and Riemannian approaches for graph clustering applications.

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Informasi Detail

Judul Seri

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE; Vol.44 No.9 Part 1 September 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 5133-5148

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

RIEMANNIAN MANIFOLDS
LOW-RANK FACTORIZATION
GRAPH-BASED CLUSTERING
CONVEX AND NON-CONVEX OPTIMIZATION

Info Detail Spesifik

10.1109/TPAMI.2021.3074467

Pernyataan Tanggungjawab

Ahmed Douik, Babak Hassibi

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