\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Convergence of different algorithms for clustering with fashion-MNIST dataset. Here, we set the rank as $r=20$ for the nonconvex approaches. The solution rank for the template\nobreakspace {}\textup {\hbox {\mathsurround \z@ \normalfont (\ignorespaces \ref {eq:sdp_svx}\unskip \@@italiccorr )}} is the number of clusters $s$ \cite [Theorem 1]{kulis2007fast}. However, as discussed in\nobreakspace {}\cite {tepper2018clustering}, setting rank $r>s$ leads more accurate reconstruction at the expense of speed, hence our choice of $r=20$. }}{10}{figure.1}\protected@file@percent }
\newlabel{fig:clustering}{{1}{10}{Convergence of different algorithms for clustering with fashion-MNIST dataset. Here, we set the rank as $r=20$ for the nonconvex approaches. The solution rank for the template~\eqref {eq:sdp_svx} is the number of clusters $s$ \cite [Theorem 1]{kulis2007fast}. However, as discussed in~\cite {tepper2018clustering}, setting rank $r>s$ leads more accurate reconstruction at the expense of speed, hence our choice of $r=20$}{figure.1}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Convergence with different subsolvers for the aforementioned nonconvex relaxation. }}{11}{figure.2}\protected@file@percent }
\newlabel{fig:bp1}{{2}{11}{Convergence with different subsolvers for the aforementioned nonconvex relaxation}{figure.2}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces {\it {(Top)}} Objective convergence for calculating top generalized eigenvalue and eigenvector of $B$ and $C$. {\it {(Bottom)}} Eigenvalue structure of the matrices. For (i),(ii) and (iii), $C$ is positive semidefinite; for (iv), (v) and (vi), $C$ contains negative eigenvalues. {[(i): Generated by taking symmetric part of iid Gaussian matrix. (ii): Generated by randomly rotating diag($1^{-p}, 2^{-p}, \cdots , 1000^{-p}$)($p=1$). (iii): Generated by randomly rotating diag($10^{-p}, 10^{-2p}, \cdots , 10^{-1000p}$)($p=0.0025$).]} }}{18}{figure.4}\protected@file@percent }
\newlabel{fig:geig1}{{4}{18}{{\it {(Top)}} Objective convergence for calculating top generalized eigenvalue and eigenvector of $B$ and $C$. {\it {(Bottom)}} Eigenvalue structure of the matrices. For (i),(ii) and (iii), $C$ is positive semidefinite; for (iv), (v) and (vi), $C$ contains negative eigenvalues. {[(i): Generated by taking symmetric part of iid Gaussian matrix. (ii): Generated by randomly rotating diag($1^{-p}, 2^{-p}, \cdots , 1000^{-p}$)($p=1$). (iii): Generated by randomly rotating diag($10^{-p}, 10^{-2p}, \cdots , 10^{-1000p}$)($p=0.0025$).]}}{figure.4}{}}