The approximation algorithm based on seeding method for functional $ k $-means problem†

Abstract

<p style='text-indent:20px;'>Different from the classical <inline-formula><tex-math id="M2">\begin{document}$ k $\end{document}</tex-math></inline-formula>-means problem, the functional <inline-formula><tex-math id="M3">\begin{document}$ k $\end{document}</tex-math></inline-formula>-means problem involves a kind of dynamic data, which is generated by continuous processes. In this paper, we mainly design an <inline-formula><tex-math id="M4">\begin{document}$ O(\ln\; k) $\end{document}</tex-math></inline-formula>-approximation algorithm based on the seeding method for functional <inline-formula><tex-math id="M5">\begin{document}$ k $\end{document}</tex-math></inline-formula>-means problem. Moreover, the numerical experiment presented shows that this algorithm is more efficient than the functional <inline-formula><tex-math id="M6">\begin{document}$ k $\end{document}</tex-math></inline-formula>-means clustering algorithm.</p>