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

Different from the classical \begin{document}$ k $\end{document}-means problem, the functional \begin{document}$ k $\end{document}-means problem involves a kind of dynamic data, which is generated by continuous processes. In this paper, we mainly design an \begin{document}$ O(\ln\; k) $\end{document}-approximation algorithm based on the seeding method for functional \begin{document}$ k $\end{document}-means problem. Moreover, the numerical experiment presented shows that this algorithm is more efficient than the functional \begin{document}$ k $\end{document}-means clustering algorithm.