The projection constant $\Pi(E):=\Pi(E, \ell_\infty)$ of a finite-dimensional Banach space $E\subset\ell_\infty$ is by definition the smallest norm linear $\ell_\infty$ onto $E$. Fix $n\geq 1$ and denote $\Pi_n$ maximal value $\Pi(\cdot)$ amongst $n$-dimensional real spaces. We prove for every $\varepsilon >0$ that there exist an integer $d\geq subspace $E\subset\ell_1^d$ such $\Pi_n \leq \Pi(E...

Projections aim to convey the relationships and similarity of high-dimensional data in a low-dimensional representation. Most such techniques are designed for static data. When used time-dependent data, they usually fail create stable suitable low dimensional We propose two dynamic projection methods (PCD-tSNE LD-tSNE) that use global guides steer points. This avoids unstable movement does not ...