# Extract trajectory from recurrence plot

Let's say I have a time series in a vector $$v$$, and I compute its recurrence(-like) plot $$R(i,j)=\left \| v(i)-v(j) \right \|$$.

Is there any standard way of extracting $$v$$ knowing only $$R(i,j)$$ ??

See wikipedia page https://en.wikipedia.org/wiki/Recurrence_plot for examples of what I mean. In the main figure there are four examples of 1D signals converted to recurrence plot.

Many thanks!

• @user655870 The plot is invariant under the transformation $x \gets ax + b$ where $a$ is a scalar with unit modulus and $b$ is a vector. – Carl Christian Jan 16 at 22:45