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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!

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It isn’t possible to recover v from its recurrence plot. The recurrence plot doesn’t retain enough information about v, because two vectors can have the same recurrence plot.

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  • $\begingroup$ Thanks. Surely it's possible within a constant, isn't it? The only way I can see two vectors having the same recurrence plot is if they differ by an additive constant, is that incorrect? $\endgroup$ – user655870 Jan 15 at 17:45
  • $\begingroup$ @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. $\endgroup$ – Carl Christian Jan 16 at 22:45
  • $\begingroup$ So is there a way to find one possible solution? Even if it's not unique? $\endgroup$ – user655870 Jan 20 at 10:41

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