carbikeplotGPCM produces the carbike plot to find best relevant clustering solutions

carbikeplotGPCM takes as input the output of function tclustICsolGPCM (that is a structure containing the best relevant solutions) and produces the car-bike plot. This plot provides a concise summary of the best relevant solutions. This plot shows on the horizontal axis the value of $c_{det}$ and $c_{shw}$ restriction factors and on the vertical axis the value of $k$. For each solution we draw two rectangle (associated with $c_{det}$ and $c_{shw}$) which are respectively referred to interval of values for which the solution is best and stable and a horizontal line which departs from the rectangle for the values of $c_{det}$ ($c_{shw}$) in which the solution is only stable.

Finally, for the best value of $c_{det}$ ($c_{shw}$) associated to the solution, we show a circle with a number indicating the ranked solution among those which are not spurious. This plot has been baptized ``car-bike'', because the first best solutions (in general 2 or 3) are generally best and stable for a large number of values of $c$ and therefore will have large rectangles. In addition, these solutions are likely to be stable for additional values of $c_det$ ($c_{shw}$) and therefore are likely to have horizontal lines departing from the rectangles (from here the name ``cars''). Finally, local minor solutions (which are associated with particular values of $c_{det}$ ($c_{shw}$) and $k$) do not generally present rectangles or lines and are shown with circles (from here the name ``bikes'')

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car-bike plot for the geyser data.`h`

=carbikeplotGPCM(`RelSol`

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`Name, Value`

)

Cerioli, A. Garcia-Escudero, L.A., Mayo-Iscar, A. and Riani, M. (2017), Finding the Number of Groups in Model-Based Clustering via Constrained Likelihoods, "Journal of Computational and Graphical Statistics", pp. 404-416, https://doi.org/10.1080/10618600.2017.1390469