This project implements the 3D-Kiviat plot technique to visualize uncertainties [Roy2019]. It proposes a solution to visualize high input and output dimensions. This solution relies on Hypothetical Outcome plot (HOPs) applied to functional response surface, Highest Density Region metrics, and a 3-dimensional version of Kiviat plot. For the 3D-Kiviat, each layer stands for a hypothetical outcome (a realization) coloured by a scalar value related to the response variable. This value is either the response variable at a given point and time or some distance computed with the HDR metrics. This solution can be augmented with data sonification to traduce the HDR metrics (see HDR-Boxplot).
sample = np.loadtxt('data/sample_mascaret.dat')
data = np.loadtxt('data/data_mascaret.dat')
kiviat = Kiviat3D(sample, data)
kiviat.plot()The output is the following figure:
Note
The package can easily be used in any framework as long as there is a dependency between input and outputs.
It consists to adapt the 3D-Kiviat plot to the visualization of both input and response variable spaces. Each plane of the Kiviat represents a realization within the dataset with as many directions as the input dimensions.
The input variables here correspond to the friction coefficients (Ks1, Ks2, Ks3) and the constant inflow Q; the output variable is the water level at the city Marmande, it is colour-coded onto the Kiviat plane. For the 3D-Kiviat, planes are stacked into a 3D object with respect to the response variable (scalar or functional) related value that is colour-coded. It should be noted that each plane is filled with only one colour to preserve readability. The benefit of 3D-Kiviat stands in the choice of both the stacking and the colouring strategies.
When representing functional output data, different stacking and colouring strategies allow to highlight different information in the dataset. Four choices of stacking and colouring are illustrated here after; the stacking and colouring choices are indicated in the legend, they are achieved with respect to the response variable at a given location and time, with respect to the HDR metric or with respect to one of the input variables.
Here, stacking is done with respect to the response variable at a given location and time while the colouring is done with respect to the difference to the median realization computed with the HDR metric. This allows to get a sense of the spatial PDF augmented with the input parameter mapping.
Another possibility consists in stacking with respect to the HDR metric and colouring with respect to the response variable value.
Here, stacking is done with respect to one of the input variable (in the present case Q) and the colouring is done with respect to the HDR metrics.
Finally, this figure displays both stacking and colouring with respect to the response variable value.
From the first, third and fourth figures, the impact of Q on the water level is easily readable; water level increases with Q. High water level values are also obtained for low Ks3 values while other parameters seem to have no significant impact on the response variable. Ks1 and Ks2 have barely any impact on the response variable. The manipulation of the animated 3D-Kiviat is even more adapted to data analysis. The coloured HDR in first and third figures indicates how each realization differs from the median realization. It appears that stacking for colouring with respect to response variable or HDR serves different purposes. Ordering by response variable allows to discriminate which input lead to specific response variable value while ordering by HDR illustrated the dispersion of the dataset with respect to a reference realization. Sounding is a supplementary way to emphasis the information, especially for large datasets.
The dependencies are:
- Python >= 2.7 or >= 3.5
- scikit-learn >= 0.18
- numpy >= 0.13
- scipy >= 0.15
- matplotlib >= 2.1
- Roy2019
Sounding Spider: An Efficient Way for Representing Uncertainties in High Dimensions. Pamphile T. Roy, S. Ricci, J.C. Jouhaud, B. Cuenot. 2019