Configure Convex Hull on Inputs

Use the hull model to check whether a candidate input setting lies inside the convex hull formed by the training data. If an input is inside the hull, model predictions are generally more reliable; if it falls outside, predictions may be extrapolations.

In two dimensions, the model forms edges around the outermost training points. In higher dimensions (n-D), these become faces. Together they enclose all training data and define the convex hull.

Distance returned by the hull model:

• Sign: Negative values indicate the point is inside the convex hull; positive values indicate it is outside.
• What is measured: For efficiency, the model computes an orthogonal projection of the distance to the nearest hull edge/face rather than the Euclidean distance to the polygon/polytope.
• Multiple hulls: A hull model often contains several pairwise or user-defined hulls. The returned value is the maximum (worst-case) distance across all evaluated hulls.
• Why this matters: The returned value can be used in optimization as a constraint or penalty term to keep solutions within the data-supported domain.

Example:

The following example shows how distances are computed:

• Black: Convex hull boundary.
• Red: Outermost training data points that form the hull.
• Green: Points for which the distance to the hull is evaluated.
• Blue: Orthogonal distance from a green point to the nearest hull edge.
• Gray: Edge extensions to construct the orthogonal projection for efficient computation.

For the first green point, the orthogonal distance to the nearest edge is shown by the blue segment.

For the second green point, two orthogonal projections to neighboring edges are possible (constructed using the gray extensions). The algorithm takes the larger of the two distances as the result.