Linear embeddings support interactive visual exploration by mapping high-dimensional (nD) data into a two-dimensional space. Despite their popularity, selecting meaningful projection parameters remains a key challenge due to the infinite 2$n$-dimensional parameter space. Once an informative projection is found, users often seek similar ones that emphasize specific items differently while preserving global structure. For instance: Do clusters become outliers under slight changes? Can grouped items separate-or merge-through parameter adjustments? Which changes to the embedding parameters lead to such projections - and do they exist at all? Answering these questions efficiently is critical for effective visual search. Yet, current methods-such as projection tours or manual parameter tuning-are time-consuming and risk overlooking important views, including those of specific interest. We propose Composition Operators, a mathematical foundation for a novel set-of-point manipulation concept for linear embeddings-such as Star Coordinates-as an alternative approach to selecting informative embedding parameters in a more controllable manner with respect to the desired outcome. Users specify item-based constraints on the projection result; the corresponding 2n parameters are then derived automatically, eliminating the need to exhaustively search the entire parameter space to get a similar outcome. Neither the embedding space nor the set of parameters is altered - only the mechanism for navigating and selecting parameters is redefined. We provide closed-form solutions for this and demonstrate our interactive prototype on nD datasets from the UCI repository.

The authors consider the problem of matching two shapes assuming these shapes are related by an elastic deformation. Using linearised elasticity theory and the finite‐element method, they seek an elastic deformation that is caused by simple external boundary forces and accounts for the difference between the two shapes. The main contribution is in proposing a cost function and an optimisation procedure to minimise the symmetric difference between the deformed and the target shapes as an alternative to point matches that guide the matching in other techniques. The authors show how to approximate the non‐linear optimisation problem by a sequence of convex problems. They demonstrate the utility of the proposed method in experiments and compare it to an iterative closest point like matching algorithm.