AutoManifold: Agentic Design of Data Visualisation Algorithms via Manifold Embedding

Manifold embedding for data visualisation is dominated by a small set of hand-designed state-of-the-art (SOTA) algorithms. Their design targets are fixed at development time, resulting in inflexible algorithmic behaviour that cannot be readily steered toward user-specified structural priorities. Hand-designing new embedding algorithms to address user priority requires highly specialised expertise and is time consuming. To address autonomous algorithm design tailored to user preference, we introduce an agentic algorithm generation pipeline AutoManifold. It composes new manifold embedding algorithms from a constrained vocabulary of affinity, cost, and optimisation primitives, supported by multi-agent large-language-model (LLM) orchestration. AutoManifold conditions every stage of its design on user-specified structural preservation preferences, and iteratively refines the algorithm configuration through an LLM-guided, metric-grounded iterative loop. We compare the generated algorithms against three strongest and most frequently used SOTA (t-SNE, UMAP, and PaCMAP) on real-world datasets spanning different difficulty regimes under identical evaluation infrastructure. The results demonstrate that LLM-driven, priority-conditioned algorithm synthesis can move beyond hyperparameter tuning, producing genuinely new algorithms that outperform traditional hand-designed methods, in their ability to steer towards user-specified properties without compromising much inherent structure in the original data.