Topic: clustering

Optimal transport supports clustering, dictionary learning and domain adaptation, but high-dimensional data often force projections that discard information. Charles Bouveyron develops an alternative for Gaussian distributions with parsimonious covariance structure and low intrinsic dimension. A low-dimensional decomposition of empirical covariance matrices gives an efficient, robust closed form for the 2-Wasserstein distance without projecting the data. An explicit Monge map uses exact covariance square roots and inverse square roots. Numerical comparisons demonstrate analytical and computati

Scott Clark discusses operating language-model systems whose failures are difficult to anticipate with offline evaluations. He distinguishes telemetry, known-signal monitoring and production analytics, and describes using trace representations and clustering to discover emergent behaviour and feed improvements into evaluations and training.

Monika Henzinger surveys algorithms that maintain graph information as vertices and edges change. The lecture explains major algorithmic techniques and open problems, and shows how dynamic data structures support applications such as clustering and recent breakthroughs in static maximum-flow and minimum-cost-flow algorithms.