Main interests

  • Nonnegative Matrix Factorization

    • Models with identifiability theorems

    • Convex and cone geometry

    • Minimum volume regularisation and singular value functions

    • log-concave / unimodal vectors and matrix

  • Tensor Factorization: CPD models and identifiability

  • Continuous Optimization

    • Nonconvex optimisation, especially coordinate descent for NMF and NTF

    • Convergence analysis of algorithm for convex and nonconvex structural optimization

Secondary interests

  • Rank minimisation problem with affine constraint

  • Non-standard algebra for NMF: max-plus semiring, exterior algebra, Clifford algebra

  • ODE / Lagrangian / Hamiltonian / Control-theoretic analysis of optimisation algorithms

  • Multi-level/grid methods for optimisation of factorisation-type structural optimisation problem

  • Laternt Dirichlet distribution for NMF-based topic modelling

Know nothing / little, but ‘‘okay’’ interested

  • Polytope geometry, extended formulations, theory of combinatorial optimisation

  • Optimal transport for matrix factorisation

  • Graph models

  • Theory of retrieval: compressive sensing, matrix completion and phase retrieval

  • Polynomial optimization

  • Control theory

  • Theoretical mechanics