Large scale bilinear modelling with missing data in Computer Vision, Image Processing and Machine Learning

This presentation will show a unified approach to solve different bilinear factorization problems in Computer Vision, Image Processing and Machine Learning. Interestingly, many known problems can be solved using bilinear factorization such as Structure from Motion, non-rigid image registration, Photometric Stereo, image pose estimation, learning via matrix factorization, recommender systems strategies, sound localisation and sensor networks calibration. In particular, I will show that the only difference among such problems is the manifold where the data lies on. Following this insight, it is possible to introduce an equivalent reformulation of the bilinear factorization problem that decouples the core bilinear aspect from the manifold specificity. Then the algorithm tackles the resulting constrained optimization problem via Augmented Lagrange Multipliers (the BALM algorithm). This creates an approach that can deal with matrix factorization problems with up to 10^{^8} entries and 90% missing data in several simulated and real experiments.