Kernel Manifold Alignment

We introduce a kernel method for manifold alignment (KEMA) and domain adaptation that can match an arbitrary number of data sources without needing corresponding pairs, just few labeled examples in all domains. KEMA has interesting properties: 1) it generalizes other manifold alignment methods, 2) it can align manifolds of very different complexities, performing a sort of manifold unfolding plus alignment, 3) it can define a domain-specific metric to cope with multimodal specificities, 4) it can align data spaces of different dimensionality, 5) it is robust to strong nonlinear feature deformations, and 6) it is closed-form invertible which allows transfer across-domains and data synthesis. We also present a reduced-rank version for computational efficiency and discuss the generalization performance of KEMA under Rademacher principles of stability. KEMA exhibits very good performance over competing methods in synthetic examples, visual object recognition and recognition of facial expressions tasks

Advances in machine learning for modelling and understanding in earth sciences

The Earth is a complex dynamic network system. Modelling and understanding the system is at the core of scientific endeavour. We approach these problems with machine learning algorithms. I will review several ML approaches we have developed in the last years: 1) advanced Gaussian processes models for bio-geo-physical parameter estimation, which can incorporate physical laws, blend multisensor data while providing credible confidence intervals for the estimates and improved interpretability, 2) nonlinear dimensionality reduction methods to decompose Earth data cubes in spatially-explicit and temporally-resolved modes of variability that summarize the information content of the data and allow for identifying relations with physical processes, and 3) advances in causal inference that can uncover cause and effect relations from purely observational data

Graph Embedding via High Dimensional Model Representation for Hyperspectral Images

Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as to encapsulate the high dimensionality in a reduced set of informative features for subsequent classification, regression, or unmixing. Manifold learning methods have shown excellent performance to deal with hyperspectral image (HSI) analysis but, unless specifically designed, they cannot provide an explicit embedding map readily applicable to out-of-sample data. A common assumption to deal with the problem is that the transformation between the high-dimensional input space and the (typically low) latent space is linear. This is a particularly strong assumption, especially when dealing with hyperspectral images due to the well-known nonlinear nature of the data. To address this problem, a manifold learning method based on High Dimensional Model Representation (HDMR) is proposed, which enables to present a nonlinear embedding function to project out-of-sample samples into the latent space. The proposed method is compared to manifold learning methods along with its linear counterparts and achieves promising performance in terms of classification accuracy of a representative set of hyperspectral images.Comment: This is an accepted version of work to be published in the IEEE Transactions on Geoscience and Remote Sensing. 11 page