Regularization approaches to hyperspectral unmixing

We consider a few different approaches to hyperspectral unmixing of remotely sensed imagery which exploit and extend recent advances in sparse statistical regularization, handling of constraints and dictionary reduction. Hyperspectral unmixing methods often use a conventional least-squares based lasso which assumes that the data follows the Gaussian distribution, we use this as a starting point. In addition, we consider a robust approach to sparse spectral unmixing of remotely sensed imagery which reduces the sensitivity of the estimator to outliers. Due to water absorption and atmospheric effects that affect data collection, hyperspectral images are prone to have large outliers. The framework comprises of several well-principled penalties. A non-convex, hyper-Laplacian prior is incorporated to induce sparsity in the number of active pure spectral components, and total variation regularizer is included to exploit the spatial-contextual information of hyperspectral images. Enforcing the sum-to-one and non-negativity constraint on the models parameters is essential for obtaining realistic estimates. We consider two approaches to account for this: an iterative heuristic renormalization and projection onto the positive orthant, and a reparametrization of the coefficients which gives rise to a theoretically founded method. Since the large size of modern spectral libraries cannot only present computational challenges but also introduce collinearities between regressors, we introduce a library reduction step. This uses the multiple signal classi fication (MUSIC) array processing algorithm, which both speeds up unmixing and yields superior results in scenarios where the library size is extensive. We show that although these problems are non-convex, they can be solved by a properly de fined algorithm based on either trust region optimization or iteratively reweighted least squares. The performance of the different approaches is validated in several simulated and real hyperspectral data experiments

Physically inspired methods and development of data-driven predictive systems

Traditionally building of predictive models is perceived as a combination of both science and art. Although the designer of a predictive system effectively follows a prescribed procedure, his domain knowledge as well as expertise and intuition in the field of machine learning are often irreplaceable. However, in many practical situations it is possible to build well–performing predictive systems by following a rigorous methodology and offsetting not only the lack of domain knowledge but also partial lack of expertise and intuition, by computational power. The generalised predictive model development cycle discussed in this thesis is an example of such methodology, which despite being computationally expensive, has been successfully applied to real–world problems. The proposed predictive system design cycle is a purely data–driven approach. The quality of data used to build the system is thus of crucial importance. In practice however, the data is rarely perfect. Common problems include missing values, high dimensionality or very limited amount of labelled exemplars. In order to address these issues, this work investigated and exploited inspirations coming from physics. The novel use of well–established physical models in the form of potential fields, has resulted in derivation of a comprehensive Electrostatic Field Classification Framework for supervised and semi–supervised learning from incomplete data. Although the computational power constantly becomes cheaper and more accessible, it is not infinite. Therefore efficient techniques able to exploit finite amount of predictive information content of the data and limit the computational requirements of the resource–hungry predictive system design procedure are very desirable. In designing such techniques this work once again investigated and exploited inspirations coming from physics. By using an analogy with a set of interacting particles and the resulting Information Theoretic Learning framework, the Density Preserving Sampling technique has been derived. This technique acts as a computationally efficient alternative for cross–validation, which fits well within the proposed methodology. All methods derived in this thesis have been thoroughly tested on a number of benchmark datasets. The proposed generalised predictive model design cycle has been successfully applied to two real–world environmental problems, in which a comparative study of Density Preserving Sampling and cross–validation has also been performed confirming great potential of the proposed methods.EThOS - Electronic Theses Online ServiceGBUnited Kingdo