In the face of growing needs for water and energy, a fundamental understanding of the environmental impacts of human activities becomes critical for managing water and energy resources, remedying water pollution, and making regulatory policy wisely. Among activities that impact the environment, oil and gas production, wastewater transport, and urbanization are included. In addition to the occurrence of anthropogenic contamination, the presence of some contaminants (e.g., methane, salt, and sulfate) of natural origin is not uncommon. Therefore, scientists sometimes find it difficult to identify the sources of contaminants in the coupled natural and human systems. In this paper, we propose a technique to simultaneously conduct source detection and prediction, which outperforms other approaches in the interdisciplinary case study of the identification of potential groundwater contamination within a region of high-density shale gas development.
Dictionary learning has been widely used in computer vision to obtain basic components and sparse representations of images @cite_7 . Recently, in order to optimize the learned dictionary for a specific task, people proposed supervised dictionary learning @cite_1 . Some methods learn discriminative dictionaries for different classes @cite_8 @cite_14 , or use label information to prune the learned dictionary by unsupervised dictionary learning @cite_5 . They actually separate the dictionary learning from the supervised learning part and may lead to inferior results. Another group of methods combine dictionary learning and supervised learning @cite_1 @cite_11 , but fail to consider the spatial temporal property for specific problems. Hence, we propose to do dictionary learning and supervised learning iteratively, and spatial and temporal regularization are added to improve the interpretation of results.
@cite_14 @cite_7 @cite_8 @cite_1 @cite_5 @cite_11
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The employed dictionary plays an important role in sparse representation or sparse coding based image reconstruction and classification, while learning dictionaries from the training data has led to state-of-the-art results in image classification tasks. However, many dictionary learning models exploit only the discriminative information in either the representation coefficients or the representation residual, which limits their performance. In this paper we present a novel dictionary learning method based on the Fisher discrimination criterion. A structured dictionary, whose atoms have correspondences to the subject class labels, is learned, with which not only the representation residual can be used to distinguish different classes, but also the representation coefficients have small within-class scatter and big between-class scatter. The classification scheme associated with the proposed Fisher discrimination dictionary learning (FDDL) model is consequently presented by exploiting the discriminative information in both the representation residual and the representation coefficients. The proposed FDDL model is extensively evaluated on various image datasets, and it shows superior performance to many state-of-the-art dictionary learning methods in a variety of classification tasks. It is now well established that sparse representation models are working effectively for many visual recognition tasks, and have pushed forward the success of dictionary learning therein. Recent studies over dictionary learning focus on learning discriminative atoms instead of purely reconstructive ones. However, the existence of intraclass diversities (i.e., data objects within the same category but exhibit large visual dissimilarities), and interclass similarities (i.e., data objects from distinct classes but share much visual similarities), makes it challenging to learn effective recognition models. To this end, a large number of labeled data objects are required to learn models which can effectively characterize these subtle differences. However, labeled data objects are always limited to access, committing it difficult to learn a monolithic dictionary that can be discriminative enough. To address the above limitations, in this paper, we propose a weakly-supervised dictionary learning method to automatically learn a discriminative dictionary by fully exploiting visual attribute correlations rather than label priors. In particular, the intrinsic attribute correlations are deployed as a critical cue to guide the process of object categorization, and then a set of subdictionaries are jointly learned with respect to each category. The resulting dictionary is highly discriminative and leads to intraclass diversity aware sparse representations. Extensive experiments on image classification and object recognition are conducted to show the effectiveness of our approach. Algorithms for data-driven learning of domain-specific overcomplete dictionaries are developed to obtain maximum likelihood and maximum a posteriori dictionary estimates based on the use of Bayesian models with concave Schur-concave (CSC) negative log priors. Such priors are appropriate for obtaining sparse representations of environmental signals within an appropriately chosen (environmentally matched) dictionary. The elements of the dictionary can be interpreted as concepts, features, or words capable of succinct expression of events encountered in the environment (the source of the measured signals). This is a generalization of vector quantization in that one is interested in a description involving a few dictionary entries (the proverbial "25 words or less"), but not necessarily as succinct as one entry. To learn an environmentally adapted dictionary capable of concise expression of signals generated by the environment, we develop algorithms that iterate between a representative set of sparse representations found by variants of FOCUSS and an update of the dictionary using these sparse representations.Experiments were performed using synthetic data and natural images. For complete dictionaries, we demonstrate that our algorithms have improved performance over other independent component analysis (ICA) methods, measured in terms of signal-to-noise ratios of separated sources. In the overcomplete case, we show that the true underlying dictionary and sparse sources can be accurately recovered. In tests with natural images, learned overcomplete dictionaries are shown to have higher coding efficiency than complete dictionaries; that is, images encoded with an overcomplete dictionary have both higher compression (fewer bits per pixel) and higher accuracy (lower mean square error). Many recent efforts have shown the effectiveness of dictionary learning methods in solving several computer vision problems. However, when designing dictionaries, training and testing domains may be different, due to different view points and illumination conditions. In this paper, we present a function learning framework for the task of transforming a dictionary learned from one visual domain to the other, while maintaining a domain-invariant sparse representation of a signal. Domain dictionaries are modeled by a linear or non-linear parametric function. The dictionary function parameters and domain-invariant sparse codes are then jointly learned by solving an optimization problem. Experiments on real datasets demonstrate the effectiveness of our approach for applications such as face recognition, pose alignment and pose estimation.