A low-complexity fuzzy activation function for artificial neural networks

A novel fuzzy-based activation function for artificial neural networks is proposed. This approach provides easy hardware implementation and straightforward interpretability in the basis of IF-THEN rules. Backpropagation learning with the new activation function also has low computational complexity. Several application examples ( XOR gate, chaotic time-series prediction, channel equalization, and independent component analysis) support the potential of the proposed scheme.     

Dosage individualization of erythropoietin using a profile-dependent support vector regression

The external administration of recombinant human erythropoietin is the chosen treatment for those patients with secondary anemia due to chronic renal failure in periodic hemodialysis. The objective of this paper is to carry out an individualized prediction of the EPO dosage to be administered to those patients. The high cost of this medication, its side-effects and the phenomenon of potential resistance which some individuals suffer all justify the need for a model which is capable of optimizing dosage individualization. A group of 110 patients and several patient factors were used to develop the models. The support vector regressor (SVR) is benchmarked with the classical multilayer perceptron (MLP) and the Autoregressive Conditional Heteroskedasticity (ARCH) model. We introduce a priori knowledge by relaxing or tightening the epsilon-insensitive region and the penalization parameter depending on the time period of the patients' follow-up. The so-called profile-dependent SVR (PD-SVR) improves results of the standard SVR method and the MLP. We perform sensitivity analysis on the MLP and inspect the distribution of the support vectors in the input and feature spaces in order to gain knowledge about the problem.     

Semi-Supervised Graph-Based Hyperspectral Image Classification

This paper presents a semi-supervised graph-based method for the classification of hyperspectral images. The method is designed to handle the special characteristics of hyperspectral images, namely, high-input dimension of pixels, low number of labeled samples, and spatial variability of the spectral signature. To alleviate these problems, the method incorporates three ingredients, respectively. First, being a kernel-based method, it combats the curse of dimensionality efficiently. Second, following a semi-supervised approach, it exploits the wealth of unlabeled samples in the image, and naturally gives relative importance to the labeled ones through a graph-based methodology. Finally, it incorporates contextual information through a full family of composite kernels. Noting that the graph method relies on inverting a huge kernel matrix formed by both labeled and unlabeled samples, we originally introduce the Nystro umlm method in the formulation to speed up the classification process. The presented semi-supervised-graph-based method is compared to state-of-the-art support vector machines in the classification of hyperspectral data. The proposed method produces better classification maps, which capture the intrinsic structure collectively revealed by labeled and unlabeled points. Good and stable accuracy is produced in ill-posed classification problems (high dimensional spaces and low number of labeled samples). In addition, the introduction of the composite-kernel framework drastically improves results, and the new fast formulation ranks almost linearly in the computational cost, rather than cubic as in the original method, thus allowing the use of this method in remote-sensing applications.     

Structured Output SVM for Remote Sensing Image Classification

Traditional kernel classifiers assume independence among the classification outputs. As a consequence, each misclassification receives the same weight in the loss function. Moreover, the kernel function only takes into account the similarity between input values and ignores possible relationships between the classes to be predicted. These assumptions are not consistent for most of real-life problems. In the particular case of remote sensing data, this is not a good assumption either. Segmentation of images acquired by airborne or satellite sensors is a very active field of research in which one tries to classify a pixel into a predefined set of classes of interest (e.g. water, grass, trees, etc.). In this situation, the classes share strong relationships, e.g. a tree is naturally (and spectrally) more similar to grass than to water. In this paper, we propose a first approach to remote sensing image classification using structured output learning. In our approach, the output space structure is encoded using a hierarchical tree, and these relations are added to the model in both the kernel and the loss function. The methodology gives rise to a set of new tools for structured classification, and generalizes the traditional non-structured classification methods. Comparison to standard SVM is done numerically, statistically and by visual inspection of the obtained classification maps. Good results are obtained in the challenging case of a multispectral image of very high spatial resolution acquired with QuickBird over a urban area.     

Spectro-temporal reflectance surfaces: a new conceptual framework for the integration of remote-sensing data from multiple different sensors

The conflict between spatial and temporal resolution of satellite systems, as well as the frequent presence of clouds in the images, has been a traditional limitation of remote sensing in the optical domain. Nevertheless, most of the conceptual tools and algorithms developed classically in remote sensing are based on the input of a series of cloud-free images from identical sensors. In this study, we propose a conceptual framework that is able to ingest data from several different sensors, make them homogeneous, eliminate clouds (virtually), and make them usable in a flexible, efficient, and transparent way. The methodology is based on previous developments such as spatial ‘downscaling’, temporal interpolation, and spectral transformations, but adds a conceptual framework that is able to integrate all of them and facilitate synergies between all these techniques.     

Robust support vector method for hyperspectral data classification and knowledge discovery

We propose the use of support vector machines (SVMs) for automatic hyperspectral data classification and knowledge discovery. In the first stage of the study, we use SVMs for crop classification and analyze their performance in terms of efficiency and robustness, as compared to extensively used neural and fuzzy methods. Efficiency is assessed by evaluating accuracy and statistical differences in several scenes. Robustness is analyzed in terms of: (1) suitability to working conditions when a feature selection stage is not possible and (2) performance when different levels of Gaussian noise are introduced at their inputs. In the second stage of this work, we analyze the distribution of the support vectors (SVs) and perform sensitivity analysis on the best classifier in order to analyze the significance of the input spectral bands. For classification purposes, six hyperspectral images acquired with the 128-band HyMAP spectrometer during the DAISEX-1999 campaign are used. Six crop classes were labeled for each image. A reduced set of labeled samples is used to train the models, and the entire images are used to assess their performance. Several conclusions are drawn: (1) SVMs yield better outcomes than neural networks regarding accuracy, simplicity, and robustness; (2) training neural and neurofuzzy models is unfeasible when working with high-dimensional input spaces and great amounts of training data; (3) SVMs perform similarly for different training subsets with varying input dimension, which indicates that noisy bands are successfully detected; and (4) a valuable ranking of bands through sensitivity analysis is achieved.     

Correction of systematic spatial noise in push-broom hyperspectral sensors: application to CHRIS/PROBA images

Hyperspectral remote sensing images are affected by different types of noise. In addition to typical random noise, nonperiodic partially deterministic disturbance patterns generally appear in the data. These patterns, which are intrinsic to the image formation process, are characterized by a high degree of spatial and spectral coherence. We present a new technique that faces the problem of removing the spatially coherent noise known as vertical striping, usually found in images acquired by push-broom sensors. The developed methodology is tested on data acquired by the Compact High Resolution Imaging Spectrometer (CHRIS) onboard the Project for On-board Autonomy (PROBA) orbital platform, which is a typical example of a push-broom instrument exhibiting a relatively high noise component. The proposed correction method is based on the hypothesis that the vertical disturbance presents higher spatial frequencies than the surface radiance. A technique to exclude the contribution of the spatial high frequencies of the surface from the destriping process is introduced. First, the performance of the proposed algorithm is tested on a set of realistic synthetic images with added modeled noise in order to quantify the noise reduction and the noise estimation accuracy. Then, algorithm robustness is tested on more than 350 real CHRIS images from different sites, several acquisition modes (different spatial and spectral resolutions), and covering the full range of possible sensor temperatures. The proposed algorithm is benchmarked against the CHRIS reference algorithm. Results show excellent rejection of the noise pattern with respect to the original CHRIS images, especially improving the removal in those scenes with a natural high contrast. However, some low-frequency components still remain. In addition, the developed correction model captures and corrects the dependency of the noise patterns on sensor temperature, which confirms the robustness of the presented approach.     

Retrieval of oceanic chlorophyll concentration with relevance vector machines

In this communication, we evaluate the performance of the relevance vector machine (RVM) for the estimation of biophysical parameters from remote sensing data. For illustration purposes, we focus on the estimation of chlorophyll-a concentrations from remote sensing reflectance just above the ocean surface. A variety of bio-optical algorithms have been developed to relate measurements of ocean radiance to in situ concentrations of phytoplankton pigments, and ultimately most of these algorithms demonstrate the potential of quantifying chlorophyll-a concentrations accurately from multispectral satellite ocean color data. Both satellite-derived data and in situ measurements are subject to high levels of uncertainty. In this context, robust and stable non-linear regression methods that provide inverse models are desirable.Lately, the use of the support vector regression (SVR) has produced good results in inversion problems, improving state-of-the-art neural networks. However, the SVR has some deficiencies, which could be theoretically alleviated by the RVM. In this paper, performance of the RVM is evaluated in terms of accuracy and bias of the estimations, sparseness of the solutions, robustness to low number of training samples, and computational burden. In addition, some theoretical issues are discussed, such as the sensitivity to training parameters setting, kernel selection, and confidence intervals on the predictions.Results suggest that RVMs offer an excellent trade-off between accuracy and sparsity of the solution, and become less sensitive to the selection of the free parameters. A novel formulation of the RVM that incorporates prior knowledge of the problem is presented and successfully tested, providing better results than standard RVM formulations, SVRs, neural networks, and classical bio-optical models for SeaWIFS, such as Morel, CalCOFI and OC2/OC4 models.     

Nonlinearities and adaptation of color vision from sequential principal curves analysis

Mechanisms of human color vision are characterized by two phenomenological aspects: the system is nonlinear and adaptive to changing environments. Conventional attempts to derive these features from statistics use separate arguments for each aspect. The few statistical explanations that do consider both phenomena simultaneously follow parametric formulations based on empirical models. Therefore, it may be argued that the behavior does not come directly from the color statistics but from the convenient functional form adopted. In addition, many times the whole statistical analysis is based on simplified databases that disregard relevant physical effects in the input signal, as, for instance, by assuming flat Lambertian surfaces. In this work, we address the simultaneous statistical explanation of the nonlinear behavior of achromatic and chromatic mechanisms in a fixed adaptation state and the change of such behavior (i.e., adaptation) under the change of observation conditions. Both phenomena emerge directly from the samples through a single data-driven method: the sequential principal curves analysis (SPCA) with local metric. SPCA is a new manifold learning technique to derive a set of sensors adapted to the manifold using different optimality criteria. Here sequential refers to the fact that sensors (curvilinear dimensions) are designed one after the other, and not to the particular (eventually iterative) method to draw a single principal curve. Moreover, in order to reproduce the empirical adaptation reported under D65 and A illuminations, a new database of colorimetrically calibrated images of natural objects under these illuminants was gathered, thus overcoming the limitations of available databases. The results obtained by applying SPCA show that the psychophysical behavior on color discrimination thresholds, discount of the illuminant, and corresponding pairs in asymmetric color matching emerge directly from realistic data regularities, assuming no a priori functional form. These results provide stronger evidence for the hypothesis of a statistically driven organization of color sensors. Moreover, the obtained results suggest that the nonuniform resolution of color sensors at this low abstraction level may be guided by an error-minimization strategy rather than by an information-maximization goal.