In this article, we present an automatic leaves image classification system for sunflower crops using neural networks, which could be used in selective herbicide applications. The system is comprised of four main stages. First, a segmentation based on rgb color space is performed. Second, many different features are detected and then extracted from the segmented image. Third, the most discriminable set of features are selected. Finally, the Generalized Softmax Perceptron (GSP) neural network architecture is used in conjunction with the recently proposed Posterior Probability Model Selection (PPMS) algorithm for complexity selection in order to select the leaves in an image and then classify them either as sunflower or non-sunflower. The experimental results show that the proposed system achieves a high level of accuracy with only five selected discriminative features obtaining an average Correct Classification Rate of 85\% and an area under the receiver operation curve over 90\%, for the test set. {\^A}{\textcopyright} 2011 Elsevier B.V.

}, keywords = {Classification rates, Computer vision, Crops, Discriminative features, Generalized softmax perceptron, Helianthus, Herbicide application, Herbicides, Image classification, Image classification systems, Leaf classification, Learning machines, Model selection, Network architecture, Neural networks, Posterior probability, RGB color space, Segmented images, Sunflower, Test sets, accuracy assessment, agricultural technology, algorithm, artificial neural network, automation, dicotyledon, experimental study, herbicide, segmentation}, issn = {01681699}, doi = {10.1016/j.compag.2011.05.007}, url = {https://www.sciencedirect.com/science/article/pii/S0168169911001220}, author = {J I Arribas and Gonzalo Vegas S{\'a}nchez-Ferrero and G Ruiz-Ruiz and Jaime Gomez-Gil} } @article {422, title = {A radius and ulna TW3 bone age assessment system}, journal = {IEEE Transactions on Biomedical Engineering}, volume = {55}, year = {2008}, pages = {1463-1476}, abstract = {An end-to-end system to automate the well-known Tanner - Whitehouse (TW3) clinical procedure to estimate the skeletal age in childhood is proposed. The system comprises the detailed analysis of the two most important bones in TW3: the radius and ulna wrist bones. First, a modified version of an adaptive clustering segmentation algorithm is presented to properly semi-automatically segment the contour of the bones. Second, up to 89 features are defined and extracted from bone contours and gray scale information inside the contour, followed by some well-founded feature selection mathematical criteria, based on the ideas of maximizing the classes{\textquoteright} separability. Third, bone age is estimated with the help of a Generalized Softmax Perceptron (GSP) neural network (NN) that, after supervised learning and optimal complexity estimation via the application of the recently developed Posterior Probability Model Selection (PPMS) algorithm, is able to accurately predict the different development stages in both radius and ulna from which and with the help of the TW3 methodology, we are able to conveniently score and estimate the bone age of a patient in years, in what can be understood as a multiple-class (multiple stages) pattern recognition approach with posterior probability estimation. Finally, numerical results are presented to evaluate the system performance in predicting the bone stages and the final patient bone age over a private hand image database, with the help of the pediatricians and the radiologists expert diagnoses. {\^A}{\textcopyright} 2006 IEEE.

}, keywords = {Age Determination by Skeleton, Aging, Algorithms, Artificial Intelligence, Automated, Bone, Bone age assessment, Clustering algorithms, Computer-Assisted, Humans, Model selection, Neural networks, Pattern recognition, Radiographic Image Interpretation, Reproducibility of Results, Sensitivity and Specificity, Skeletal maturity, algorithm, article, artificial neural network, automation, bone age, bone maturation, childhood, instrumentation, radius, ulna}, issn = {00189294}, doi = {10.1109/TBME.2008.918554}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-42249094547\&partnerID=40\&md5=2cecfea5f75a61b048611f2391b00aed}, author = {Antonio Trist{\'a}n-Vega and J I Arribas} } @inbook {418, title = {A statistical-genetic algorithm to select the most significant features in mammograms}, booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)}, volume = {4673 LNCS}, year = {2007}, pages = {189-196}, abstract = {An automatic classification system into either malignant or benign microcalcification from mammograms is a helpful tool in breast cancer diagnosis. From a set of extracted features, a classifying method using neural networks can provide a probability estimation that can help the radiologist in his diagnosis. With this objective in mind, this paper proposes a feature selection algorithm from a massive number of features based on a statistical distance method in conjunction with a genetic algorithm (GA). The use of a statistical distance as optimality criterion was improved with genetic algorithms for selecting an appropriate subset of features, thus making this algorithm capable of performing feature selection from a massive set of initial features. Additionally, it provides a criterion to select an appropriate number of features to be employed. Experimental work was performed using Generalized Softmax Perceptrons (GSP), trained with a Strict Sense Bayesian cost function for direct probability estimation, as microcalcification classifiers. A Posterior Probability Model Selection (PPMS) algorithm was employed to determine the network complexity. Results showed that this algorithm converges into a subset of features which has a good classification rate and Area Under Curve (AUC) of the Receiver Operating Curve (ROC). {\^A}{\textcopyright} Springer-Verlag Berlin Heidelberg 2007.

}, keywords = {Breast cancer, Diagnosis, Feature extraction, Genetic algorithms, Mammography, Microcalcification classification, Network complexity, Neural network classifiers, Neural networks, Tumors}, isbn = {9783540742715}, issn = {03029743}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-38149142403\&partnerID=40\&md5=ef139db3a0e5d603c4f721316abdcf2c}, author = {Gonzalo Vegas S{\'a}nchez-Ferrero and J I Arribas} } @article {420, title = {A model selection algorithm for a posteriori probability estimation with neural networks}, journal = {IEEE Transactions on Neural Networks}, volume = {16}, year = {2005}, pages = {799-809}, abstract = {This paper proposes a novel algorithm to jointly determine the structure and the parameters of a posteriori probability model based on neural networks (NNs). It makes use of well-known ideas of pruning, splitting, and merging neural components and takes advantage of the probabilistic interpretation of these components. The algorithm, so called a posteriori probability model selection (PPMS), is applied to an NN architecture called the generalized softmax perceptron (GSP) whose outputs can be understood as probabilities although results shown can be extended to more general network architectures. Learning rules are derived from the application of the expectation-maximization algorithm to the GSP-PPMS structure. Simulation results show the advantages of the proposed algorithm with respect to other schemes. {\^A}{\textcopyright} 2005 IEEE.

}, keywords = {Algorithms, Automated, Biological, Breast Neoplasms, Computer simulation, Computer-Assisted, Computing Methodologies, Decision Support Techniques, Diagnosis, Estimation, Expectation-maximization, Generalized Softmax Perceptron (GSP), Humans, Mathematical models, Model selection, Models, Neural Networks (Computer), Neural networks, Numerical Analysis, Objective function, Pattern recognition, Posterior probability, Probability, Statistical, Stochastic Processes, algorithm, article, artificial neural network, automated pattern recognition, biological model, breast tumor, classification, cluster analysis, computer analysis, computer assisted diagnosis, decision support system, evaluation, human, mathematical computing, methodology, statistical model, statistics}, issn = {10459227}, doi = {10.1109/TNN.2005.849826}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-23044459586\&partnerID=40\&md5=f00e7d86a625cfc466373a2a938276d0}, author = {J I Arribas and Jes{\'u}s Cid-Sueiro} } @conference {417, title = {A radius and ulna skeletal age assessment system}, booktitle = {2005 IEEE Workshop on Machine Learning for Signal Processing}, year = {2005}, address = {Mystic, CT}, abstract = {An end to end system to partially automate the TW3 bone age assessment procedure is proposed. The system comprises the detailed analysis of the two more important bones in TW3: the radius and ulna wrist bones. First, a generalization of K-means algorithm is presented to semi-automatically segment the contour of the bones and thus extract up to 89 features describing shapes and textures from bones. Second, a well-founded feature selection criterion based on the statistical properties of data is used in order to properly choose the most relevant features. Third, bone age is estimated with the help of a Generalized Softmax Perceptron (GSP) Neural Network (NN) whose optimal complexity is estimated via the Posterior Probability Model Selection (PPMS) algorithm. We can then predict the different development stages in both radius and ulna, from which we are able to score and estimate the bone age of a patient in years and finally we compare the NN results with those from the pediatrician expert discrepancies. {\^A}{\textcopyright} 2005 IEEE.

}, keywords = {Algorithms, Bone, Feature extraction, Generalized Softmax Perceptron (GSP), Living systems studies, Neural networks, Probability Model Selection (PPMS), Skeletal age assessment system}, isbn = {0780395174; 9780780395176}, doi = {10.1109/MLSP.2005.1532903}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-33749052083\&partnerID=40\&md5=eefa29ac09f4efa304b613cf07ab8d10}, author = {Antonio Trist{\'a}n-Vega and J I Arribas} } @article {409, title = {Cost functions to estimate a posteriori probabilities in multiclass problems}, journal = {IEEE Transactions on Neural Networks}, volume = {10}, year = {1999}, pages = {645-656}, abstract = {The problem of designing cost functions to estimate a posteriori probabilities in multiclass problems is addressed in this paper. We establish necessary and sufficient conditions that these costs must satisfy in one-class one-output networks whose outputs are consistent with probability laws. We focus our attention on a particular subset of the corresponding cost functions; those which verify two usually interesting properties: symmetry and separability (well-known cost functions, such as the quadratic cost or the cross entropy are particular cases in this subset). Finally, we present a universal stochastic gradient learning rule for single-layer networks, in the sense of minimizing a general version of these cost functions for a wide family of nonlinear activation functions.

}, keywords = {Cost functions, Estimation, Functions, Learning algorithms, Multiclass problems, Neural networks, Pattern recognition, Probability, Problem solving, Random processes, Stochastic gradient learning rule}, issn = {10459227}, doi = {10.1109/72.761724}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-0032643080\&partnerID=40\&md5=d528195bd6ec84531e59ddd2ececcd46}, author = {Jes{\'u}s Cid-Sueiro and J I Arribas and S Urban-Munoz and A R Figueiras-Vidal} } @conference {412, title = {Estimates of constrained multi-class a posteriori probabilities in time series problems with neural networks}, booktitle = {Proceedings of the International Joint Conference on Neural Networks}, year = {1999}, publisher = {IEEE, United States}, organization = {IEEE, United States}, address = {Washington, DC, USA}, abstract = {In time series problems, where time ordering is a crucial issue, the use of Partial Likelihood Estimation (PLE) represents a specially suitable method for the estimation of parameters in the model. We propose a new general supervised neural network algorithm, Joint Network and Data Density Estimation (JNDDE), that employs PLE to approximate conditional probability density functions for multi-class classification problems. The logistic regression analysis is generalized to multiple class problems with softmax regression neural network used to model the a-posteriori probabilities such that they are approximated by the network outputs. Constraints to the network architecture, as well as to the model of data, are imposed, resulting in both a flexible network architecture and distribution modeling. We consider application of JNDDE to channel equalization and present simulation results.

}, keywords = {Approximation theory, Computer simulation, Constraint theory, Data structures, Joint network-data density estimation (JNDDE), Mathematical models, Multi-class a posteriori probabilities, Neural networks, Partial likelihood estimation (PLE), Probability density function, Regression analysis}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-0033325263\&partnerID=40\&md5=8c6134020b0b2a9c5ab05b131c070b88}, author = {J I Arribas and Jes{\'u}s Cid-Sueiro and T Adali and H Ni and B Wang and A R Figueiras-Vidal} } @conference {411, title = {Neural architectures for parametric estimation of a posteriori probabilities by constrained conditional density functions}, booktitle = {Neural Networks for Signal Processing - Proceedings of the IEEE Workshop}, year = {1999}, publisher = {IEEE, Piscataway, NJ, United States}, organization = {IEEE, Piscataway, NJ, United States}, address = {Madison, WI, USA}, abstract = {A new approach to the estimation of {\textquoteright}a posteriori{\textquoteright} class probabilities using neural networks, the Joint Network and Data Density Estimation (JNDDE), is presented in this paper. It is based on the estimation of the conditional data density functions, with some restrictions imposed by the classifier structure; the Bayes{\textquoteright} rule is used to obtain the {\textquoteright}a posteriori{\textquoteright} probabilities from these densities. The proposed method is applied to three different network structures: the logistic perceptron (for the binary case), the softmax perceptron (for multi-class problems) and a generalized softmax perceptron (that can be used to map arbitrarily complex probability functions). Gaussian mixture models are used for the conditional densities. The method has the advantage of establishing a distinction between the network parameters and the model parameters. Complexity on any of them can be fixed as desired. Maximum Likelihood gradient-based rules for the estimation of the parameters can be obtained. It is shown that JNDDE exhibits a more robust convergence characteristics than other methods of a posteriori probability estimation, such as those based on the minimization of a Strict Sense Bayesian (SSB) cost function.

}, keywords = {Asymptotic stability, Constraint theory, Data structures, Gaussian mixture models, Joint network and data density estimation, Mathematical models, Maximum likelihood estimation, Neural networks, Probability}, doi = {https://doi.org/10.1109/NNSP.1999.788145}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-0033321049\&partnerID=40\&md5=7967fa377810cc0c3e6a4d9020024b80}, author = {J I Arribas and Jes{\'u}s Cid-Sueiro and T Adali and A R Figueiras-Vidal} } @conference {410, title = {Neural networks to estimate ML multi-class constrained conditional probability density functions}, booktitle = {Proceedings of the International Joint Conference on Neural Networks}, year = {1999}, publisher = {IEEE, United States}, organization = {IEEE, United States}, address = {Washington, DC, USA}, abstract = {In this paper, a new algorithm, the Joint Network and Data Density Estimation (JNDDE), is proposed to estimate the {\textquoteleft}a posteriori{\textquoteright} probabilities of the targets with neural networks in multiple classes problems. It is based on the estimation of conditional density functions for each class with some restrictions or constraints imposed by the classifier structure and the use Bayes rule to force the a posteriori probabilities at the output of the network, known here as a implicit set. The method is applied to train perceptrons by means of Gaussian mixture inputs, as a particular example for the Generalized Softmax Perceptron (GSP) network. The method has the advantage of providing a clear distinction between the network architecture and the model of the data constraints, giving network parameters or weights on one side and data over parameters on the other. MLE stochastic gradient based rules are obtained for JNDDE. This algorithm can be applied to hybrid labeled and unlabeled learning in a natural fashion.

}, keywords = {Generalized softmax perceptron (GSP) network, Joint network and data density estimation (JNDDE), Mathematical models, Maximum likelihood estimation, Neural networks, Probability density function, Random processes}, doi = {https://doi.org/10.1109/IJCNN.1999.831174}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-0033326060\&partnerID=40\&md5=bb38c144dac0872f3a467dc12170e6b6}, author = {J I Arribas and Jes{\'u}s Cid-Sueiro and T Adali and A R Figueiras-Vidal} }