Archetypal Analysis: Mining Weather and Climate Extremes

Conventional analysis methods in weather and climate science (e.g., EOF analysis) exhibit a number of drawbacks including scaling and mixing. These methods focus mostly on the bulk of the probability distribution of the system in state space and overlook its tail. This paper explores a different method, the archetypal analysis (AA), which focuses precisely on the extremes. AA seeks to approximate the convex hull of the data in state space by finding “corners” that represent “pure” types or archetypes through computing mixture weight matrices. The method is quite new in climate science, although it has been around for about two decades in pattern recognition. It encompasses, in particular, the virtues of EOFs and clustering. The method is presented along with a new manifold-based optimization algorithm that optimizes for the weights simultaneously, unlike the conventional multistep algorithm based on the alternating constrained least squares. The paper discusses the numerical solution and then applies it to the monthly sea surface temperature (SST) from HadISST and to the Asian summer monsoon (ASM) using sea level pressure (SLP) from ERA-40 over the Asian monsoon region. The application to SST reveals, in particular, three archetypes, namely, El Niño, La Niña, and a third pattern representing the western boundary currents. The latter archetype shows a particular trend in the last few decades. The application to the ASM SLP anomalies yields archetypes that are consistent with the ASM regimes found in the literature. Merits and weaknesses of the method along with possible future development are also discussed

Landmarks Augmentation with Manifold-Barycentric Oversampling

The training of Generative Adversarial Networks (GANs) requires a large amount of data, stimulating the development of new augmentation methods to alleviate the challenge. Oftentimes, these methods either fail to produce enough new data or expand the dataset beyond the original manifold. In this paper, we propose a new augmentation method that guarantees to keep the new data within the original data manifold thanks to the optimal transport theory. The proposed algorithm finds cliques in the nearest-neighbors graph and, at each sampling iteration, randomly draws one clique to compute the Wasserstein barycenter with random uniform weights. These barycenters then become the new natural-looking elements that one could add to the dataset. We apply this approach to the problem of landmarks detection and augment the available annotation in both unpaired and in semi-supervised scenarios. Additionally, the idea is validated on cardiac data for the task of medical segmentation. Our approach reduces the overfitting and improves the quality metrics beyond the original data outcome and beyond the result obtained with popular modern augmentation methods.Comment: 11 pages, 4 figures, 3 tables. I.B. and N.B. contributed equally. D.V.D. is the corresponding autho

A hybrid one-class approach for detecting anomalies in industrial systems

Financiado para publicación en aberto: Universidade da Coruña/CISUG[Abstract]: The significant advance of Internet of Things in industrial environments has provided the possibility of monitoring the different variables that come into play in an industrial process. This circumstance allows the supervision of the current state of an industrial plant and the consequent decision making possibilities. Then, the use of anomaly detection techniques are presented as a powerful tool to determine unexpected situations. The present research is based on the implementation of one-class classifiers to detect anomalies in two industrial systems. The proposal is validated using two real datasets registered during different operating points of two industrial plants. To ensure a better performance, a clustering process is developed prior the classifier implementation. Then, local classifiers are trained over each cluster, leading to successful results when they are tested with both real and artificial anomalies. Validation results present in all cases, AUC values above 90%.Xunta de Galicia. Consellería de Educación, Universidade e Formación Profesional; ED431G 2019/0

Representation Learning via Manifold Flattening and Reconstruction

This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening Networks (FlatNet), are theoretically interpretable, computationally feasible at scale, and generalize well to test data, a balance not typically found in manifold-based learning methods. We present empirical results and comparisons to other models on synthetic high-dimensional manifold data and 2D image data. Our code is publicly available.Comment: 44 pages, 19 figure

A Framework for Modeling the Growth and Development of Neurons and Networks

The development of neural tissue is a complex organizing process, in which it is difficult to grasp how the various localized interactions between dividing cells leads relentlessly to global network organization. Simulation is a useful tool for exploring such complex processes because it permits rigorous analysis of observed global behavior in terms of the mechanistic axioms declared in the simulated model. We describe a novel simulation tool, CX3D, for modeling the development of large realistic neural networks such as the neocortex, in a physical 3D space. In CX3D, as in biology, neurons arise by the replication and migration of precursors, which mature into cells able to extend axons and dendrites. Individual neurons are discretized into spherical (for the soma) and cylindrical (for neurites) elements that have appropriate mechanical properties. The growth functions of each neuron are encapsulated in set of pre-defined modules that are automatically distributed across its segments during growth. The extracellular space is also discretized, and allows for the diffusion of extracellular signaling molecules, as well as the physical interactions of the many developing neurons. We demonstrate the utility of CX3D by simulating three interesting developmental processes: neocortical lamination based on mechanical properties of tissues; a growth model of a neocortical pyramidal cell based on layer-specific guidance cues; and the formation of a neural network in vitro by employing neurite fasciculation. We also provide some examples in which previous models from the literature are re-implemented in CX3D. Our results suggest that CX3D is a powerful tool for understanding neural development

Multiobjective optimization of classifiers by means of 3-D convex hull based evolutionary algorithms

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The receiver operating characteristic (ROC) and detection error tradeoff(DET) curves are frequently used in the machine learning community to analyze the performance of binary classifiers. Recently, the convex-hull-based multiobjective genetic programming algorithm was proposed and successfully applied to maximize the convex hull area for binary classifi- cation problems by minimizing false positive rate and maximizing true positive rate at the same time using indicator-based evolutionary algorithms. The area under the ROC curve was used for the performance assessment and to guide the search. Here we extend this re- search and propose two major advancements: Firstly we formulate the algorithm in detec- tion error tradeoffspace, minimizing false positives and false negatives, with the advantage that misclassification cost tradeoffcan be assessed directly. Secondly, we add complexity as an objective function, which gives rise to a 3D objective space (as opposed to a 2D pre- vious ROC space). A domain specific performance indicator for 3D Pareto front approxima- tions, the volume above DET surface, is introduced, and used to guide the indicator-based evolutionary algorithm to find optimal approximation sets. We assess the performance of the new algorithm on designed theoretical problems with different geometries of Pareto fronts and DET surfaces, and two application-oriented benchmarks: (1) Designing spam filters with low numbers of false rejects, false accepts, and low computational cost us- ing rule ensembles, and (2) finding sparse neural networks for binary classification of test data from the UCI machine learning benchmark. The results show a high performance of the new algorithm as compared to conventional methods for multicriteria optimization

Interpretable Models Capable of Handling Systematic Missingness in Imbalanced Classes and Heterogeneous Datasets

Application of interpretable machine learning techniques on medical datasets facilitate early and fast diagnoses, along with getting deeper insight into the data. Furthermore, the transparency of these models increase trust among application domain experts. Medical datasets face common issues such as heterogeneous measurements, imbalanced classes with limited sample size, and missing data, which hinder the straightforward application of machine learning techniques. In this paper we present a family of prototype-based (PB) interpretable models which are capable of handling these issues. The models introduced in this contribution show comparable or superior performance to alternative techniques applicable in such situations. However, unlike ensemble based models, which have to compromise on easy interpretation, the PB models here do not. Moreover we propose a strategy of harnessing the power of ensembles while maintaining the intrinsic interpretability of the PB models, by averaging the model parameter manifolds. All the models were evaluated on a synthetic (publicly available dataset) in addition to detailed analyses of two real-world medical datasets (one publicly available). Results indicated that the models and strategies we introduced addressed the challenges of real-world medical data, while remaining computationally inexpensive and transparent, as well as similar or superior in performance compared to their alternatives