Possibilistic KNN regression using tolerance intervals

International audienceBy employing regression methods minimizing predictive risk, we are usually looking for precise values which tends to their true response value. However, in some situations, it may be more reasonable to predict intervals rather than precise values. In this paper, we focus to find such intervals for the K-nearest neighbors (KNN) method with precise values for inputs and output. In KNN, the prediction intervals are usually built by considering the local probability distribution of the neighborhood. In situations where we do not dispose of enough data in the neighborhood to obtain statistically significant distributions, we would rather wish to build intervals which takes into account such distribution uncertainties. For this latter we suggest to use tolerance intervals to build the maximal specific possibility distribution that bounds each population quantiles of the true distribution (with a fixed confidence level) that might have generated our sample set. Next we propose a new interval regression method based on KNN which take advantage of our possibility distribution in order to choose, for each instance, the value of K which will be a good trade-off between precision and uncertainty due to the limited sample size. Finally we apply our method on an aircraft trajectory prediction problem

Non-parametric high confidence interval prediction: application to aircraft trajectory prediction

Air traffic in Europe represents about 30,000 flights each day and forecasts from Eurocontrol predict a growth of 70% by 2020 (50,000 flights per day). The airspace, made up of numerous control sectors, will soon be saturated given the current planification and control methods. In order to make the system able to cope with the predicted traffic growth, the air traffic controllers workload has to be reduced by automated systems that help them handle the aircraft separation task. Based on the traffic demand by airlines, this study proposes a new planning method for 4D trajectories that provides conflict-free traffic to the controller. This planning method consists of two successive steps, each handling a unique flight parameter : a flight level allocation phase followed by a ground holding scheme.We present constraint programming models and an evolutionary algorithm to solve these large scale combinatorial optimization problems, as well as techniques for improving the robustness of the model by handling uncertainties of takeoff times and trajectory prediction. Simulations carried out over the French airspace successfully solved all conflicts, with a mean of one minute allocated delay (80 to 90 minutes for the most delayed flight) and a discrepancy from optimal altitude of one flight level for most of the flights. Handling uncertainties with a static method leads to a dramatic increase in the cost of the previous non-robust solutions. However, we propose a dynamic model to deal with this matter, based on a sliding time horizon, which is likely to be able to cope with a few minutes of uncertainty with reasonable impact on the cost of the solutions

Statistical prediction of aircraft trajectory : regression methods vs point-mass model

International audienceGround-based aircraft trajectory prediction is a critical issue for air traffic management. A safe and efficient prediction is a prerequisite for the implementation of automated tools that detect and solve conflicts between trajectories. Moreover, regarding the safety constraints, it could be more reasonable to predict intervals rather than precise aircraft positions . In this paper, a standard point-mass model and statistical regression method is used to predict the altitude of climbing aircraft. In addition to the standard linear regression model, two common non-linear regression methods, neural networks and Loess are used. A dataset is extracted from two months of radar and meteorological recordings, and several potential explanatory variables are computed for every sampled climb segment. A Principal Component Analysis allows us to reduce the dimensionality of the problems, using only a subset of principal components as input to the regression methods. The prediction models are scored by performing a 10-fold cross-validation. Statistical regression results method appears promising. The experiment part shows that the proposed regression models are much more efficient than the standard point-mass model. The prediction intervals obtained by our methods have the advantage of being more reliable and narrower than those found by point-mass model

Naive possibilistic classifiers for imprecise or uncertain numerical data

International audienceIn real-world problems, input data may be pervaded with uncertainty. In this paper, we investigate the behavior of naive possibilistic classifiers, as a counterpart to naive Bayesian ones, for dealing with classification tasks in the presence of uncertainty. For this purpose, we extend possibilistic classifiers, which have been recently adapted to numerical data, in order to cope with uncertainty in data representation. Here the possibility distributions that are used are supposed to encode the family of Gaussian probabilistic distributions that are compatible with the considered dataset. We consider two types of uncertainty: (i) the uncertainty associated with the class in the training set, which is modeled by a possibility distribution over class labels, and (ii) the imprecision pervading attribute values in the testing set represented under the form of intervals for continuous data. Moreover, the approach takes into account the uncertainty about the estimation of the Gaussian distribution parameters due to the limited amount of data available. We first adapt the possibilistic classification model, previously proposed for the certain case, in order to accommodate the uncertainty about class labels. Then, we propose an algorithm based on the extension principle to deal with imprecise attribute values. The experiments reported show the interest of possibilistic classifiers for handling uncertainty in data. In particular, the probability-to-possibility transform-based classifier shows a robust behavior when dealing with imperfect data

An Integrated Fuzzy Inference Based Monitoring, Diagnostic, and Prognostic System

To date the majority of the research related to the development and application of monitoring, diagnostic, and prognostic systems has been exclusive in the sense that only one of the three areas is the focus of the work. While previous research progresses each of the respective fields, the end result is a variable grab bag of techniques that address each problem independently. Also, the new field of prognostics is lacking in the sense that few methods have been proposed that produce estimates of the remaining useful life (RUL) of a device or can be realistically applied to real-world systems. This work addresses both problems by developing the nonparametric fuzzy inference system (NFIS) which is adapted for monitoring, diagnosis, and prognosis and then proposing the path classification and estimation (PACE) model that can be used to predict the RUL of a device that does or does not have a well defined failure threshold. To test and evaluate the proposed methods, they were applied to detect, diagnose, and prognose faults and failures in the hydraulic steering system of a deep oil exploration drill. The monitoring system implementing an NFIS predictor and sequential probability ratio test (SPRT) detector produced comparable detection rates to a monitoring system implementing an autoassociative kernel regression (AAKR) predictor and SPRT detector, specifically 80% vs. 85% for the NFIS and AAKR monitor respectively. It was also found that the NFIS monitor produced fewer false alarms. Next, the monitoring system outputs were used to generate symptom patterns for k-nearest neighbor (kNN) and NFIS classifiers that were trained to diagnose different fault classes. The NFIS diagnoser was shown to significantly outperform the kNN diagnoser, with overall accuracies of 96% vs. 89% respectively. Finally, the PACE implementing the NFIS was used to predict the RUL for different failure modes. The errors of the RUL estimates produced by the PACE-NFIS prognosers ranged from 1.2-11.4 hours with 95% confidence intervals (CI) from 0.67-32.02 hours, which are significantly better than the population based prognoser estimates with errors of ~45 hours and 95% CIs of ~162 hours

Partner selection in sustainable supply chains: a fuzzy ensemble learning model

With the increasing demands on businesses to operate more sustainably, firms must ensure that the performance of their whole supply chain in sustainability is optimized. As partner selection is critical to supply chain management, focal firms now need to select supply chain partners that can offer a high level of competence in sustainability. This paper proposes a novel multi-partner classification model for the partner qualification and classification process, combining ensemble learning technology and fuzzy set theory. The proposed model enables potential partners to be classified into one of four categories (strategic partner, preference partner, leverage partner and routine partner), thereby allowing distinctive partner management strategies to be applied for each category. The model provides for the simultaneous optimization of both efficiency in its use of multi-partner and multi-dimension evaluation data, and effectiveness in dealing with the vagueness and uncertainty of linguistic commentary data. Compared to more conventional methods, the proposed model has the advantage of offering a simple classification and a stable prediction performance. The practical efficacy of the model is illustrated by an application in a listed electronic equipment and instrument manufacturing company based in southeastern China

Evolving fuzzy and neuro-fuzzy approaches in clustering, regression, identification, and classification: A Survey

Major assumptions in computational intelligence and machine learning consist of the availability of a historical dataset for model development, and that the resulting model will, to some extent, handle similar instances during its online operation. However, in many real world applications, these assumptions may not hold as the amount of previously available data may be insufficient to represent the underlying system, and the environment and the system may change over time. As the amount of data increases, it is no longer feasible to process data efficiently using iterative algorithms, which typically require multiple passes over the same portions of data. Evolving modeling from data streams has emerged as a framework to address these issues properly by self-adaptation, single-pass learning steps and evolution as well as contraction of model components on demand and on the fly. This survey focuses on evolving fuzzy rule-based models and neuro-fuzzy networks for clustering, classification and regression and system identification in online, real-time environments where learning and model development should be performed incrementally. (C) 2019 Published by Elsevier Inc.Igor Škrjanc, Jose Antonio Iglesias and Araceli Sanchis would like to thank to the Chair of Excellence of Universidad Carlos III de Madrid, and the Bank of Santander Program for their support. Igor Škrjanc is grateful to Slovenian Research Agency with the research program P2-0219, Modeling, simulation and control. Daniel Leite acknowledges the Minas Gerais Foundation for Research and Development (FAPEMIG), process APQ-03384-18. Igor Škrjanc and Edwin Lughofer acknowledges the support by the ”LCM — K2 Center for Symbiotic Mechatronics” within the framework of the Austrian COMET-K2 program. Fernando Gomide is grateful to the Brazilian National Council for Scientific and Technological Development (CNPq) for grant 305906/2014-3

An Analysis of Muon Neutrino Disappearance from the NuMI Beam Using an Optimal Track Fitter

Thesis (Ph.D.) - Indiana University, Physics, 2015The NOvA experiment is a long-baseline neutrino oscillation experiment based out of Fermilab National Accelerator Laboratory that uses two liquid scintillator detectors, one at Fermilab (the "near" detector) and a second 14 kton detector in northern Minnesota (the "far" detector.) The primary physics goals of the NOvA experiment are to measure neutrino mixing parameters through both the $\nu_{\mu}$ disappearance and $\nu_{e}$ appearance channels using neutrinos from the newly upgraded NuMI beam line. The NOvA $\nu_{\mu}$ disappearance analysis can significantly improve the world's best measurement of $\sin^{2}\theta_{23}$. This analysis proceeds by using the measured $\nu_{\mu}$ charged-current energy spectrum in the near detector to predict the spectrum in the far detector, and comparing this to the measured spectrum to obtain a best fit for the oscillation parameters $\sin^{2}\theta_{23}$ and $\Delta m^{2}_{32}$. Since this fit is governed by the shape of the energy spectrum, the best fit will be maximized by obtaining the best possible energy resolution for the individual neutrino events. This dissertation describes an alternate $\nu_{\mu}$ disappearance analysis technique for the NOvA experiment, based on the idea that estimating the energy resolution of the individual events will allow them to be separated into different energy resolution samples in order to improve the final fit. This involves using an optimal tracker to reconstruct particle tracks and momenta, and multivariate methods for estimating the event energies and energy resolutions. The data used for this analysis was taken by the NOvA experiment from February 2014 to May 2015, representing approximately $3.52 \times 10^{20}$ protons on target from the NuMI beam. The best fit oscillation parameters obtained by this alternate technique are $|\Delta m^{2}_{32}| = 2.49^{+0.19}_{-0.17}$~$[\times 10^{-3} {\rm eV}^{2}]$ and $\sin^{2} \theta_{23} =$~$0.51 \pm 0.08$ which is consistent with the hypothesis of maximal mixing, and with the results from T2K and MINOS+ published in 2015

Optimization Models Using Fuzzy Sets and Possibility Theory

Optimization is of central concern to a number of disciplines. Operations Research and Decision Theory are often considered to be identical with optimization. But also in other areas such as engineering design, regional policy, logistics and many others, the search for optimal solutions is one of the prime goals. The methods and models which have been used over the last decades in these areas have primarily been "hard" or "crisp", i.e. the solutions were considered to be either feasible or unfeasible, either above a certain aspiration level or below. This dichotomous structure of methods very often forced the modeler to approximate real problem situations of the more-or-less type by yes-or-no-type models, the solutions of which might turn out not to be the solutions to the real problems. This is particularly true if the problem under consideration includes vaguely defined relationships, human evaluations, uncertainty due to inconsistent or incomplete evidence, if natural language has to be modeled or if state variables can only be described approximately. Until recently, everything which was not known with certainty, i.e. which was not known to be either true or false or which was not known to either happen with certainty or to be impossible to occur, was modeled by means of probabilities. This holds in particular for uncertainties concerning the occurrence of events. probability theory was used irrespective of whether its axioms (such as, for instance, the law of large numbers) were satisfied or not, or whether the "events" could really be described unequivocally and crisply. In the meantime one has become aware of the fact that uncertainties concerning the occurrence as well as concerning the description of events ought to be modeled in a much more differentiated way. New concepts and theories have been developed to do this: the theory of evidence, possibility theory, the theory of fuzzy sets have been advanced to a stage of remarkable maturity and have already been applied successfully in numerous cases and in many areas. Unluckily, the progress in these areas has been so fast in the last years that it has not been documented in a way which makes these results easily accessible and understandable for newcomers to these areas: text-books have not been able to keep up with the speed of new developments; edited volumes have been published which are very useful for specialists in these areas, but which are of very little use to nonspecialists because they assume too much of a background in fuzzy set theory. To a certain degree the same is true for the existing professional journals in the area of fuzzy set theory. Altogether this volume is a very important and appreciable contribution to the literature on fuzzy set theory

Automatic signal and image-based assessments of spinal cord injury and treatments.

Spinal cord injury (SCI) is one of the most common sources of motor disabilities in humans that often deeply impact the quality of life in individuals with severe and chronic SCI. In this dissertation, we have developed advanced engineering tools to address three distinct problems that researchers, clinicians and patients are facing in SCI research. Particularly, we have proposed a fully automated stochastic framework to quantify the effects of SCI on muscle size and adipose tissue distribution in skeletal muscles by volumetric segmentation of 3-D MRI scans in individuals with chronic SCI as well as non-disabled individuals. We also developed a novel framework for robust and automatic activation detection, feature extraction and visualization of the spinal cord epidural stimulation (scES) effects across a high number of scES parameters to build individualized-maps of muscle recruitment patterns of scES. Finally, in the last part of this dissertation, we introduced an EMG time-frequency analysis framework that implements EMG spectral analysis and machine learning tools to characterize EMG patterns resulting in independent or assisted standing enabled by scES, and identify the stimulation parameters that promote muscle activation patterns more effective for standing. The neurotechnological advancements proposed in this dissertation have greatly benefited SCI research by accelerating the efforts to quantify the effects of SCI on muscle size and functionality, expanding the knowledge regarding the neurophysiological mechanisms involved in re-enabling motor function with epidural stimulation and the selection of stimulation parameters and helping the patients with complete paralysis to achieve faster motor recovery