Nonlinear Decision Functions Research Articles

Maritime risk assessment using a non-linear spatial multi-criteria decision method: A case study in the Bohai Sea and Yellow Sea, China

The risk caused by different environmental factors in the navigation of ships is not uniform. The univariant (e.g., sea fog), covariant (e.g., wind and waves), and spatially restricted (e.g., offshore distance) risk factors present a complex non-linearity impact on the navigation of ships. This means that a comprehensive evaluation of the environmental risk for navigation should consider the risk characteristics of different factors. In this paper, a non-linear spatial multi-criteria decision (SMCD) method-based evaluation framework was developed to evaluate the potential environmental risk of navigating ships. (1) Non-linear weight adjustment and risk decision functions were proposed to spatially evaluate the comprehensive risk and avoid diluting the critical impact of high-risk factors. (2) The double thresholds standardization approach was developed to construct the risk association between different tonnage ships and environmental factors. (3) The developed methods were used in the Bohai and Yellow Seas as a case study to verify the validity and practicability. The quantitative analysis, historical accident matching (82% accident matching rate), and a real accident case proved the validity of the developed model.

Making sense of kernel spaces in neural learning

Kernel-based and Deep Learning methods are two of the most popular approaches in Computational Natural Language Learning. Although these models are rather different and characterized by distinct strong and weak aspects, they both had impressive impact on the accuracy of complex Natural Language Processing tasks. An advantage of kernel-based methods is their capability of exploiting structured information induced from examples. For instance, Sequence or Tree kernels operate over structures reflecting linguistic evidence, such as syntactic information encoded in syntactic parse trees. Deep Learning approaches are very effective as they can learn non-linear decision functions: however, general models require input instances to be explicitly modeled via vectors or tensors, and operating on structured data is made possible only by using ad-hoc architectures.In this work, we discuss a novel architecture that efficiently combines kernel methods and neural networks, in the attempt at squeezing the best from the two paradigms. The so-called Kernel-based Deep Architecture (KDA) adopts a Nyström-based projection function to approximate any valid kernel function and convert any structure they operate on (for instance, linguistic structures, such as trees) into dense linear embeddings. These can be used as input of a Deep Feed-forward Neural Network that exploits such embeddings to learn non-linear classification functions. KDA is a mathematically justified integration of expressive kernel functions and deep neural architectures, with several advantages: it (i) directly operates over complex non-tensor structures, e.g., trees, without ad hoc manual feature engineering or architectural design, (ii) achieves a drastic reduction of the computational cost w.r.t. pure kernel methods, and (iii) exploits the non-linearity of Deep Architectures to produce accurate models. We experimented the KDA in three rather different semantic inference tasks: Semantic Parsing, Question Classification, and Community Question Answering. Results show that the KDA achieves state-of-the-art accuracy, with a computational cost that is much lower than the one necessary to train and test a pure kernel-based method, such as the SVM algorithm.

Deep Convolutional Neural Network for Flood Extent Mapping Using Unmanned Aerial Vehicles Data.

Flooding is one of the leading threats of natural disasters to human life and property, especially in densely populated urban areas. Rapid and precise extraction of the flooded areas is key to supporting emergency-response planning and providing damage assessment in both spatial and temporal measurements. Unmanned Aerial Vehicles (UAV) technology has recently been recognized as an efficient photogrammetry data acquisition platform to quickly deliver high-resolution imagery because of its cost-effectiveness, ability to fly at lower altitudes, and ability to enter a hazardous area. Different image classification methods including SVM (Support Vector Machine) have been used for flood extent mapping. In recent years, there has been a significant improvement in remote sensing image classification using Convolutional Neural Networks (CNNs). CNNs have demonstrated excellent performance on various tasks including image classification, feature extraction, and segmentation. CNNs can learn features automatically from large datasets through the organization of multi-layers of neurons and have the ability to implement nonlinear decision functions. This study investigates the potential of CNN approaches to extract flooded areas from UAV imagery. A VGG-based fully convolutional network (FCN-16s) was used in this research. The model was fine-tuned and a k-fold cross-validation was applied to estimate the performance of the model on the new UAV imagery dataset. This approach allowed FCN-16s to be trained on the datasets that contained only one hundred training samples, and resulted in a highly accurate classification. Confusion matrix was calculated to estimate the accuracy of the proposed method. The image segmentation results obtained from FCN-16s were compared from the results obtained from FCN-8s, FCN-32s and SVMs. Experimental results showed that the FCNs could extract flooded areas precisely from UAV images compared to the traditional classifiers such as SVMs. The classification accuracy achieved by FCN-16s, FCN-8s, FCN-32s, and SVM for the water class was 97.52%, 97.8%, 94.20% and 89%, respectively.

Prediction on Combat Effectiveness of Amphibious Assault Vehicles Based on Supporting-Vector Regression

In this paper, a predictive model has been established for the combat effectiveness of amphibious assault vehicles by the method of supporting-vector regression. It has a good fitting result after trained with the samples. Then this model is used to predict the combat effectiveness of the sample under evaluation. The SVR approach can convert the practical questions into the high-dimensional feature space through non-linear transfer, and construct the linear decision functions in the space to realize the original non-linear decision functions. This approach has its significance for the prediction of combat effectiveness of AAVs.

Statistical Machine Learning and Dissolved Gas Analysis: A Review

Dissolved gas analysis (DGA) of the insulation oil of power transformers is an investigative tool to monitor their health and to detect impending failures by recognizing anomalous patterns of DGA concentrations. We handle the failure prediction problem as a simple data-mining task on DGA samples, optionally exploiting the transformer's age, nominal power and voltage, and consider two approaches: 1) binary classification and 2) regression of the time to failure. We propose a simple logarithmic transform to preprocess DGA data in order to deal with long-tail distributions of concentrations. We have reviewed and evaluated 15 standard statistical machine-learning algorithms on that task, and reported quantitative results on a small but published set of power transformers and on proprietary data from thousands of network transformers of a utility company. Our results confirm that nonlinear decision functions, such as neural networks, support vector machines with Gaussian kernels, or local linear regression can theoretically provide slightly better performance than linear classifiers or regressors. Software and part of the data are available at http://www.mirowski.info/pub/dga.

Design of Robust Approach for Failure Detection in Dynamic Control Systems

This paper presents a robust instrument fault detection (IFD) scheme based on modified immune mechanism based evolutionary algorithm (MIMEA) that determines on line the optimal control actions, detects faults quickly in the control process, and reconfigures the controller structure. To ensure the capability of the proposed MIMEA, repeating cycles of crossover, mutation, and clonally selection are included through the sampling time. This increases the ability of the proposed algorithm to reach the global optimum performance and optimize the controller parameters through a few generations. A fault diagnosis logic system is created based on the proposed algorithm, nonlinear decision functions, and its derivatives with respect to time. Threshold limits are implied to improve the system dynamics and sensitivity of the IFD scheme to the faults. The proposed algorithm is able to reconfigure the control law safely in all the situations. The presented false alarm rates are also clearly indicated. To illustrate the performance of the proposed MIMEA, it is applied successfully to tune and optimize the controller parameters of the nonlinear nuclear power reactor such that a robust behavior is obtained. Simulation results show the effectiveness of the proposed IFD scheme based MIMEA in detecting and isolating the dynamic system faults.

Seizure Detection: An Assessment of Time- and Frequency-Based Features in a Unified Two-Dimensional Decisional Space Using Nonlinear Decision Functions

This study proposes a new approach for offline seizure detection in intracranial (subdural) electroencephalogram recordings using nonlinear decision functions. It implements well-established features that are designed to deal with complex signals, such as brain recordings, and proposes a two-dimensional (2D) domain of analysis that overcomes the dilemma faced with the selection of empirical thresholds often used to delineate epileptic events. This unifying approach makes it possible for researchers in epilepsy to establish other performance evaluation criteria on the basis of the proposed nonlinear decision functions as well as introduce additional dimensions toward multidimensional analysis because the mathematics of these decision functions allows for any number of dimensions and any degree of complexity. Furthermore, because the features considered assume both time and frequency domains, the analysis is performed both temporally and as a function of different frequency ranges to ascertain those measures that are most suitable for seizure detection. In retrospect, by using nonlinear decision functions and by establishing a unified 2D domain of analysis, this study establishes a generalized approach to seizure detection that works across several features and across patients. Clinical experiments involved 14 patients with intractable seizures that were evaluated for potential surgical interventions. Of the total 157 files considered, 35 (21 interictal and 14 ictal) intracranial electroencephalogram data files or 22% were used initially in a training phase to ascertain the reliability of the formulated features that were implemented in the seizure detection process. The remaining 122 intracranial electroencephalogram data files or 78% were then used in the testing phase to assess the merits of each feature considered as means to detect a seizure. The testing phase using the remaining 122 intracranial electroencephalogram data files revealed that the gamma power in the frequency domain is the feature that performed best across all patients with a sensitivity of 96.296%, an accuracy of 96.721%, and a specificity of 96.842%. The second best feature in the time domain was the mobility with a sensitivity of 81.481% an accuracy of 90.169%, and a specificity of 92.632%. In the frequency domain, all of the five other spectral bands lesser than 36 Hz revealed mixed results in terms of low sensitivity in some frequency bands and low accuracy in other frequency bands, which is expected given that the dominant frequencies during an ictal state are those higher than 30 Hz. In the time domain, other features, including complexity and correlation sum, revealed mixed success. All the features that are based on the time domain performed well, with mobility being the optimal feature for seizure detection. In the frequency domain, the gamma power outperformed the other frequency bands. Within this 2D plane, the best results were also observed when the degree of complexity is 3 or 4 in the implementation of the proposed nonlinear decision functions. : A singular contribution of this study is in creating a common 2D space for analysis through the use of nonlinear decision functions for delineating data clusters of ictal files from data clusters of interictal files. This is critically important in establishing unifying measures that work across different features as expressed by the weight vector of the decision functions for a standardized assessment. The mathematical foundation is consequently established in support of a generalized seizure detection algorithm that works across patients, and in which all type of features that have been amply tested in the literature could be assessed within the realm of nonlinear decision functions.

A Comparative Study of Intracranial EEG Files Using Nonlinear Classification Methods

This study is a comparative evaluation of nonlinear classification methods with a focus on nonlinear decision functions and the standard method of support vector machines for seizure detection. These nonlinear classification methods are used on key features that were extracted on subdural EEG data after a thorough evaluation of all the frequency bands from 1 to 44 Hz. The sensitivity, specificity, and accuracy of seizure detection reveal that the gamma frequencies (36-44 Hz) are most suitable for detecting seizure files using a unique 2D decisional plane. We evaluated 157 intracranial EEG files from 14 patients by calculating the spectral power using nonoverlapping 1-s windows on different frequency bands. A key finding is in establishing a 2D decision plane, where duration of the seizure is used as the first dimension (x coordinate) and the maximum of the gamma frequency components is used as the second dimension (y coordinate). Within this 2D plane, the best results were observed when the nonlinearity degree is three for the proposed nonlinear decision functions, with a sensitivity of 96.3%, a specificity of 96.8%, and accuracy of 96.7%.

Classification of electroencephalographic seizure recordings into ictal and interictal files using correlation sum

This study provides a performance evaluation of the correlation sum in terms of accuracy, sensitivity, and specificity in its ability to classify seizure files from non-seizure files. The main thrust of the study is whether computable properties (“metrics”) of EEG tracings over time allow a seizure to be detected. This study evaluates raw intracranial EEG (iEEG) recordings with the intent to detect a seizure and classify different EEG epoch files. One hundred twenty-six iEEG files from eleven sequential patients are processed and the correlation sum is extracted from non-overlapping scrolling windows of 1-s duration. The novelty of this research is in defining a generalized nonlinear approach to classify EEG seizure segments by introducing nonlinear decision functions with the flexibility in choosing any degree of complexity and with any number of dimensions, lending resiliency to data overlap and opportunity for multidimensional data analysis. A singular contribution of this work is in determining a 2-D decision plane, in this case, where duration is one dimension and window-based minima of the correlation sum is the second dimension. Also, experimental observations clearly indicate that a significant drop in the magnitude of the correlation sum signal actually coincides with the clinical seizure onset more so than the electrographic seizure onset as provided by the medical experts. The method with k-fold cross validation performed with an accuracy of 91.84%, sensitivity of 92.31%, and specificity of 91.67%, which makes this classification method most suitable for offline seizure detection applications.

Optimum feature selection for decision functions

AbstractFeature selection is one of the most important processes in the design of pattern classifiers. This paper presents an optimum feature selection method which is applicable to arbitrary (nonlinear) decision functions. It is assumed that a finite number of training samples (training set) is given for each pattern class, and the decision function is designed based on the training sets. The training sets are edited by removing the samples which are classified incorrectly by the decision function. Then the feature selection problem is transformed to a modified zero‐one integer program. In this method, under a chosen permissible error, a minimum feature subset can be found which is combinationally optimum. Numerical examples of feature selection for a linear and a quadratic decision function are presented.

Optimal Transient Removal in a Power System

After a transient disturbance in a power system, some of the generators will have advanced in phase and some will have been retarded in phase. The deviation from steady-state operation can be removed in minimum time by optimal nonlinear bang-bang control. For each generator whose phase has advanced, the optimal control consists of exciting the field with maximum voltage, followed by a period of reversed voltage on the generator field, a period of maximum positive voltage on the generator field, and then a return to normal excitation. This sequence is controlled by nonlinear decision functions which obtain their information from the state of the system. The most desirable state variables are shaft angle, shaft velocity, and field current. Experimental tests have shown significant increases in transient stability [1]-[3].