Mahalanobis Kernel Research Articles

Rotating machinery health state assessment under multi-working conditions based on a deep fuzzy clustering network

Rotating machinery, as an important transmission component, works in complex and variable environments. Therefore, the health state assessment of rotating machinery under multi-working conditions is a challenging task to improve the safety of mechanical equipment. To achieve accurate health state assessment of rotating machinery, a fault assessment method based on deep fuzzy clustering networks (DFCNN) is proposed. The proposed novel DFCNN model combines the supervised feature extraction layer of the Generalized Supervised Deep Autoencoder (GSDAE) with an improved kernel Mahalanobis distance fuzzy C-means algorithm (KMDFCM). Specifically, the gearbox and rolling bearing vibration signal are input into DFCNN, GSDAE is used to eliminate the difference of feature changes caused by the change of working conditions, and then the KMDFCM in DFCNN is used to evaluate the health status of rotating machinery. The vibration signal tests on a planetary gearbox test bench and a full-life bearing test bench validated the effectiveness of the proposed method for evaluating the severity of faults.

Impacts of small-scale irrigation on farmers' livelihood: Evidence from the drought prone areas of upper Awash sub-basin, Ethiopia

Irrigation is an important mechanism to mitigate risks associated with the variability in rainfall for the smallholder subsistence farming system. This study analyzed how practicing small-scale irrigation (SSI) impacts the key livelihood assets on farm households' human, physical, natural, financial, and social capitals in Ethiopia's upper Awash sub-basin. The household-level survey data, collected from the 396 sample households, was used to carry out the current study. A Propensity Score Matching (PSM) analytical model was applied to match the SSI user and non-user groups. The difference between the five capital assets of livelihood was estimated using the PSM's Nearest Neighbor, Radius, Kernel Mahalanobis, and Stratification matching criteria. The results indicated that farmers' participation in SSI has enhanced the capital assets of the farm households. Compared to the non-users, the irrigation users were better off in the number variety of food consumed (0.28 ± 0.13 Standard Error [SE]), types of crops produced (0.60 ± 0.17 SE), expenditures on land renting, and agricultural inputs (3118 ± 877 SE) measured in Ethiopian Birr (ETB), as well as on-farm (9024 ± 2267 SE ETB) and non-farm (3766 ± 1466 SE ETB) incomes. Challenges such as the involvement of local brokers in the market value chain and the absence of farmers' marketing cooperatives have reduced the benefit of irrigated agriculture. Hence, the expansion of SSI schemes for the non-user farmers should consider improving the water usage mechanism and productivity, establishing proper water allocation institutions between up and down streams and limiting the role of brokers in the irrigation product marketing chain be future policy directions.

Computing committors in collective variables via Mahalanobis diffusion maps

The study of rare events in molecular and atomic systems such as conformal changes and cluster rearrangements has been one of the most important research themes in chemical physics. Key challenges are associated with long waiting times rendering molecular simulations inefficient, high dimensionality impeding the use of PDE-based approaches, and the complexity or breadth of transition processes limiting the predictive power of asymptotic methods. Diffusion maps are promising algorithms to avoid or mitigate all these issues. We adapt the diffusion map with Mahalanobis kernel proposed by Singer and Coifman (2008) for the SDE describing molecular dynamics in collective variables in which the diffusion matrix is position-dependent and, unlike the case considered by Singer and Coifman, is not associated with a diffeomorphism. We offer an elementary proof showing that one can approximate the generator for this SDE discretized to a point cloud via the Mahalanobis diffusion map. We use it to calculate the committor functions in collective variables for two benchmark systems: alanine dipeptide, and Lennard-Jones-7 in 2D. For validating our committor results, we compare our committor functions to the finite-difference solution or by conducting a “committor analysis” as used by molecular dynamics practitioners. We contrast the outputs of the Mahalanobis diffusion map with those of the standard diffusion map with isotropic kernel and show that the former gives significantly more accurate estimates for the committors than the latter.

Fault diagnosis of complex hydraulic system based on fast Mahalanobis classification system with high-dimensional imbalanced data

Due to the complexity of hydraulic systems, the data generated is prone to be high-dimensional and imbalanced, posing a challenge for fault diagnosis. This paper proposes a fast Mahalanobis classification system (FMCS). At the dimensionality reduction stage, smymetrical uncertainty and Mahalanobis kernel principal component analysis are used to construct a two-stage fast dimensionality reduction method. At the weight distribution stage, Mahalanobis distance is used to measure the similarity between the main feature and other features to determine the feature weights. At the fault diagnosis stage, Mahalanobis-Taguchi system is improved in threshold determination by atom search optimization to achieve fault diagnosis. Experiments show that FMCS has better classification performance (accuracy = 0.92, F1 = 0.94, G-mean = 0.91) and shorter computing time (4.9045 s) compared with 24 baseline algorithms. FMCS promotes the development of intelligent fault diagnosis for complex hydraulic systems.

Modified t-Distribution Stochastic Neighbor Embedding Using Augmented Kernel Mahalanobis-Distance for Dynamic Multimode Chemical Process Monitoring

The traditional data-driven process monitoring methods may not be applicable for the system which has dynamic and multimode characteristics. In this paper, a novel scheme named modified t-distribution stochastic neighbor embedding using augmented Mahalanobis-distance for dynamic multimode chemical process monitoring (AKMD-t-SNE) is proposed to realize dynamic multimodal process monitoring. First, the augmented matrix strategy is utilized to ensure the sample contains the autocorrelation of the process. Moreover, AKMD-t-SNE method eliminates the scale and spatial distribution differences among multiple modes by calculating the kernel Mahalanobis distance between the samples to establish the global model. The features extracted via the proposed method are obviously non-Gaussian, and there will be a deviation in the construction of traditional statistics. Then, the support vector data description (SVDD) method is used to construct statistics to deal with this problem. In addition, a hybrid correlation coefficient method (HCC) is proposed to achieve fault isolation and improve the accuracy of isolation results. The advantages of the proposed scheme are illustrated by a numerical case and the Multimode Tennessee Eastman Process (MTEP) benchmark.

Computing committors via Mahalanobis diffusion maps with enhanced sampling data.

The study of phenomena such as protein folding and conformational changes in molecules is a central theme in chemical physics. Molecular dynamics (MD) simulation is the primary tool for the study of transition processes in biomolecules, but it is hampered by a huge timescale gap between the processes of interest and atomic vibrations that dictate the time step size. Therefore, it is imperative to combine MD simulations with other techniques in order to quantify the transition processes taking place on large timescales. In this work, the diffusion map with Mahalanobis kernel, a meshless approach for approximating the Backward Kolmogorov Operator (BKO) in collective variables, is upgraded to incorporate standard enhanced sampling techniques, such as metadynamics. The resulting algorithm, which we call the target measure Mahalanobis diffusion map (tm-mmap), is suitable for a moderate number of collective variables in which one can approximate the diffusion tensor and free energy. Imposing appropriate boundary conditions allows use of the approximated BKO to solve for the committor function and utilization of transition path theory to find the reactive current delineating the transition channels and the transition rate. The proposed algorithm, tm-mmap, is tested on the two-dimensional Moro-Cardin two-well system with position-dependent diffusion coefficient and on alanine dipeptide in two collective variables where the committor, the reactive current, and the transition rate are compared to those computed by the finite element method (FEM). Finally, tm-mmap is applied to alanine dipeptide in four collective variables where the use of finite elements is infeasible.

Interval Prediction of Photovoltaic Power Using Improved NARX Network and Density Peak Clustering Based on Kernel Mahalanobis Distance

Photovoltaic (PV) power forecasting can provide strong support for the safe operation of the power system. Existing forecasting methods are ineffective for grid scheduling decisions or risk analysis. The novel multicluster interval prediction method is proposed to consider the volatility and randomness of PV power output. First, this method utilizes the sparse autoencoder (SAE) and Bayesian regularized NARX network (BRNARX) for point forecasting of PV power. Second, density peak clustering improved by kernel Mahalanobis distance (KMDDPC) is applied to classify the dataset into multiple clusters, including forecasting error and meteorological factors. Finally, the joint probability density is established by multivariate kernel density estimation (MKDE) to accomplish the PV power interval prediction. The proposed hybrid method is applied for the interval prediction of PV power at Yulara, Australia. Comparative research of point forecasting is implemented to evaluate the machine learning and deep learning methods, with the proposed SAE‐BRNARX under four different periods. Results shows that the average values of nRMSE, MRE, nMAE, and R2 for the four periods are 4.45%, 0.90%, −0.15%, 3.39%, and 95.93%, respectively. Moreover, the results of interval prediction obtained by the other interval prediction approaches are compared with the proposed KMDDPC‐MKDE. It shows that the average values of PICP, PINAW, ACE, and nMPICD for four periods are 93.93%, 9.50%, 3.93%, and 7.10% at 90% confidence level, respectively. Outcomes demonstrate that the proposed method can obtain more accuracy, a higher coverage rate, narrower average bandwidth, and a closer distance between the middle of interval and actual value than other methods.

Data-driven Transient Stability Assessment Model Considering Network Topology Changes via Mahalanobis Kernel Regression and Ensemble Learning

Transient stability assessment (TSA) is of great importance in power system operation and control. One of the usual tasks in TSA is to estimate the critical clearing time (CCT) of a given fault under the given network topology and pre-fault power flow. Data-driven methods try to obtain models describing the mapping between these factors and the CCT from a large number of samples. However, the influence of network topology on CCT is hard to be analyzed and is often ignored, which makes the models inaccurate and unpractical. In this paper, a novel data-driven TSA model combining Mahalanobis kernel regression and ensemble learning is proposed to deal with the problem. The model is a weighted sum of several sub-models. Each sub-model only uses the data of one topology to construct a kernel regressor. The weights are determined by both the topological similarity and numerical similarity between the samples. The similarities are decided by the parameters in Mahalanobis distance, and the parameters are to be trained. To reduce the model complexity, sub-models within the same topology category share the same parameters. When estimating CCT, the model uses not only the sub-model which the sample topology belongs to, but also other sub-models. Thus, it avoids the problem that there may be too few data under some topologies. It also efficiently utilizes information of data under all the topologies. Moreover, its decision-making process is clear and understandable, and an effective training algorithm is also designed. Test results on both the IEEE 10-machine 39-bus and a real system verify the effectiveness of the proposed model.

Mahalanobis-Taguchi System for Symbolic Interval Data Based on Kernel Mahalanobis Distance

Mahalanobis-Taguchi System (MTS), as a pattern recognition method by constructing a continuous measurement scale, has a very good performance on classification and feature selection for real-valued data. However, the record of symbolic interval data has become a common practice with the recent advances in database technologies. Kernel methods not only are powerful statistical nonlinear learning methods, but also can be defined over objects as diverse as graphs, sets, strings, and text documents. In this paper, we derive kernel Mahalanobis distance (KMD) to extend MTS to symbolic interval data. To evaluate the proposed method, four experiments with synthetic symbolic interval data sets and seven experiments with real symbolic interval data sets are performed and we have compared our method with MTS based on interval Mahalanobis distance (IMD). The experimental results show our method has a better classification performance than MTS based on IMD on Accuracy, Specificity, Sensitivity, and G-means. However, MTS based on IMD has a stronger dimension reduction rate than our method.

Multi-Scale Mahalanobis Kernel-Based Support Vector Machine for Classification of High-Resolution Remote Sensing Images

Support vector machine (SVM) is a powerful cognitive and learning algorithm in the domain of pattern recognition and image classification. However, the generalization ability of SVM is limited when processing classification of high-resolution remote sensing images. One chief reason for this is that the Euclidean distance-based distance matrix in traditional SVM treats different samples equally and overlooks the global distribution of samples. To construct a more effective SVM-based classification method, this paper proposes a multi-scale Mahalanobis kernel-based SVM classifier. In this new method, we first introduce a Mahalanobis distance kernel to improve the global cognitive learning ability of SVM. Then, the Mahalanobis distance kernel is embedded to the multi-scale kernel learning (MSKL) to construct a novel multi-scale Mahalanobis kernel, in which the parameters are optimized by a bio-inspired algorithm, named differential evolution. Finally, the new method is extended to the classification of high-resolution remote sensing images based on the spatial-spectral features. The comparison experiments of five public UCI datasets and two high-resolution remote sensing images verify that the Mahalanobis distance-based method can obtain more accurate classification results than that of the Euclidean distance-based method. In addition, the proposed method produced the best classification results in all the experiments. The global cognitive learning ability of Mahalanobis distance-based method is stronger than that of the Euclidean distance-based method. In addition, this study indicates that the optimized MSKL are potential for the interpretation and understanding of complicated high-resolution remote sensing scene.

Stationary Mahalanobis kernel SVM for credit risk evaluation

This paper proposed Mahalanobis distance induced kernels in Support Vector Machines (SVMs) with applications in credit risk evaluation. We take a particular interest in stationary ones. Compared to traditional stationary kernels, Mahalanobis kernels take into account on feature's correlation and can provide a more suitable description on the behavior of the data sets. Results on real world credit data sets show that stationary kernels with Mahalanobis distance outperform the stationary kernels with various distance measures and they can also compete with frequently used kernels in SVM. The superior performance of our proposed kernels over other classical machine learning methods and the successful application of the kernels in large scale credit risk evaluation problems may imply that we have proposed a new class of kernels appropriate for credit risk evaluations.

Spatio-Temporal River Contamination Measurements with Electrochemical Probes and Mobile Sensor Networks

The pollution of the rivers running through the cities or near to them is a current world-wide problem and requires actions and new technologically available approaches to control and restore those waters. In this work, we hypothesized that last-generation mobile sensor networks can be combined with emergent electrochemical probes and with recently proposed spatio-temporal analysis of the measurement dynamics using machine learning tools. With this purpose, we designed a mobile system to measure five variables: two environmental and three water quality variables in rivers: dissolved oxygen with an electrochemical probe, water temperature, electrical conductivity, air temperature and percentage of relative humidity using solid-state sensors, in each monitoring station. Our main contribution is a first mobile-sensor system that allows mobile campaigns for acquiring measurements with increased temporal and spatial resolution, which in turn allows for better capturing the spatio-temporal behavior of water quality parameters than conventional campaign measurements. Up to 23 monitoring campaigns were carried out, and the resulting measurements allowed the generation of spatio-temporal maps of first and second order statistics for the dynamics of the variables measured in the San Pedro River (Ecuador), by using previously proposed suitable machine learning algorithms. Significantly lower mean absolute interpolation errors were obtained for the set of mean values of the measurements interpolated with Support Vector Regression and Mahalanobis kernel distance, specifically 0.8 for water temperature, 0.4 for dissolved oxygen, 3.0 for air temperature, 11.6 for the percentage relative humidity, and 33.4 for the electrical conductivity of the water. The proposed system paves the way towards a new generation of contamination measurement systems, taking profit of information and communication technologies in several fields.

Semi-supervised active learning for support vector machines: A novel approach that exploits structure information in data

In today’s information society more and more data emerges, e.g., in social networks, technical applications, or business practice. Companies try to commercialize these data using data mining or machine learning methods. For this purpose, the data are often categorized or classified, but many times at high (monetary or temporal) cost. An effective approach to reduce these cost is to apply any kind of active learning (AL) methods, as AL controls the training process of a classifier by specifically querying individual data points (samples), which are then labeled (e.g., provided with class memberships) by a domain expert. However, an analysis of current AL research shows that AL still has some shortcomings. In particular, structure information given by the spatial pattern of the (un)labeled data in the input space of a classification (e.g., cluster information), is used in an insufficient way. To meet this challenge, this article presents a new approach for AL based on support vector machines (SVM) for classification. Structure information is captured by means of probabilistic models that are iteratively improved at run-time when label information becomes available. The probabilistic models are then considered in a selection strategy based on distance, density, diversity, and distribution information for AL (4DS strategy) and in a particular kernel function for SVM (Responsibility Weighted Mahalanobis kernel). With 20 benchmark data sets and with the MNIST data set it is shown that our new solution yields significantly better results than state-of-the-art methods.

Fault detection based on augmented kernel Mahalanobis distance for nonlinear dynamic processes

This paper presents a fault detection method based on augmented kernel Mahalanobis distance (AKMD) for monitoring nonlinear dynamic processes. In order to reflect the information of dynamic correlations, the measurements are stacked into augmented vectors at adjacent sampling instants. The augmented kernel Mahalanobis distance serves as the detection index, and its control limit is determined by the empirical method with assigning a significance level. Contrary to the mainstream of process monitoring methods based on principal component analysis (PCA), dimensionality reduction is not used here. The disadvantage of dimensionality reduction and space partition is discussed, and the improvement of fault detectability via data augmentation is analyzed. In addition, the computational complexity of the proposed method is acceptable. For training dataset containing m variables and n samples, if n≫m, the online computational burden of the proposed method is about O(n2). Simulations about a nonlinear dynamic process and the benchmark Tennessee Eastman process (TEP) both illustrate higher detection rates of the proposed method, compared with conventional multivariate statistical process monitoring (MSPM) methods such as PCA and its variants.

European Exchange Trading Funds Trading with Locally Weighted Support Vector Regression

In this paper, two different Locally Weighted Support Vector Regression (wSVR) algorithms are generated and applied to the task of forecasting and trading five European Exchange Traded Funds. The trading application covers the recent European Monetary Union debt crisis. The performance of the proposed models is benchmarked against traditional Support Vector Regression (SVR) models. The Radial Basis Function, the Wavelet and the Mahalanobis kernel are explored and tested as SVR kernels. Finally, a novel statistical SVR input selection procedure is introduced based on a principal component analysis and the Hansen, Lunde, and Nason (2011) model confidence test. The results demonstrate the superiority of the wSVR models over the traditional SVRs and of the v-SVR over the ε-SVR algorithms. We note that the performance of all models varies and considerably deteriorates in the peak of the debt crisis. In terms of the kernels, our results do not confirm the belief that the Radial Basis Function is the optimum choice for financial series.

Monitoring the mean vector with Mahalanobis kernels

Statistical process control (SPC) applies the science of statistics to various process controls in order to provide higher-quality products and better services. Multivariate control charts are essential tools in multivariate SPC. Hotelling’s charts based on rational subgroups of sample sizes larger than one are very sensitive for detecting relatively large shifts in the process mean vectors. However, it makes some very restrictive assumptions (multivariate normal distribution) that are usually difficult to be satisfied in real applications. Modern processes do not satisfy classical methods assumptions, such as normality or linearity. To overcome this issue, introduction of new techniques from statistical machine learning theory has been applied. Control charts based on Support Vector Data Description (SVDD), a popular data classifier method inspired by Support Vector Machines, benefit from a wide variety of choices of kernels, which determine the effectiveness of the whole model. Among the most popular choices of kernels is the Euclidean distance-based Gaussian kernel, which enables SVDD to obtain a flexible data description, thus enhances its overall predictive capability. This paper explores an even more robust approach by incorporating the Mahalanobis distance-based kernel (hereinafter referred to as Mahalanobis kernel) to SVDD and compares it with SVDD using the traditional Gaussian kernel.

A Mahalanobis metric learning-based polynomial kernel for classification of hyperspectral images

In this paper, to combine the advantage of both polynomial kernel and the Mahalanobis distance metric learning (DML) methods, we propose a Mahalanobis DML based polynomial kernel for the classification of hyperspectral images. To ensure the method is computing-saving, we adapt a fast iterative method to learn the Mahalanobis matrix. Simulation experiment is conducted on two real hyperspectral data sets. To evaluate the proposed method, we compare it with the traditional radial basis function (RBF) kernel, polynomial kernel and the RBF-based Mahalanobis kernel, the result shows the performance of the proposed method did improve the capability of the polynomial kernel and also perform better than the RBF-based Mahalanobis kernel.

A dual-layer supervised Mahalanobis kernel for the classification of hyperspectral images

To address the drawback of traditional Mahalanobis distance metric learning (DML) methods that learn the matrix without considering the weights of each class, in this paper, a novel dual-layer supervised Mahalanobis kernel is proposed for the classification of hyperspectral images. By modifying the traditional unsupervised Mahalanobis kernel, a supervised Mahalanobis matrix that can include more relativity information of different types of real materials in hyperspectral images is learned to obtain a new kernel. The proposed Mahalanobis matrix is obtained in two steps. In step one, we learn the first traditional Mahalanobis matrix with all samples to map the raw data. In step two, based on the data mapped by the first matrix, we pick several hard-to-identify classes from all the classes and learn the second Mahalanobis matrix using only these data. Finally, by combining these two matrices, we construct a new form of the Mahalanobis kernel. Simulation experiments are conducted on three real hyperspectral data sets. We use SVM as the kernel-based classifier to classify the dimensionally reduced data and compare with several methods from various aspects. The results show that the proposed methods perform better than other unsupervised or single-layer DML methods in classifying the hard-to-identify classes, especially under an extreme condition.

Using Generalized Entropies and OC-SVM with Mahalanobis Kernel for Detection and Classification of Anomalies in Network Traffic

Network anomaly detection and classification is an important open issue in network security. Several approaches and systems based on different mathematical tools have been studied and developed, among them, the Anomaly-Network Intrusion Detection System (A-NIDS), which monitors network traffic and compares it against an established baseline of a “normal” traffic profile. Then, it is necessary to characterize the “normal” Internet traffic. This paper presents an approach for anomaly detection and classification based on Shannon, Rényi and Tsallis entropies of selected features, and the construction of regions from entropy data employing the Mahalanobis distance (MD), and One Class Support Vector Machine (OC-SVM) with different kernels (Radial Basis Function (RBF) and Mahalanobis Kernel (MK)) for “normal” and abnormal traffic. Regular and non-regular regions built from “normal” traffic profiles allow anomaly detection, while the classification is performed under the assumption that regions corresponding to the attack classes have been previously characterized. Although this approach allows the use of as many features as required, only four well-known significant features were selected in our case. In order to evaluate our approach, two different data sets were used: one set of real traffic obtained from an Academic Local Area Network (LAN), and the other a subset of the 1998 MIT-DARPA set. For these data sets, a True positive rate up to 99.35%, a True negative rate up to 99.83% and a False negative rate at about 0.16% were yielded. Experimental results show that certain q-values of the generalized entropies and the use of OC-SVM with RBF kernel improve the detection rate in the detection stage, while the novel inclusion of MK kernel in OC-SVM and k-temporal nearest neighbors improve accuracy in classification. In addition, the results show that using the Box-Cox transformation, the Mahalanobis distance yielded high detection rates with an efficient computation time, while OC-SVM achieved detection rates slightly higher, but is more computationally expensive.

The responsibility weighted Mahalanobis kernel for semi-supervised training of support vector machines for classification

Kernel functions in support vector machines (SVM) are needed to assess the similarity of input samples in order to classify these samples, for instance. Besides standard kernels such as Gaussian (i.e., radial basis function, RBF) or polynomial kernels, there are also specific kernels tailored to consider structure in the data for similarity assessment. In this paper, we will capture structure in data by means of probabilistic mixture density models, for example Gaussian mixtures in the case of real-valued input spaces. From the distance measures that are inherently contained in these models, e.g., Mahalanobis distances in the case of Gaussian mixtures, we derive a new kernel, the responsibility weighted Mahalanobis (RWM) kernel. Basically, this kernel emphasizes the influence of model components from which any two samples that are compared are assumed to originate (that is, the “responsible” model components). We will see that this kernel outperforms the RBF kernel and other kernels capturing structure in data (such as the LAP kernel in Laplacian SVM) in many applications where partially labeled data are available, i.e., for semi-supervised training of SVM. Other key advantages are that the RWM kernel can easily be used with standard SVM implementations and training algorithms such as sequential minimal optimization, and heuristics known for the parametrization of RBF kernels in a C-SVM can easily be transferred to this new kernel. Properties of the RWM kernel are demonstrated with 20 benchmark data sets and an increasing percentage of labeled samples in the training data.