Nonlinear Principal Component Analysis Research Articles

Damage detection methodology under variable load conditions based on strain field pattern recognition using FBGs, nonlinear principal component analysis, and clustering techniques

Structural health monitoring consists of using sensors integrated within structures together with algorithms to perform load monitoring, damage detection, damage location, damage size and severity, and prognosis. One possibility is to use strain sensors to infer structural integrity by comparing patterns in the strain field between the pristine and damaged conditions. In previous works, the authors have demonstrated that it is possible to detect small defects based on strain field pattern recognition by using robust machine learning techniques. They have focused on methodologies based on principal component analysis (PCA) and on the development of several unfolding and standardization techniques, which allow dealing with multiple load conditions. However, before a real implementation of this approach in engineering structures, changes in the strain field due to conditions different from damage occurrence need to be isolated. Since load conditions may vary in most engineering structures and promote significant changes in the strain field, it is necessary to implement novel techniques for uncoupling such changes from those produced by damage occurrence. A damage detection methodology based on optimal baseline selection (OBS) by means of clustering techniques is presented. The methodology includes the use of hierarchical nonlinear PCA as a nonlinear modeling technique in conjunction with Q and nonlinear-T2 damage indices. The methodology is experimentally validated using strain measurements obtained by 32 fiber Bragg grating sensors bonded to an aluminum beam under dynamic bending loads and simultaneously submitted to variations in its pitch angle. The results demonstrated the capability of the methodology for clustering data according to 13 different load conditions (pitch angles), performing the OBS and detecting six different damages induced in a cumulative way. The proposed methodology showed a true positive rate of 100% and a false positive rate of 1.28% for a 99% of confidence.

A hybrid classifier based on nonlinear-PCA and deep belief networks with applications in dysphagia diagnosis

Traditional dysphagia prescreening diagnostic methods require doctors specialists to give patients a total score based on a water swallow test scale. This method is limited by the high dimensionality of the diagnostic elements in the water swallow test scale with heavy workload (Towards each patient, the scale requires the doctors give score for 18 diagnostic elements respectively) as well as the difficulties of extracting and using the diagnostic scale data’s non-linear features and hidden expertise information (Even with the scale scores, specific diagnostic conclusions are still given by expert doctors under the expertise). In this paper, a hybrid classifier model based on Nonlinear-Principal Component Analysis (NPCA) and Deep Belief Networks (DBN) is proposed in order to effectively extract the diagnostic scale data’s nonlinear features and hidden information and to provide the key scale elements’ locating methods towards the diagnostic results (The key scale elements that affect different diagnostic conclusions are given to improve the efficiency and pertinence of diagnosis and reduce the workload of diagnosis). We demonstrate the effectiveness of the proposed method using the frame of ‘information entropy theory’. Real dysphagia diagnosis examples from the China-Japanese Friendship Hospital are used to demonstrate applications of the proposed methods. The examples show satisfactory results compared to the traditional classifier.

Identifying Global Value Chain Governance Determinants in Kenya’s Horticultural Oriented Export Sector by Nonlinear Principal Component Analysis

The objective of this work is to empirically assess the determinants used in global value chain governance trade through interfirm relationship and their effect on competitive advantage of horticultural value chains in developing economies. The paper is based on a Kenyan survey of 83 horticultural exporters of fresh fruits and vegetables accessed out of 120 exporters registered with Fresh Produce Association of Kenya (FPEAK) and Horticultural Crops Directorate (HCD). It employs a nonlinear principal component analysis procedure of categorical principal component analysis (CATPCA). From the CATPCA output, five components considered to be key food value chain governance determinants affecting the export oriented horticultural value chain in Kenya were extracted and named as standards & certification, nature of transactions, level of chain integration, nature of contract and relational characteristics. The current research shows that with prioritisation of requisite food safety standards & certification schemes and discernment of transactional demands of heterogeneous export markets, horticultural exporters may expect to be competitive by means of improved product differentiation, process flows, logistical advantage and promotion of marketing & organisation management innovativeness. The implication therefore to the chain managers that standards & certification schemes are taking a critical position in determining food value chain governance especially through remote governance or governance from a distance other than the governance structure continuum of markets and hierarchies previously defined by transactional cost economics.

Inherent vulnerability assessment of rural households based on socio-economic indicators using categorical principal component analysis: A case study of Kimsar region, Uttarakhand

The recent trend of shifting focus from hazard centric drivers of vulnerability towards the social and economic drivers of vulnerability has led to a number of conceptual frameworks for social vulnerability assessment. Contributing towards this growing trend of social vulnerability assessment, this study proposes a framework to measure inherent vulnerability, which is centered on hazard generic and livelihood oriented socioeconomic factors of vulnerability. Inherent vulnerability is defined as the predisposition of a household to suffer harm. The study focuses on the mountainous communities in Kimsar region, located in Uttarakhand state, India. The communities in the region suffer from multiple stressors including extreme precipitation, drought, landslides, cloudbursts and flash floods. Vulnerability indicators with mixed scaling are used, to capture household’s perception and other socio-economic attributes, which contribute towards its inherent vulnerability. Data was collected by conducting household surveys in nine villages of Kimsar region. In order to process the indicators with mixed scaling, and obtain an empirical summary of the data set, the method of Non-Linear Principal Component Analysis was used for computing a household level Inherent Vulnerability Index. Results obtained revealed that principal components explaining a major variance in the data set were — access to employment opportunities, effectiveness of local government, access to food, occupational diversity, access to resources, educational attainment and access to water. It was observed that the villages of Dharkot, Kandakhal and Bhumiyakisar have the highest percentage of households, which were relatively less vulnerable to environmental stressors. Higher vulnerability was observed in majority of households in the village Kimsar, Ramjeewala and Malla Banas. A majority of households in Talla Banas, Jogiyana and Kasan were moderately vulnerable. Inherent vulnerability assessment has the potential to predict the future harm a household might suffer due to hazard events.

Shallow and deep learning for image classification

The paper is focused on the idea to demonstrate the advantages of deep learning approaches over ordinary shallow neural network on their comparative applications to image classifying from such popular benchmark databases as FERET and MNIST. An autoassociative neural network is used as a standalone program realized the nonlinear principal component analysis for prior extracting the most informative features of input data for neural networks to be compared further as classifiers. A special study of the optimal choice of activation function and the normalization transformation of input data allows to improve efficiency of the autoassociative program. One more study devoted to denoising properties of this program demonstrates its high efficiency even on noisy data. Three types of neural networks are compared: feed-forward neural net with one hidden layer, deep network with several hidden layers and deep belief network with several pretraining layers realized restricted Boltzmann machine. The number of hidden layer and the number of hidden neurons in them were chosen by cross-validation procedure to keep balance between number of layers and hidden neurons and classification efficiency. Results of our comparative study demonstrate the undoubted advantage of deep networks, as well as denoising power of autoencoders. In our work we use both multiprocessor graphic card and cloud services to speed up our calculations. The paper is oriented to specialists in concrete fields of scientific or experimental applications, who have already some knowledge about artificial neural networks, probability theory and numerical methods.

New tools for the visualization of biological pathways.

This paper presents several geometrically motivated techniques for the visualization of high-dimensional biological data sets. The Grassmann manifold provides a robust framework for measuring data similarity in a subspace context. Sparse radial basis function classification as a visualization technique leverages recent advances in radial basis function learning via convex optimization. In the spirit of deep belief networks, supervised centroid-encoding is proposed as a way to exploit class label information. These methods are compared to linear and nonlinear principal component analysis (autoencoders) in the context of data visualization; these approaches may perform poorly for visualization when the variance of the data is spread across more than three dimensions. In contrast, the proposed methods are shown to capture significant data structure in two or three dimensions, even when the information in the data lives in higher dimensional subspaces. To illustrate these ideas, the visualization techniques are applied to gene expression data sets that capture the host immune system's response to infection by the Ebola virus in non-human primate and collaborative cross mouse.

Statistical analysis of rock-burst events in underground mines and excavations to present reasonable data-driven predictors

ABSTRACTRock bursts are sudden and violent failures of surrounding rockmasses in underground mines and excavations. In this paper, a database consisting of 188 case histories was collected. Each case history contains some of the predictor variables ‘overburden thickness, maximum tangential stress, uniaxial compressive strength of rock, tensile strength of rock, stress ratio, brittleness ratio and elastic energy index’ and one of the four defined classes for the dependent variable ‘rock burst intensity’. A strategy, including ‘outlier detection and substitution, normality evaluation, deduction of distribution functions, estimation of mean and mean variation ranges, evaluation of mean-equality and distribution function-equality hypotheses, correlation analysis and factor analysis for in-review variables’, was implemented. The strategy led to conclude that some predictor variables with available case histories have no contributions for rock burst prediction. These inferences were in accordance with the results of regression techniques for qualitative dependent variables. Besides, many predictor variable arrangements were incompatible with factor analysis. In the case of compatible arrangements, the variation of the predictor variables cannot be considerably reflected. Application of nonlinear principal component analysis using auto-associative neural networks did not also lead to representative components. Therefore, the significant predictor variables can only be used to design new classifiers.

Are they telling the truth? Revealing hidden traits of satisfaction with a public bike-sharing service

ABSTRACTPublic bike-sharing systems (BSSs) are an emerging mode of transportation introduced by municipalities to solve congestion problems in metropolitan areas, especially when integrated with other types of transportation. In the last years, the number of public bike-sharing services has been constantly on the rise all over the world, and generally the overall satisfaction with them is high. However, satisfaction with public services is driven by mechanisms that can differ from those in the private sector. It is important to establish to what extent a high satisfaction is genuine or simply ephemeral. Even “old” public services (like public transportation) become “gold” when accompanied by the introduction of new technologies. In this paper we analyze this phenomenon using data from a satisfaction web-survey conducted among customers of the public BSS “BikeMi” in Milan, Italy, in a period when mobile technologies have been introduced to speed up the service. On analyzing the responses to satisfaction questions using simple summary statistics, the level of satisfaction resulted very high. However, our aim was to look for potential “darker” sides of the service by detecting possible hidden satisfaction components. For this purpose, we used the Nonlinear Principal Components Analysis, which is particularly powerful in this context. A simple textual analysis was also performed as a validating test. Results from our analysis indicated that satisfaction is flawed by a set of factors like the mechanics of the bikes, the picking and dropping system, and the apps used to organize the service. Less concern was detected for more general aspects of the service.

Assessment of the water quality monitoring network of the Piabanha River experimental watersheds in Rio de Janeiro, Brazil, using autoassociative neural networks.

Water quality monitoring is a complex issue that requires support tools in order to provide information for water resource management. Budget constraints as well as an inadequate water quality network design call for the development of evaluation tools to provide efficient water quality monitoring. For this purpose, a nonlinear principal component analysis (NLPCA) based on an autoassociative neural network was performed to assess the redundancy of the parameters and monitoring locations of the water quality network in the Piabanha River watershed. Oftentimes, a small number of variables contain the most relevant information, while the others add little or no interpretation to the variability of water quality. Principal component analysis (PCA) is widely used for this purpose. However, conventional PCA is not able to capture the nonlinearities of water quality data, while neural networks can represent those nonlinear relationships. The results presented in this work demonstrate that NLPCA performs better than PCA in the reconstruction of the water quality data of Piabanha watershed, explaining most of data variance. From the results of NLPCA, the most relevant water quality parameter is fecal coliforms (FCs) and the least relevant is chemical oxygen demand (COD). Regarding the monitoring locations, the most relevant is Poço Tarzan (PT) and the least is Parque Petrópolis (PP).

Multiple imputation of rainfall missing data in the Iberian Mediterranean context

Given the increasing need for complete rainfall data networks, in recent years have been proposed diverse methods for filling gaps in observed precipitation series, progressively more advanced that traditional approaches to overcome the problem. The present study has consisted in validate 10 methods (6 linear, 2 non-linear and 2 hybrid) that allow multiple imputation, i.e., fill at the same time missing data of multiple incomplete series in a dense network of neighboring stations. These were applied for daily and monthly rainfall in two sectors in the Júcar River Basin Authority (east Iberian Peninsula), which is characterized by a high spatial irregularity and difficulty of rainfall estimation. A classification of precipitation according to their genetic origin was applied as pre-processing, and a quantile-mapping adjusting as post-processing technique. The results showed in general a better performance for the non-linear and hybrid methods, highlighting that the non-linear PCA (NLPCA) method outperforms considerably the Self Organizing Maps (SOM) method within non-linear approaches. On linear methods, the Regularized Expectation Maximization method (RegEM) was the best, but far from NLPCA. Applying EOF filtering as post-processing of NLPCA (hybrid approach) yielded the best results.

Improved Statistical Fault Detection Technique and Application to Biological Phenomena Modeled by S-Systems.

In our previous work, we have demonstrated the effectiveness of the linear multiscale principal component analysis (PCA)-based moving window (MW)-generalized likelihood ratio test (GLRT) technique over the classical PCA and multiscale principal component analysis (MSPCA)-based GLRT methods. The developed fault detection algorithm provided optimal properties by maximizing the detection probability for a particular false alarm rate (FAR) with different values of windows, and however, most real systems are nonlinear, which make the linear PCA method not able to tackle the issue of non-linearity to a great extent. Thus, in this paper, first, we apply a nonlinear PCA to obtain an accurate principal component of a set of data and handle a wide range of nonlinearities using the kernel principal component analysis (KPCA) model. The KPCA is among the most popular nonlinear statistical methods. Second, we extend the MW-GLRT technique to one that utilizes exponential weights to residuals in the moving window (instead of equal weightage) as it might be able to further improve fault detection performance by reducing the FAR using exponentially weighed moving average (EWMA). The developed detection method, which is called EWMA-GLRT, provides improved properties, such as smaller missed detection and FARs and smaller average run length. The idea behind the developed EWMA-GLRT is to compute a new GLRT statistic that integrates current and previous data information in a decreasing exponential fashion giving more weight to the more recent data. This provides a more accurate estimation of the GLRT statistic and provides a stronger memory that will enable better decision making with respect to fault detection. Therefore, in this paper, a KPCA-based EWMA-GLRT method is developed and utilized in practice to improve fault detection in biological phenomena modeled by S-systems and to enhance monitoring process mean. The idea behind a KPCA-based EWMA-GLRT fault detection algorithm is to combine the advantages brought forward by the proposed EWMA-GLRT fault detection chart with the KPCA model. Thus, it is used to enhance fault detection of the Cad System in E. coli model through monitoring some of the key variables involved in this model such as enzymes, transport proteins, regulatory proteins, lysine, and cadaverine. The results demonstrate the effectiveness of the proposed KPCA-based EWMA-GLRT method over Q , GLRT, EWMA, Shewhart, and moving window-GLRT methods. The detection performance is assessed and evaluated in terms of FAR, missed detection rates, and average run length (ARL1) values.

Voice assessments for detecting patients with neurological diseases using PCA and NPCA

In this study, we wanted to discriminate between 30 patients who suffer from Parkinson’s disease (PD) and 20 patients with other neurological diseases (ND). All participants were asked to pronounce sustained vowel /a/ hold as long as possible at comfortable level. The analyses were done on these voice samples. Firstly, an initial feature vector extracted from time, frequency and cepstral domains. Then we used principal component analysis (PCA) and nonlinear PCA (NPCA). These techniques reduce the number of parameters and select the most effective ones to be used for classification. Support vector machine and k-nearest neighbor with different kernels was used for classification. We obtained accuracy up to 88% for discrimination between PD patients ND patients using KNN with k equal to three and five.

New Discrimination Procedure of Location Model for Handling Large Categorical Variables

The location model proposed in the past is a predictive discriminant rule that can classify new observations into one of two predefined groups based on mixtures of continuous and categorical variables. The ability of location model to discriminate new observation correctly is highly dependent on the number of multinomial cells created by the number of categorical variables. This study conducts a preliminary investigation to show the location model that uses maximum likelihood estimation has high misclassification rate up to 45% on average in dealing with more than six categorical variables for all 36 data tested. Such model indicated highly incorrect prediction as this model performed badly for large categorical variables even with large sample size. To alleviate the high rate of misclassification, a new strategy is embedded in the discriminant rule by introducing nonlinear principal component analysis (NPCA) into the classical location model (cLM), mainly to handle the large number of categorical variables. This new strategy is investigated on some simulation and real datasets through the estimation of misclassification rate using leave-one-out method. The results from numerical investigations manifest the feasibility of the proposed model as the misclassification rate is dramatically decreased compared to the cLM for all 18 different data settings. A practical application using real dataset demonstrates a significant improvement and obtains comparable result among the best methods that are compared. The overall findings reveal that the proposed model extended the applicability range of the location model as previously it was limited to only six categorical variables to achieve acceptable performance. This study proved that the proposed model with new discrimination procedure can be used as an alternative to the problems of mixed variables classification, primarily when facing with large categorical variables.

Nonlinear Spectral Unmixing for the Characterisation of Volcanic Surface Deposit and Airborne Plumes from Remote Sensing Imagery

In image processing, it is commonly assumed that the model ruling spectral mixture in a given hyperspectral pixel is linear. However, in many real life cases, the different objects and materials determining the observed spectral signatures overlap in the same scene, resulting in nonlinear mixture. This is particularly evident in volcanoes-related imagery, where both airborne plumes of effluents and surface deposit of volcanic ejecta can be mixed in the same observation line of sight. To tackle this intrinsic complexity, in this paper, we perform a pilot test using Nonlinear Principal Component Analysis (NLPCA) as a nonlinear transformation, that projects a hyperspectral image onto a reduced-dimensionality feature space. The use of NLPCA is twofold: (1) it is used to reduce the dimensionality of the original spectral data and (2) it performs a linearization of the information, thus allowing the effective use of successive linear approaches for spectral unmixing. The proposed method has been tested on two different hyperspectral datasets, dealing with active volcanoes at the time of the observation. The dimensionality of the spectroscopic problem is reduced of up to 95% (ratio of the elements of compressed nonlinear vectors and initial spectral inputs), by the use of NLPCA. The selective use of an atmospheric correction pre-processing is applied, demonstrating how individual plume and volcanic surface deposit components can be discriminated, paving the way to future application of this method.

Fishers' Perceived Objectives of Community-Based Coastal Resource Management in the Kei Islands, Indonesia

Community-based resource management is a key approach to achieve successful small-scale fisheries and marine conservation. Many local management initiatives worldwide have been successfully managing aquatic resources and livelihoods of communities depending on them. Community-based management is particularly prevalent in small tropical islands where communities are frequently heavily dependent on coral reef ecosystems and small-scale reef fisheries for their livelihoods. Community-based management is, however, not always a panacea since there are inherit trade-offs among multiple objectives which are sometimes accentuated by community heterogeneity. It is well recognized that perceived and real evidence of community benefits are key to attributing success to local community-based management. However, broader understanding of community-based management objectives and how fishers' perceived personal objectives and characteristics affect management outcomes remains limited. We apply a non-linear Principle Component Analysis (PCA) to explore variations in personally held community-based management objectives, based on local surveys for fishing communities in the Kei Islands in Indonesia. We then examine whether these variations also explain their perceptions of environmental and economic outcomes that are achieved by this management systems. In this study important differences are found in the perceptions fishers have of the relative importance of different community management objectives. The value people attribute to aspects of community management can be related to their socio-demographic characteristics and experienced fishers tend to focus more on environmental objectives. Given that strong links were found between community management outcomes and terrestrially based activities there is an opportunity to link in the terrestrial and coastal systems management and achieve multiple objective outcomes.

Multivariate Statistical Process Control Using Enhanced Bottleneck Neural Network

Monitoring process upsets and malfunctions as early as possible and then finding and removing the factors causing the respective events is of great importance for safe operation and improved productivity. Conventional process monitoring using principal component analysis (PCA) often supposes that process data follow a Gaussian distribution. However, this kind of constraint cannot be satisfied in practice because many industrial processes frequently span multiple operating states. To overcome this difficulty, PCA can be combined with nonparametric control charts for which there is no assumption need on the distribution. However, this approach still uses a constant confidence limit where a relatively high rate of false alarms are generated. Although nonlinear PCA (NLPCA) using autoassociative bottle-neck neural networks plays an important role in the monitoring of industrial processes, it is difficult to design correct monitoring statistics and confidence limits that check new performance. In this work, a new monitoring strategy using an enhanced bottleneck neural network (EBNN) with an adaptive confidence limit for non Gaussian data is proposed. The basic idea behind it is to extract internally homogeneous segments from the historical normal data sets by filling a Gaussian mixture model (GMM). Based on the assumption that process data follow a Gaussian distribution within an operating mode, a local confidence limit can be established. The EBNN is used to reconstruct input data and estimate probabilities of belonging to the various local operating regimes, as modelled by GMM. An abnormal event for an input measurement vector is detected if the squared prediction error (SPE) is too large, or above a certain threshold which is made adaptive. Moreover, the sensor validity index (SVI) is employed successfully to identify the detected faulty variable. The results demonstrate that, compared with NLPCA, the proposed approach can effectively reduce the number of false alarms, and is hence expected to better monitor many practical processes.

Nonlinear Multivariate Spatial Modeling Using NLPCA and Pair‐Copulas

A novel geostatistical modeling approach is developed to model nonlinear multivariate spatial dependence using nonlinear principal component analysis (NLPCA) and pair‐copulas. In spatial studies, multivariate measurements are frequently collected at each location. The dependence between such measurements can be complex. In this article, a multivariate geostatistical model is developed that can capture both nonlinear spatial dependence across locations and nonlinear dependence between measurements at a particular location. Nonlinear multivariate dependence between spatial variables is removed using NLPCA. Subsequently, a pair‐copula based model is fitted to each transformed variable to model the univariate nonlinear spatial dependencies. NLPCA and pair‐copulas, within the proposed model, are compared with stepwise conditional transformation (SCT) and conventional kriging. The results show that, for the two case studies presented, the proposed model that utilizes NLPCA and pair‐copulas reproduces nonlinear multivariate structures and univariate distributions better than existing methods based on SCT and kriging.

Route effect on the perception of public transport services quality

User satisfaction is a key indicator of public service quality, especially for those services considered basic necessities. The conceptualization and measurement of transport service quality—a fundamental determinant of demand—poses challenges for conducting economic analyses and designing mobility policies.Several operating companies are involved in the transport sector. In this paper, the bus network of the metropolitan area of Granada, Spain, is taken as a case study. The aim is to design a model of overall satisfaction based on level of satisfaction using a specific set of factors that take into account the individual characteristics of users and the differential effect of using different bus lines.A combined method using nonlinear principal component analysis (NLPCA) and a logit multilevel model (LMLM) in two steps is applied to a satisfaction survey conducted by the Metropolitan Transport Consortium of Granada (Consorcio de Transporte Metropolitano del área de Granada) in 2013. The survey shows that even though customers within the metropolitan area of Granada are satisfied with the service received (67.26%), the level of satisfaction is not equal for all bus lines, with the perceived quality of some lines being above or below the average. This differential effect is due to different reasons, including the technical and functional performance of the operating companies, commercial speed and length and type of route, among others. Both the operators and the public administration need to focus their attention on these lines in order to design economic policy measures to improve bus lines with below standard compliance.

A data-driven approach for evaluating multi-modal therapy in traumatic brain injury

Combination therapies targeting multiple recovery mechanisms have the potential for additive or synergistic effects, but experimental design and analyses of multimodal therapeutic trials are challenging. To address this problem, we developed a data-driven approach to integrate and analyze raw source data from separate pre-clinical studies and evaluated interactions between four treatments following traumatic brain injury. Histologic and behavioral outcomes were measured in 202 rats treated with combinations of an anti-inflammatory agent (minocycline), a neurotrophic agent (LM11A-31), and physical therapy consisting of assisted exercise with or without botulinum toxin-induced limb constraint. Data was curated and analyzed in a linked workflow involving non-linear principal component analysis followed by hypothesis testing with a linear mixed model. Results revealed significant benefits of the neurotrophic agent LM11A-31 on learning and memory outcomes after traumatic brain injury. In addition, modulations of LM11A-31 effects by co-administration of minocycline and by the type of physical therapy applied reached statistical significance. These results suggest a combinatorial effect of drug and physical therapy interventions that was not evident by univariate analysis. The study designs and analytic techniques applied here form a structured, unbiased, internally validated workflow that may be applied to other combinatorial studies, both in animals and humans.

Statistical learning on emerging economies

ABSTRACTBRIC is an acronym coined by Jim O'Neill from Goldman Sachs in 2001 to abbreviate four emerging economies, Brazil, Russia, India and China, based on economic data at the time. Later, as new data became available, Goldman Sachs updated this list to include Mexico, Indonesia, Nigeria and Turkey, which was referred to as MINT. This list, as well as some other similar lists of emerging economies, is based on descriptive statistics of the economic data combined with economists' insights. The purpose of this study is twofold: to see if these insights into the global economic trends can be learned with statistical learning tools, and, if so, to identify the next emerging countries. We apply both unsupervised and supervised learning methods, which include linear and nonlinear principle component analysis, and nonlinear sufficient dimension reduction, to 13 years worth of economic data. Our results show that these statistical learning techniques, and in particular the kernel sliced inverse regression algorithm, can serve as a useful tool for economists and policy-makers for analyzing global economic trends, by its ability to incorporate large amount of economic data and previous experts' judgments, which otherwise may take years of experiences to acquire.