Projection Pursuit Research Articles

A new method for small sample space components screening: Challenges, algorithms and a case-study with Microchip

Screening electronic components in space industry is a difficult challenge because there are many tests, and the sample sizes are small. In statistics, this situation is called HDLSS (High Dimension Low Sample Size) and specific methods must be developed to propose an efficient screening, with a good detection of outliers which could transform in future reliability issues. In this paper we present the six challenges of screening and we propose a solution which is a complex algorithm, including a new multivariate approach, a dimension reduction for low sample size, and a controlled projection pursuit method adapted to a very large number of tests. A case-study at Microchip will be presented, with actual examples and a demo of the software. Measurement issues and detectability will also be discussed. Finally, the summary of the results at Microchip and the perspectives and future work will be addressed.

Projection pursuit evaluation model of a regional surface water environment based on an Ameliorative Moth-Flame Optimization algorithm

Abstract In order to improve the accuracy of regional water environment assessments, an improved projection pursuit water quality evaluation model (AMFO-PPE) was developed that was based on the Ameliorative Moth-Flame Optimization (AMFO) algorithm. This approach utilized the Moth-Flame Optimization, which added the dynamic inertia weight, and the Kent chaotic map search strategy. The model was used to evaluate 16 typical riverside irrigation districts in the Sanjiang Plain. The spatial differentiation law and possible causes of the surface water quality were explored. The stability and reliability of the AMFO-PPE model for the regional water quality assessments were evaluated. The results showed that the water quality of the study area was generally excellent, but the TP index content was high. Areas with water quality Grades III and IV were mainly concentrated in the central and western regions. Regions with water quality Grades I and II were mainly concentrated in the central and eastern regions. The river network density is the main influencing factor of the water quality spatial distribution characteristics. Regions with a large river network density tend to have a better water quality. The application and utilization rates of phosphorus fertilizer have an important impact on the TP index. The NIM, RAGA-PPE model, FA-PPE model, and AMFO-PPE model were compared. The sum of the Spearman correlation coefficients calculated by randomly extracting 10 irrigation district values 25 times was 24.07906. The NIM distinction degree was greater than 1.09875 of the AMFO-PPE model. However, the NIM of standard values dot pitch was obviously insufficient. The AMFO-PPE model has a better stability and reliability than the other models. Therefore, this model performed as expected and has a value for application in regional water environment assessments.

Kurtosis-based projection pursuit for outlier detection in financial time series

Outlier detection in financial time series is made difficult by serial dependence, volatility clustering and heavy tails. Projections achieving maximal kurtosis proved to be useful for outlier detection in multivariate datasets but their widespread application has been hampered by computational and inferential difficulties. This paper addresses both problems within the framework of univariate and multivariate financial time series. Computation of projections with maximal kurtoses in univariate financial time series is simplified to a eigenvalue problem. Projections with maximal kurtoses in multivariate financial time series best separate outliers from the bulk of the data, under a finite mixture model. The paper also addresses kurtosis optimization within the framework of portfolio selection. Practical relevance of these theoretical results is illustrated with univariate and multivariate time series from several financial markets. Empirical results also suggest that projections removing excess kurtosis could transform a univariate financial time series to a time series very similar to a Gaussian process, while the effect of outliers might be alleviated by projections achieving minimal kurtosis.

Assessing the sustainability of renewable energy: An empirical analysis of selected 18 European countries.

There are many studies on the sustainability of renewable energy, mainly focusing on energy supply, economic, social, environmental and technological aspects, but there are few studies on the sustainability of renewable energy itself. This work focuses on the systematic and quantitative assessment of the sustainability of renewable energy itself by analyzing the sustainability of renewable energy in selected 18 European countries from 2007 to 2016. The consumption of renewable energy in these selected 18 countries accounts for ~95% of the consumption of renewable energy in the European Union. To scientifically evaluate the sustainability of renewable energy, 17 indicators are selected based on the energy-economy-environment theory. In order to deal with the high-dimensional, non-normal, and nonlinear complex data, and to assess the sustainability of renewable energy without standards, the projection pursuit algorithm and the real-coded accelerating genetic algorithm are combined to establish a comprehensive model to assess the sustainability of renewable energy. The results show that (i) the sustainability of renewable energy in Germany, the UK, France, and Italy is better than that in the other investigated countries; (ii) in the 17 indicators selected by the energy-economy-environment model, the factors of total energy demand, energy taxes, carbon dioxide emissions, sulfur oxides emissions, and nitrous oxides emissions exert a stronger impact on the sustainability of renewable energy; (iii) time-series analysis show that the general sustainable level is a wave of growth. Moreover, the proposed comprehensive model can effectively deal with the high-dimensional, non-normal, and nonlinear complex data, thus providing a feasible method for the quantitative analysis and evaluation of the sustainability of renewable energy.

Assessment and validation of groundwater vulnerability to nitrate in porous aquifers based on a DRASTIC method modified by projection pursuit dynamic clustering model

The groundwater vulnerability assessment has been identified as an important tool of groundwater pollution prevention. In this study, the DRASTIC method was modified to estimate the groundwater vulnerability of porous aquifers to nitrate. The parameter system was optimized by replacing the original parameters of aquifer media, soil media, impact of the vadose zone and hydraulic conductivity with quantitative parameters of aquifer thickness, nitrate attenuation intensity, hydraulic resistance and groundwater velocity and adding pollutant input intensity to develop the DRANTHVP method. In addition, the rating scale of the DRASTIC method was revised, and the weight and influence degree of each parameter were determined using the projection pursuit dynamic clustering (PPDC) model. The DRANTHVP method was applied to the plain area of western Jilin Province, and the vulnerability index map of groundwater to nitrate pollution was established. The DRANTHVP method improved the correlation coefficient between vulnerability index and nitrate concentration to 0.720, which was more than three times that of the original DRASTIC method. And the high variance of the (ANOVA) F statistic indicated that there was less overlap between the nitrate values in different vulnerability classes. Furthermore, the DRANTHVP method produced a more uniform distribution of vulnerability classes. In short, the DRANTHVP method using the PPDC model was suitable to assess the groundwater vulnerability of porous aquifers to nitrate in the study area. Hence, the mapping of groundwater vulnerability to nitrate can provide a scientific and reasonable basis for the formulation of groundwater resource protection plan.

Evaluation and Prediction of Water Resources Utilization Structure Based on Projection Pursuit Method

All Based on the statistics of water use in the past five years, this paper uses the projection pursuit method to evaluate the rational use of water resources in various provinces and cities in China, and establishes corresponding prediction models for the completion of red line indicators. Perform preliminary statistical analysis on the data, select relevant indicators to establish a projection pursuit evaluation model, and use the genetic algorithm to solve the problem, display the projection values of each province and city on the map, and point out the existing problems. Four of the red line indicators were exponentially fitted and predicted. The final water quality compliance rate did not reach the red line target value of 2030, and the deviation from the target was 13.68%.

Organizational ambidexterity: using project portfolio management to support project-level ambidexterity

The aim of this study is to assess the ability of project portfolio management practices to support the pursuit of ambidexterity at the project level through engagement with specific dimensions and mechanisms. The focus is on examining the operating/business model and challenges that are imposed on the firms, but deemed resolvable through the simultaneous pursuit of multiple projects emphasizing contradictory strategic goals. Data are obtained from multiple exploratory interviews of senior executives involved in project-level activities who were drawn from 12 case organizations in the Middle East. The study finds evidence of four forms of ambidexterity dimensions and mechanisms. Analysis undertaken against operating/business model and challenges of these dimensions and mechanisms of ambidexterity suggests that they are not only inter-related, but do so at various organizational levels.

Principal Components Analysis as enhancement Operator and Compression factor

Principal components analysis (PCA) is effective at compressing information in multivariate data sets by computing orthogonal projections that maximize the amount of data variance. Unfortunately, information content in hyper spectral images does not always coincide with such projections. We propose an application of projection pursuit (pp), which seeks to find a set of projections that are "interesting" in the sense that they deviate from the Gaussian distribution assumption.
 Once these projections are obtained, they can be used for image compression, segmentation, or enhancement for visual analysis. To find these projections, a two –step iterative process is followed where we first search for a projection that maximizes a projection index based on the information divergence of the projections estimated probability distribution from the Gaussian distribution and then reduce the rank by projections the data on to the subspace orthogonal to the previous projection . To calculate each projections, we use a simplified approach to maximizing the projection index, which does not require optimization algorithm. It searches for a solution by obtaining a set of candidate projections from the data and choosing the one with the highest projection index. The effectiveness of the method is demonstrated through simulated examples as well as data from the hyper spectral digital imagery collection experiment and the spatially enhanced broadband and array spectrograph system.

REPPlab: An R package for detecting clusters and outliers using exploratory projection pursuit

The R-package REPPlab is designed to explore multivariate data sets using one-dimensional unsupervised projection pursuit. It is useful as a preprocessing step to find clusters or as an outlier detection tool for multivariate data. Except from the packages tourr and rggobi, there is no implementation of exploratory projection pursuit tools available in R. REPPlab is an R interface for the Java program EPP-lab that implements four projection indices and three biologically inspired optimization algorithms. It also proposes new tools for plotting and combining the results and specific tools for outlier detection. The functionality of the package is illustrated through some simulations and using some real data.

Projection Pursuit Based on Gaussian Mixtures and Evolutionary Algorithms

We propose a projection pursuit (PP) algorithm based on Gaussian mixture models (GMMs). The negentropy obtained from a multivariate density estimated by GMMs is adopted as the PP index to be maximized. For a fixed dimension of the projection subspace, the GMM-based density estimation is projected onto that subspace, where an approximation of the negentropy for Gaussian mixtures is computed. Then, genetic algorithms are used to find the optimal, orthogonal projection basis by maximizing the former approximation. We show that this semiparametric approach to PP is flexible and allows highly informative structures to be detected, by projecting multivariate datasets onto a subspace, where the data can be feasibly visualized. The performance of the proposed approach is shown on both artificial and real datasets. Supplementary materials for this article are available online.

On the optimal solution to maximum margin projection pursuit

Most existing dimensionality reduction methods have been applied as a separable data preprocessing step before classification algorithms. This reduces the flexibility of classification algorithms. To handle this limitation, recently, a novel method, namely maximum margin projection pursuit (MMPP), was developed by simultaneously taking into account dimensionality reduction and classification in the criterion function. MMPP alternatively updates the projection matrix and normal vector of classifications hyperplane by optimizing the min-max problem. This results in the following two problems: (1) It does not guarantee both the convergence of the proposed iterative algorithm in real applications and minimization of the objective function; (2) It heavily depends on learning rate and does not get the global optimal solution. In this paper, we simultaneously solve both the projection matrix and norm vector of classification hyperplane by non-iterative method which not only optimizes the criterion function but also is faster than traditional MMPP algorithm. Furthermore, we extend our method to solve multiclass classification problems. Experiments on the Yale, ORL, AR and COIL20 databases have been conducted to evaluate our method. The results illustrate that, compared with the iterative algorithm, our no-iteration algorithm achieves higher efficiency, more stable recognition, and smaller objective value.

Comprehensive evaluation model for water environment carrying capacity based on VPOSRM framework: A case study in Wuhan, China

Constructing an objective and reasonable evaluation index system was the key to scientifically evaluate the carrying capacity of water environment. The paper proposed a conceptual framework of vigor–pressure–organization-state-resilience-management (VPOSRM) and chose 22 indicators to establish the evaluation index system. The projection pursuit model optimized by quantum genetic algorithm was used to calculate comprehensive evaluating indicators. The results showed that Wuhan's Water Environmental Carrying Capacity (WECC) increased in 2006–2015 and the evaluation grade changed from grade IV unhealthy to grade III health. Through analysis the influence weights of indicators, per capital water resource, the proportion of irrigated area in commonly used cultivated land, water consumption of ten thousand Yuan industrial value-added, percentage of collective disposal of sewage and population density were top 5 indicators that affected Water Environmental Carrying Capacity significantly. By analysis the evaluation results, the improvement of WECC was attributed to the increase of daily sewage treatment capacity in resilience subsystem. The decrease of per capital water resources was the real reason for the change of WECC in 2010–2011. The development of agriculture and industry had put Wuhan city under great pressure for many years.

The Power Transformer Operating Condition Evaluation Based on the Genetic Projection Pursuit Model

Transformer is a key equipment in the power system, and it is very important to accurately evaluate its operating state. In this paper, a new method is proposed to evaluate the operating state of the power transformer based on the genetic projection pursuit model. The proposed method can provide a more objective evaluation result for the health condition of the transformers compared with the traditional methods. Firstly, a three-layer evaluation index system is established with the precautionary test, oil chromatographic analysis and insulating oil properties as the core content. And then, the grading standard of the lowest level index in the indicator system is established. Secondly, the genetic projection pursuit model is used in combination with the grading standard to obtain the intermediate layer evaluation results, which overcomes the disadvantages of the traditional transformer evaluation method which is greatly influenced by subjective factors. Finally, the eigenvalue weighting method is used to integrate the intermediate layer evaluation results to obtain the final result. Case study results show that the evaluation method of transformer operating state based on genetic projection pursuit model is reasonable and effective.

National development through global production networks? The case of Dongguan, China

The wide-ranging implications of globalised production networks (GPNs) for national varieties of capitalism are only now beginning to be broached by political economists and human geographers. As production processes increasingly striate national political territories, an area in need of further research is the impact of GPNs on developing economies’ state architectures — which have historically utilised state-owned or state-directed industries in pursuit of national development projects. The advent of GPNs radically altered the possibilities for such strategies by apparently undermining the ability of developing states to develop national champions — large, vertically integrated firms either nationally owned if not subject to great levels of state control. Does the preponderance of transnational production networks, SMEs, foreign direct investment, and export processing zones entail an end to the significance of national states and politics for development trajectories? Experience suggests otherwise, and a literature is beginning to theorise various forms by which statehood, sovereignty and politics continue to shape GPN-organised manufacturing. The reciprocal interactivity of networks and institutions remains in need of further research, however.This article probes these questions with reference to a detailed case study of the developmental experience of Dongguan city in China between 1978 and 2008. In this period, Dongguan (a major export manufacturing hub on the southern coast) came to the forefront of China's national strategy of export-led industrialisation — but simultaneously crystallised the rise of fragmented production. The city's industrialisation was governed by this contradictory dynamic – on the one hand, GPN-integration transformed its social and political order, while subsequent interventions by the provincial and national states aimed to envelop the city in the institutional framework of China's political economy.

A method for the hazard assessment of regional geological disasters: a case study of the Panxi area, China

ABSTRACT A novel geological hazard assessment model was developed by integrating an analytic hierarchy process (AHP) and a projection pursuit model (PPM) in this study. Remote sensing (RS) and geographic information system (GIS) techniques were also coupled and the hazard risk of the Panxi area in western China was assessed to test the model feasibility. The results show the model coupled with the GIS technique not only enables regional geological hazard risk assessment but also quantitatively visualizes its spatial distribution; and the model is ideally suitable for regional geological hazard risk assessment because it fully considers the subjective and objective factors.

Analysis of influencing factors of Chinese provincial carbon emissions based on projection pursuit model and Markov transfer matrix

Purpose Climate change has aroused widespread concern around the world, which is one of the most complex challenges encountered by human beings. The underlying cause of climate change is the increase of carbon emissions. To reduce carbon emissions, the analysis of the factors affecting this type of emission is of practical significance. Design/methodology/approach This paper identified five factors affecting carbon emissions using the logarithmic mean Divisia index (LMDI) decomposition model (e.g. per capita carbon emissions, industrial structure, energy intensity, energy structure and per capita GDP). Besides, based on the projection pursuit method, this paper obtained the optimal projection directions of five influencing factors in 30 provinces (except for Tibet). Based on the data from 2000 to 2014, the authors predicted the optimal projection directions in the next six years under the Markov transfer matrix. Findings The results indicated that per capita GDP was the critical factor for reducing carbon emissions. The industrial structure and population intensified carbon emissions. The energy structure had seldom impacted on carbon emissions. The energy intensity obviously inhibited carbon emissions. The best optimal projection direction of each index in the next six years remained stable. Finally, this paper proposed the policy implications. Originality/value This paper provides an insight into the current state and the future changes in carbon emissions.

A note on the coefficients of elliptical random variables

It is well-known that the sum of elliptical random variables with constant coefficients is also an elliptical random variable. In this note, we prove that the coefficients can also be random variables, such that the sum of elliptical random variables with random coefficients on a circle is also elliptically distributed. We then examine statistical implications by considering the projection pursuit with the underlying random variables.

Evaluating investment strategies for distribution networks based on yardstick competition and DEA

The traditional investment for distribution networks is mainly evaluated and conducted from the static perspective. A dynamic comprehensive evaluation method is essential to obtain an efficient investment strategy. Firstly, a hierarchical evaluation index system is constructed to describe the overall performance of the distribution network, which includes six types of criteria such as information level, power supply capacity, asset utilization efficiency and economy, power supply quality and loss, power supply reliability, and sustainable development level. Each criterion is composed of input and output indicators. Then, using projection pursuit method considering subjective weight constraints, a combined weight optimization model is proposed to calculate the weight vector of each criterion. Furthermore, the data envelopment analysis (DEA) based dynamic evaluation approach is set up to compute the investment efficiency defined as ratio of output and input. The time degree theory is also introduced to realize dynamic evaluation. Via yardstick competition among multiple regions and “reward and punishment” rule, a precise investment planning strategy can be achieved while minimizing construction cost and maximizing efficiency of the resource allocation. The numerical results on a practical 10-region distribution system in four planning cycles verify the effectiveness of the proposed method.

Bioavailability Evaluation of Dissolved Organic Matter Derived from Compost-Amended Soils.

In this study, hetero-two-dimensional correlation spectroscopy (hetero-2DCOS) combined with parallel factor analysis (PARAFAC) was employed to reveal the inner changes in the dissolved organic matter (DOM) components derived from soil amended with seven different composts. The dynamics of the four DOM components showed that the fluorescence peaks in each component varied in different directions during mineralization. Structural equation models (SEMs) demonstrated that the compost amendments changed the correlations of the total organic carbon (TOC), total nitrogen (TN), and bacterial community composition with DOM components and strengthened the cooperative function related to transformation of DOM components. The compost sources were further ranked as cabbage waste (CW) > chicken manure (CM), dairy cattle manure (DCM), tomato stem waste (TSW), peat (P) > municipal solid waste (MSW), sewage sludge (SS) by projection pursuit regression (PPR) analysis. It is helpful to improve the bioavailability of compost products to obtain composts with a particular function.

Research on optimal decision-making of cloud manufacturing service provider based on grey correlation analysis and TOPSIS

It is of great practical significance to optimise the decision-making of cloud manufacturing service providers, which can ensure the efficient operation of the cloud manufacturing services. In order to effectively optimise, this paper constructs the evaluation index system, sorts out 7 important evaluation indexes. A method is proposed on the basis of the TOPSIS method and Grey Correlation Analysis (GRA), which is a decision-making method combining static distance and dynamic trend, and make the evaluation results more reasonable. In addition, in order to reflect the true weight of the high dimensional index, the evaluation model of projection pursuit index is established. The improved Particle Swarm Optimisation (PSO) algorithm is used to optimise the projection index function and model parameters, and to obtain the objective weights of evaluation indexes. Then the objective weights combine with the subjective weights obtained by the Analytic hierarchy process (AHP), which makes the weights of the evaluation indexes achieve the unity of subjective and objective. Finally, 20 sets of simulation examples are given to illustrate the feasibility and effectiveness of the proposed method.