Projection Pursuit Research Articles

How are you doing, really? Personal project pursuit and human flourishing.

How are you doing, really? Personal project pursuit and human flourishing.

Projection pursuit algorithms to detect outliers

In this paper, we compare the methods proposed by Peña and Prieto (2001), and Filzmoser, Maronna, and Werner (2008) to detect outliers in a set of Argentine companies that quote their shares in the Stock Exchange. A significant heterogeneity between observations can be a consequence of the presence of outliers. The detection of outliers is an important task for the statistical analysis since they distort descriptive measures and parameters estimators. There are different multivariate methods to detect outliers, such as distance-based methods and projection pursuit methods.

A Low Complexity, High Throughput DoA Estimation Chip Design for Adaptive Beamforming

Direction of Arrival (DoA) estimation is essential to adaptive beamforming widely used in many radar and wireless communication systems. Although many estimation algorithms have been investigated, most of them focus on the performance enhancement aspect but overlook the computing complexity or the hardware implementation issues. In this paper, a low-complexity yet effective DoA estimation algorithm and the corresponding hardware accelerator chip design are presented. The proposed algorithm features a combination of signal sub-space projection and parallel matching pursuit techniques, i.e., applying signal projection first before performing matching pursuit from a codebook. This measure helps minimize the interference from noise sub-space and makes the matching process free of extra orthogonalization computations. The computing complexity can thus be reduced significantly. In addition, estimations of all signal sources can be performed in parallel without going through a successive update process. To facilitate an efficient hardware implementation, the computing scheme of the estimation algorithm is also optimized. The most critical part of the algorithm, i.e., calculating the projection matrix, is largely simplified and neatly accomplished by using QR decomposition. In addition, the proposed scheme supports parallel matches of all signal sources from a beamforming codebook to improve the processing throughput. The algorithm complexity analysis shows that the proposed scheme outperforms other well-known estimation algorithms significantly under various system configurations. The performance simulation results further reveal that, subject to a beamforming codebook with a 5° angular resolution, the Root Mean Square (RMS) error of angle estimations is only 0.76° when Signal to Noise Ratio (SNR) = 20 dB. The estimation accuracy outpaces other matching pursuit based approaches and is close to that of the classic Estimation of Signal Parameters Via Rotational Invariance Techniques (ESPRIT) scheme but requires only one fifth of its computing complexity. In developing the hardware accelerator design, pipelined Coordinate Rotation Digital Computer (CORDIC) processors consisting of simple adders and shifters are employed to implement the basic trigonometric operations needed in QR decomposition. A systolic array architecture is developed as the computing kernel for QR decomposition. Other computing modules are also realized using various linear systolic arrays and chained together seamlessly to maximize the computing throughput. A Taiwan Semiconductor Manufacturing Company (TSMC) 40 nm CMOS process was chosen as the implementation technology. The gate count of the chip design is 454.4k, featuring a core size of 0.76 mm 2 , and can operate up to 333 MHz. This suggests that one DoA estimation, with up to three signal sources, can be performed every 2.38 μs.

Experimental Design for Optimization of Orthogonal Projection Pursuit Models

Bayesian optimization and kernelized bandit algorithms are widely used techniques for sequential black box function optimization with applications in parameter tuning, control, robotics among many others. To be effective in high dimensional settings, previous approaches make additional assumptions, for example on low-dimensional subspaces or an additive structure. In this work, we go beyond the additivity assumption and use an orthogonal projection pursuit regression model, which strictly generalizes additive models. We present a two-stage algorithm motivated by experimental design to first decorrelate the additive components. Subsequently, the bandit optimization benefits from the statistically efficient additive model. Our method provably decorrelates the fully additive model and achieves optimal sublinear simple regret in terms of the number of function evaluations. To prove the rotation recovery, we derive novel concentration inequalities for linear regression on subspaces. In addition, we specifically address the issue of acquisition function optimization and present two domain dependent efficient algorithms. We validate the algorithm numerically on synthetic as well as real-world optimization problems.

Projection pursuit random forest using discriminant feature analysis model for churners prediction in telecom industry

A major and demanding issue in the telecommunications industry is the prediction of churn customers. Churn describes the customer who is attrite from one Telecom service provider to competitors searching for better services offers. Companies from the Telco sector frequently have customer relationship management offices it is the main objective in how to win back defecting clients because preserve long-term customers can be much more beneficial to a company than gain newly recruited customers. Researchers and practitioners are paying great attention and investing more in developing a robust customer churn prediction model, especially in the telecommunication business by proposed numerous machine learning approaches. Many approaches of Classification are established, but the most effective in recent times is a tree-based method. The main contribution of this research is to predict churners/non-churners in the Telecom sector based on project pursuit Random Forest (PPForest) that uses discriminant feature analysis as a novelty extension of the conventional Random Forest approach for learning oblique Project Pursuit tree (PPtree). The proposed methodology leverages the advantage of two discriminant analysis methods to calculate the project index used in the construction of PPtree. The first method used Support Vector Machines (SVM) as a classifier in the construction of PPForest to differentiate between churners and non-churners customers. The second method is a Linear Discriminant Analysis (LDA) to achieve linear splitting of variables node during oblique PPtree construction to produce individual classifiers that are robust and more diverse than classical Random Forest. It found that the proposed methods enjoy the best performance measurements e.g. Accuracy, hit rate, ROC curve, Gini coefficient, Kolmogorov-Smirnov statistic and lift coefficient, H-measure, AUC. Moreover, PPForest based on direct applied of LDA on the raw data delivers an effective evaluator for the customer churn prediction model.

Motion similarity comprehensive evaluation of humanoid robot arm based on dynamic comprehensive evaluation method

The purpose of this paper is to propose a suitable comprehensive evaluation method for motion similarity comprehensive evaluation of humanoid robot. Different humanoid robot operation tasks with different complexity degree were selected. The indexes of humanoid robot arm motion were used in the fields of robotics and ergonomics. A static comprehensive evaluation model was established based on the projection pursuit evaluation method. However, the static evaluation model is only suitable for single time point evaluation without the time dimension. A dynamic comprehensive evaluation method, based on the projection pursuit evaluation method with information entropy and time degrees, was proposed by linearly weighting the index weight of the static model at each time point according to the timing-weighted vectors. The comparison between the motion similarity comprehensive evaluation results obtained from the static and the dynamic comprehensive evaluation models demonstrated that the similarity in motion based on the dynamic comprehensive evaluation model is higher. The comparison of the reliability, similarity, and dispersion between the static and the dynamic comprehensive evaluation models showed that the dynamic comprehensive evaluation result had better accuracy, stability, and lower dispersion, and the result was more reasonable and credible. Therefore, the dynamic comprehensive evaluation method proposed in this paper is more suitable for the motion similarity comprehensive evaluation of humanoid robot arm.

Research on Dynamic Comprehensive Evaluation of Resource Allocation Efficiency of Technology Innovation in the Aerospace Industry

From the perspective of input and output, this paper constructs an evaluation index system for the status quo of technology innovation resource allocation in China’s aerospace industry. Taking the industrial panel data of 20 provincial regions from 2007 to 2016 in China as samples, this paper uses the stochastic frontier method, which is improved by the projection pursuit model based on accelerated genetic algorithm, to analyze the factors influencing the allocation efficiency of technology innovation resource in the aerospace industry and then make a static evaluation for the current situation. In addition, based on the perspective of velocity characteristics, this study uses the dynamic comprehensive evaluation model to evaluate the resource allocation of technology innovation in the aerospace industry. The empirical research shows that the resource allocation efficiency of technology innovation in the aerospace industry is generally at the lower middle level, indicating an unbalanced trend of “reverse” allocation with the level of regional economic development. It is also found that the efficiency improvement effect in recent years is not obvious. At last, based on the study’s findings, some countermeasures and suggestions are put forward to improve the current situation.

Data projections by skewness maximization under scale mixtures of skew-normal vectors

Multivariate scale mixtures of skew-normal distributions are flexible models that account for the non-normality of data by means of a tail weight parameter and a shape vector representing the asymmetry of the model in a directional fashion. Its stochastic representation involves a skew-normal vector and a non negative mixing scalar variable, independent of the skew-normal vector, that injects tail weight behavior into the model. In this paper we look into the problem of finding the projection that maximizes skewness for vectors that follow a scale mixture of skew-normal distribution; when a simple condition on the moments of the mixing variable is fulfilled, it can be shown that the direction yielding the maximal skewness is proportional to the shape vector. This finding stresses the directional nature of the shape vector to regulate the asymmetry; it also provides the theoretical foundations motivating the skewness based projection pursuit problem in this class of distributions. Some examples that illustrate the application of our results are also given; they include a simulation experiment with artificial data, which sheds light on the usefulness and implications of our results, and the application to real data.

Application of Projection Pursuit Model to Water Resources Carrying Capacity Assessment in Longitudinal Ridge-gorge Region of Yunnan

Water resources carrying capacity (WRCC) assessment is an effective way to evaluate the coordinated development of water resources, economic society and ecological environment, thus, it is significant to study WRCC to realize the harmony among water resources, economy and society in region. In this paper, an index system for evaluating WRCC was constructed from the perspective of water quantity and water quality. Moreover, the projection pursuit technique was applied to evaluate WRCC. Based on the grade division standard of WRCC, the projection function which could reflect the variability of the WRCC was constructed, and genetic algorithm was introduced to optimize the function and seek the optimum projection vector, while the projection pursuit model to evaluation of WRCC was built by the data of the vector. WRCC of the 80 counties in Longitudinal Ridge-gorge Region of Yunnan was evaluated by this model, and the results which accord with the fact were gained. The result showed that WRCC is dynamic with evaluation index value was presented as the logistic curve. The WRCC in research region was good overall, but that in three counties and four counties was already in overload and nearly overload, respectively. Potential of WRCC in mid and western of research region was higher than the other area. The evaluation results were given with continuous real number, which could reveal the temporal-spatial change characteristics of WRCC accurately. Evaluation model of WRCC based on projection pursuit model was practical and feasible for dynamic evaluation of regional WRCC.

Modern Monetary Theory: Some Additional Dimensions

The objective of this paper is to examine the foundations of Modern Monetary Theory (MMT) by building upon the individual papers in this issue of the Atlantic Economic Journal by Mark Skousen and Patrick Newman. The foundations of MMT include five cornerstones. First, sovereign governments that are the sole supplier of a national currency (e.g., United States) can issue as much currency as they want, have unlimited ability to fulfill promised future payments, and cannot go bankrupt. Second, legislation enables spending while taxes neither place a limit nor specify government spending (earmarked taxes would be an exception). Third, a sovereign government can borrow as much as it likes in pursuit of laudable public sector projects or fiscal policy programs to manage the economic cycle. Fourth, a huge and growing national debt is beneficial to the economy as long as inflation remains contained. A fifth feature, the blogosphere, shaped the emergence of MMT largely in the absence of technical vetting and critical empirical examination. The popularization derived for MMT through the blogosphere will have a profound effect on U.S. politics and economic policy in the 2020s and 2030s. The foundations of MMT are refuted by the work of public finance theorists David Ricardo, James Buchanan, Robert Barro, and Alberto Alesina.

A Decision-Making Model Under Probabilistic Linguistic Circumstances with Unknown Criteria Weights for Online Customer Reviews

Online customer reviews (OCRs) provide much information about products or service, but the mass of information increases the difficulty for customers to make decisions. Thus, we establish a multi-criteria decision making (MCDM) model to evaluate products or service. To analyze OCRs, the sentiment analysis (SA) is introduced to identify the sentiment orientation of reviews. Considering that the textual information in OCRs is linguistic information, probabilistic linguistic term sets (PLTSs) are applied to present the results of the SA. A process of extracting probabilistic linguistic information based on SA from OCRs is also presented. Then, for the MCDM problems with unknown criteria weights, we combine the PP (projection pursuit) method and the MULTIMOORA (multiplicative multi-objective optimization by ratio analysis) method, and develop an extended method (named as the PP-MULTIMOORA method). The projection pursuit (PP) method is developed to derive objective criteria weights and the MULTIMOORA method is to derive final rankings of products or service. Finally, we apply the proposed model to a case of evaluating doctors’ service quality and further conduct a comparative analysis to illustrate the effectiveness of our work.

Abstract TP417: An Autoregulation-Derived Prediction Model for Midline Shift After Ischemic Stroke

Introduction: Identification of patients likely to develop midline shift (MLS) after large-vessel occlusion (LVO) stroke is essential for appropriate triage and patient disposition. Studies have identified clinical and radiographic predictors of MLS, but with limited accuracy. Using an innovative assessment of cerebral autoregulation, we sought to develop an accurate predictive model for MLS. Methods: We prospectively enrolled 73 patients with LVO stroke. Beat-by-beat cerebral blood flow (transcranial Doppler) and arterial pressure (arterial catheter or finger photoplethysmography) were recorded within 24 hours of the stroke, and a 24-hour brain MRI was obtained to determine infarct volume and MLS. Autoregulatory function was quantified from pressure-flow relation via projection pursuit regression (PPR), allowing for characterization of 5 hemodynamic markers (Figure 1A). We assessed the predictive relation of autoregulatory capacity and radiological and clinical variables to MLS using recursive classification tree models. Results: PPR successfully quantified autoregulatory function in 50/73 (68.5%) patients within 24 hours of LVO ischemic stroke (age 63.9±13.6, 66% F, NIHSS 15.8±6.7). Of these 50 patients, most (78%) underwent endovascular therapy. Thirteen (26%) experienced 24-h MLS; in these patients, infarct volumes were larger (140.2 vs. 48.6 mL, P<0.001 ), and ipsilateral (but not contralateral) falling slopes were steeper (1.1 vs. 0.7 cm·s -1 ·mmHg -1 , P=0.001 ). Among all clinical, demographic, and hemodynamic variables, only two (infarct volume, ipsilateral falling slope) significantly contributed to prediction of MLS (accuracy 94%; Figure 1B). Conclusions: This predictive model of MLS wields translatable potential for triaging level of care in patients suffering from LVO ischemic stroke, but further research, including optimization of the PPR algorithm as well as prospective use of the predictive model, is needed.

Using tours to visually investigate properties of new projection pursuit indexes with application to problems in physics

Projection pursuit is used to find interesting low-dimensional projections of high-dimensional data by optimizing an index over all possible projections. Most indexes have been developed to detect departure from known distributions, such as normality, or to find separations between known groups. Here, we are interested in finding projections revealing potentially complex bivariate patterns, using new indexes constructed from scagnostics and a maximum information coefficient, with a purpose to detect unusual relationships between model parameters describing physics phenomena. The performance of these indexes is examined with respect to ideal behaviour, using simulated data, and then applied to problems from gravitational wave astronomy. The implementation builds upon the projection pursuit tools available in the R package, tourr, with indexes constructed from code in the R packages, binostics, minerva and mbgraphic.

Unsupervised classification of specialty coffees in Homogeneous sensory attributes through machine learning

Brazil is the largest exporter of coffee beans, 29% world exports, 15% this volume in specialty coffees. Thereby researches are done, so that identify different segments in the market, in order to direct the end consumer to a better quality product. New technologies are explored to meet an increasing demand for high quality coffees. Therefore, in this article has an objective to propose the use of machine learning techniques combined with projection pursuit in the construction of unsupervised classification models, in a sensory acceptance experiment, applied to four groups of trained and untrained consumers, in four classes of specialty coffees in which they were evaluated sensory characteristics: aroma, body coffee, sweetness and general note. For evaluating classifier performance, in the data with reduced dimension, all instances were used, and considering four groupings, the models were adjusted. The results obtained from the groupings formed were compared with pre-established classes to confirm the model. Success and error rates were obtained, considering the rate of false positives and false negatives, sensitivity and classification methods accuracy. It was concluded that, machine learning use in data with reduced dimensions is feasible, as it allows unsupervised classification of specialty coffees, produced at different altitudes and processes, considering the heterogeneity among consumers involved in sensory analysis, and the high homogeneity of sensory attributes among the analyzed classes, obtaining good hit rates in some classifiers. Key words: Classification models; Data dimension reduction; Groupings identification; Projection pursuit.

An Evolutionary Distributed Framework for Projection Pursuit

Abstract Projection Pursuit is a methodology for deriving meaningful low-dimensional representations of data. It generally aims at extracting features as linear combinations of the original attributes, under an algorithm which optimizes a function that quantifies the interestingness of the projection. The current paper builds on our previous research, extending an algorithmic framework based on evolutionary algorithms in two directions: at its roots a one-dimensional PP framework, we enhance it with two-dimensional search capabilities providing meaningful planar views (rotations) of the data; moreover, we provide a distributed implementation under Apache Spark. The distributed implementation is not meant only to deal with large data, but also to exploit the inherent parallelism of the evolutionary paradigm, enhancing the efficiency of the method not only when run on a cluster, but also on a single machine, exploiting the existing virtual CPUs. Several case studies illustrate the applicability of our framework and demonstrate its efficiency.

Principal Component Analysis and Mapping to Characterize the Emission of Volatile Organic Compounds in a Typical Petrochemical Industrial Park

ABSTRACT The petrochemical industry generates a notorious amount of VOC pollution. Given the vastness and complexity of this particular industry as well as dissimilarities between the sectors and companies, comprehensively understanding and controlling these VOC emissions is a challenge in many countries. This study demonstrates an approach of characterizing and identifying critical sources by using multivariate analysis, including principal component analysis (PCA) and projection pursuit. A representative petrochemical industrial park in southern Taiwan comprising 20 up-, mid-, and downstream companies and 519,442 emission sources from 2012 till 2014 was selected for analysis. The results indicated that although the total emissions decreased during this period, which was attributable to controlling upstream vendors (65.5–72.1% of the total emission) and larger sources, such as equipment components (ECs; 63.5% of the total emission in 2012, which decreased to 59.3% in 2014), significant emissions were associated with the mid- and downstream companies and other sources, such as cooling towers (CTs) and storage tanks. PCA revealed that the sources in 5 PCs—namely, in decreasing importance, storage tanks, CTs, ECs, wastewater treatment plants, and stacks—explained 88.7% of the data variability. Furthermore, the variance in emission exhibited stronger correlations with the mid- and downstream sectors than their upstream counterpart. In addition to the amount of emissions they produce, key sources that must be controlled in order to effectively reduce VOCs in the petrochemical industry may be indicated by the correlation among their emission variations.

High-dimensional data visualisation with the grand tour

In physics we often encounter high-dimensional data, in the form of multivariate measurements or of models with multiple free parameters. The information encoded is increasingly explored using machine learning, but is not typically explored visually. The barrier tends to be visualising beyond 3D, but systematic approaches for this exist in the statistics literature. I use examples from particle and astrophysics to show how we can use the “grand tour” for such multidimensional visualisations, for example to explore grouping in high dimension and for visual identification of multivariate outliers. I then discuss the idea of projection pursuit, i.e. searching the high-dimensional space for “interesting” low dimensional projections, and illustrate how we can detect complex associations between multiple parameters.

Coupling Coordination Degree of Government Support, Financial Support and Innovation and its Impact on Economic Development

This paper reveals the coupling mechanism of government support, financial support, and innovation. Using panel data from 28 provinces in China from 2007 to 2016 as a research sample, the coupling coordination degree model is used to measure the coupling coordination degree of government support, financial support, and innovation, and the empirical analysis of its relationship with economic development is conducted through projection pursuit model, static panel data model and dynamic panel data model. The main results show that: (1) The coupling coordination degree of government support, financial support, and innovation in the eastern, central, and western region is on the rise, but there are large differences between regions. (2) The coupling coordination degree of government support, financial support, and innovation has a significant positive impact on economic development, and there are regional differences in its role in promoting economic development. That is, the coupling coordination degree of government support, financial support, and innovation has significantly promoted the economic development of the eastern region, but has no significant impact on the economic development of the central and western region.

Research on the evaluation of the resilience of subway station projects to waterlogging disasters based on the projection pursuit model.

To improve sustainable development, increasingly more attention has been paid to the evaluation of the resilience to waterlogging disasters. This paper proposed a projection pursuit model (PPM) improved by quantum particle swarm optimization (QPSO) for the evaluation of the resilience of subway station projects to waterlogging disasters. In view of the lack of research results related to the evaluation of the resilience of subway station projects to waterlogging disasters, 16 secondary indicators that affected the ability of subway station projects to recover from waterlogging disasters were identified from defense, recovery, and adaptability, for the first time. A PPM improved by QPSO was then proposed to effectively deal with the high-dimensional data about the resilience of subway station projects to waterlogging disasters. The QPSO was used to solve the best projection vector of the PPM, and interpolation algorithm was used to construct the mathematical model of evaluation. Finally, four station projects of Chengdu Metro Line 11 in China were selected for a case study analysis. The case study revealed that, among the secondary indicators, the emergency plan of construction order, the exercise frequency of emergency plans, and relief supplies had the greatest weights. The recovery was found to be the most important in the primary indicators. The values of the resilience of Lushan Avenue Station, Miaoeryan Station, Shenyang Road Station, and Tianfu CBD North Station to waterlogging disasters were found to be 2, 1.6571, 2.8318, and 3 respectively. This resilience ranking was consistent with the actual disaster situation in the flood season of 2019. In addition, the case study results showed that QPSO had the advantages of fewer parameter settings and a faster convergence speed as compared with PSO and the genetic algorithm.

Research on Chinese well-known e-commerce enterprises' innovation ability based on real comment

Based on the real comments from Jingdong Mall, T-mall and other e-commerce platforms as for the data resource, according to analysis to the customers' online shopping comments' vocabularies, obtained 11 indicators which are constituted e vocabularies, obtained 11 indicators which are constituted e-commerce platform customer satisfaction index system and the satisfaction indicator value, using projection pursuit model (PPM) and genetic algorithms to make a further calculation to satisfaction indicators. The results show that: which has the greatest impact on e-commerce platforms' overall satisfaction is the product reputation and popularity; Jingdong Mall has the best overall satisfaction among Jingdong Mall, T-mall, and Amazon this three e-commerce platforms. Meanwhile, each ecommerce platforms has its own superiority and own superiority and weakness.