Statistical Dimension Reduction Research Articles

A new way of environmentally sustainable manufacturing with assessing transformation through the green deployment of Lean Six Sigma projects

Green deployment of Continuous Improvement (CI) projects such as Lean Six Sigma (LSS) is unknown among scholars and practitioners in contrast with green outcomes of LSS. Therefore, the aim of this study is to identify top factors to transform towards the green deployment of LSS projects as an untapped phenomenon for scholars and practitioners. A survey questionnaire was distributed globally to collect the data from LSS practitioners and consultants followed by the Principal Component Analysis (PCA) as a statistical dimension reduction method via Statistical Package for Social sciences (SPSS) software. New dimensions for critical success factors (CSFs), critical failure factors (CFFs) and barriers, and motivators were revealed to recommend top factors for green LSS project deployment. In addition to some factors similar to green LSS integration for green outcomes, we found some new factors suggested for green deployment of LSS projects. However, scarcity was also found in green LSS deployment for practitioners and scholars. Further in-depth studies including case studies could be conducted to assess the negative environmental impact of LSS projects. This study serves as an initial call for managers, consultants and research scholars to favour the sustainable deployment of LSS projects in manufacturing alongside the use of traditional approaches with a focus on costs, quality and delivery. This is the first study exposing the possibility of a paradigm shift in environmental sustainability integration with LSS project deployment in manufacturing operations.

A slice of multivariate dimension reduction

We describe how many dimension reduction strategies are connected conceptually and philosophically, paving the way for a unified approach to multivariate dimension reduction in statistics. Specific methods covered include envelopes, sufficient dimension reduction methods like SIR and SAVE, principal components, principal fitted components, and partial least squares.

Comparison of dimension reduction techniques in the analysis of mass spectrometry data

Abstract. Online analysis with mass spectrometers produces complex data sets, consisting of mass spectra with a large number of chemical compounds (ions). Statistical dimension reduction techniques (SDRTs) are able to condense complex data sets into a more compact form while preserving the information included in the original observations. The general principle of these techniques is to investigate the underlying dependencies of the measured variables by combining variables with similar characteristics into distinct groups, called factors or components. Currently, positive matrix factorization (PMF) is the most commonly exploited SDRT across a range of atmospheric studies, in particular for source apportionment. In this study, we used five different SDRTs in analysing mass spectral data from complex gas- and particle-phase measurements during a laboratory experiment investigating the interactions of gasoline car exhaust and α-pinene. Specifically, we used four factor analysis techniques, namely principal component analysis (PCA), PMF, exploratory factor analysis (EFA) and non-negative matrix factorization (NMF), as well as one clustering technique, partitioning around medoids (PAM). All SDRTs were able to resolve four to five factors from the gas-phase measurements, including an α-pinene precursor factor, two to three oxidation product factors, and a background or car exhaust precursor factor. NMF and PMF provided an additional oxidation product factor, which was not found by other SDRTs. The results from EFA and PCA were similar after applying oblique rotations. For the particle-phase measurements, four factors were discovered with NMF: one primary factor, a mixed-LVOOA factor and two α-pinene secondary-organic-aerosol-derived (SOA-derived) factors. PMF was able to separate two factors: semi-volatile oxygenated organic aerosol (SVOOA) and low-volatility oxygenated organic aerosol (LVOOA). PAM was not able to resolve interpretable clusters due to general limitations of clustering methods, as the high degree of fragmentation taking place in the aerosol mass spectrometer (AMS) causes different compounds formed at different stages in the experiment to be detected at the same variable. However, when preliminary analysis is needed, or isomers and mixed sources are not expected, cluster analysis may be a useful tool, as the results are simpler and thus easier to interpret. In the factor analysis techniques, any single ion generally contributes to multiple factors, although EFA and PCA try to minimize this spread. Our analysis shows that different SDRTs put emphasis on different parts of the data, and with only one technique, some interesting data properties may still stay undiscovered. Thus, validation of the acquired results, either by comparing between different SDRTs or applying one technique multiple times (e.g. by resampling the data or giving different starting values for iterative algorithms), is important, as it may protect the user from dismissing unexpected results as “unphysical”.

A Neural Network Approach to Navigation of a Mobile Robot and Obstacle Avoidance in Dynamic and Unknown Environments

Mobile robot navigation and obstacle avoidance in dynamic and unknown environments is one of the most challenging problems in the field of robotics. Considering that a robot must be able to interact with the surrounding environment and respond to it in real time, and given the limited sensing range, inaccurate data, and noisy sensor readings, this problem becomes even more acute. In this paper, we attempt to develop a neural network approach equipped with statistical dimension reduction techniques to perform exact and fast robot navigation, as well as obstacle avoidance in such a manner. In order to increase the speed and precision of the network learning and reduce the noise, kernel principal component analysis is applied to the training patterns of the network. The proposed method uses two feed-forward neural networks based on function approximation with a back-propagation learning algorithm. Two different data sets are used for training the networks. In order to visualize the robot environment, 180◦ laser range sensor (SICK) readings are employed. The method is tested on real-world data and experimental results are included to verify the effectiveness of the proposed method.

Ordinal Distance Metric Learning with MDS for Image Ranking

Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric [Formula: see text] as [Formula: see text], the problem can be cast as looking for a linear map between two sets of points in different spaces, meanwhile maintaining some data structures. The ordinal relation of the labels can be maintained via classical multidimensional scaling, a popular tool for dimension reduction in statistics. A least squares fitting term is then introduced to the cost function, which can also maintain the local data structure. The resulting model is an unconstrained problem, and can better fit the data structure. Extensive numerical results demonstrate the improvement of the new approach over the linear distance metric learning model both in speed and ranking performance.

A neural network approach to navigation of a mobile robot and obstacle avoidance in dynamic and unknown environments

Mobile robot navigation and obstacle avoidance in dynamic and unknown environments is one of the most challenging problems in the field of robotics. Considering that a robot must be able to interact with the surrounding environment and respond to it in real time, and given the limited sensing range, inaccurate data, and noisy sensor readings, this problem becomes even more acute. In this paper, we attempt to develop a neural network approach equipped with statistical dimension reduction techniques to perform exact and fast robot navigation, as well as obstacle avoidance in such a manner. In order to increase the speed and precision of the network learning and reduce the noise, kernel principal component analysis is applied to the training patterns of the network. The proposed method uses two feed-forward neural networks based on function approximation with a back-propagation learning algorithm. Two different data sets are used for training the networks. In order to visualize the robot environment, 180◦ laser range sensor (SICK) readings are employed. The method is tested on real-world data and experimental results are included to verify the effectiveness of the proposed method.

Selected statistical methods of data analysis for multivariate functional data

Data in the form of a continuous vector function on a given interval are referred to as multivariate functional data. These data are treated as realizations of multivariate random processes. The paper is devoted to three statistical dimension reduction techniques for multivariate data. For the first one, principal components analysis, the authors present a review of a recent paper (Jacques and Preda in, Comput Stat Data Anal, 71:92–106, 2014). For two others one, canonical variables and discriminant coordinates, the authors extend existing works for univariate functional data to multivariate. These methods for multivariate functional data are presented, illustrated and discussed in the context of analyzing real data sets. Each of these techniques is applied on real data set.

Dynamic Analysis Using Gene Expression Post-Kidney Transplantation Resulted in a Set of Molecular Markers for Monitoring Graft Function.

Background. Short-term kidney graft survival after kidney transplantation (KT) has continuously improved in recent years.However, allograft attrition over time remains undiminished mainly due to chronic allograft dysfunction (CAD). Biomarkers for continuing monitoring of graft function and prediction of CAD progression are needed in KT. Material and Methods. A total of 158 deceased donor kidney transplant patients were included (age range: 21-83 years). Three available time point biopsies at pre-implantation, (K1); 3-(K3) and 12-months (K12) post-KT were used for gene expression analysis using microarrays (474 kidney samples) and for the time-course analyses. Probeset summaries were obtained using Robust Multiarray Analyses (RMA) algorithm. Logistic regression models, a method to determine the L1 constraint in order to force the model to the number of estimates within m/10 where m=min(n1,n0) non-zero parameters, were used. Results. Aiming to investigate the time-course genomic of gene expression data from a pre-KT time to continuous post-KT times up to 2-yr, we identified 26 genes that were significantly associated with KT long-term outcomes. CAD at 2-yr post-KT was used as study end-point (defined using graft function and histological findings). We confirmed that many of these 26 genes were related to kidney failure (e.g., lipocalin 2 (LCN2))and renal damage (e.g., interleukin 18 (IL18)) (IPA, Ingenuity Systems, Redwood City, CA). Using a statistical dimension reduction technique, we developed multivariate statistical models on these genes from 3-mo post-KT organ biopsy samples (K3), and then independently tested their prediction performance on samples from different time points: pre-KT (K1) and 12-month post-KT (K12). In these independent predictions, our multi-gene models showed a highly significant and consistent prediction performance for the patient sets at all three time points. In particular, the prediction was highly significant based on the K1 samples for 15 to 22 gene models (Wilcoxon rank sum test p-value<0.01), suggesting that we could predict KT long-term outcomes based on pre-KT biopsy samples from donor organs. Conclusions. Dynamic analysis using gene expression at multiple time points post-KT resulted in a reduced set of markers for monitoring graft function. Moreover, there markers may allow to identify grafts at high risk of chronic allograft dysfunction post-KT.

REGRESSOR DIMENSION REDUCTION WITH ECONOMIC CONSTRAINTS: THE EXAMPLE OF DEMAND SYSTEMS WITH MANY GOODS

Microeconomic theory often yields models with multiple nonlinear equations, nonseparable unobservables, nonlinear cross equation restrictions, and many potentially multicolinear covariates. We show how statistical dimension reduction techniques can be applied in models with these features. In particular, we consider estimation of derivatives of average structural functions in large consumer demand systems, which depend nonlinearly on the prices of many goods. Utility maximization imposes nonlinear cross equation constraints including Slutsky symmetry, and preference heterogeneity yields demand functions that are nonseparable in unobservables. The standard method of achieving dimension reduction in demand systems is to impose strong, empirically questionable economic restrictions such as separability. In contrast, the validity of statistical methods of dimension-reduction such as principal components has not hitherto been studied in contexts like these. We derive the restrictions implied by utility maximization on dimension-reduced demand systems and characterize the implications for identification and estimation of structural marginal effects. We illustrate the results by reporting estimates of the effects of gasoline prices on the demands for many goods, without imposing any economic separability assumptions.

앙상블 접근법을 이용한 반감독 차원 감소 방법

While LDA is a supervised dimension reduction method which finds projective directions to maximize separability between classes, the performance of LDA is severely degraded when the number of labeled data is small. Recently semi-supervised dimension reduction methods have been proposed which utilize abundant unlabeled data and overcome the shortage of labeled data. However, matrix computation usually used in statistical dimension reduction methods becomes hindrance to make the utilization of a large number of unlabeled data difficult, and moreover too much information from unlabeled data may not so helpful compared to the increase of its processing time. In order to solve these problems, we propose an ensemble approach for semi-supervised dimension reduction. Extensive experimental results in text classification demonstrates the effectiveness of the proposed method.

A Comparison of Methods for Classifying Clinical Samples Based on Proteomics Data: A Case Study for Statistical and Machine Learning Approaches

The discovery of protein variation is an important strategy in disease diagnosis within the biological sciences. The current benchmark for elucidating information from multiple biological variables is the so called “omics” disciplines of the biological sciences. Such variability is uncovered by implementation of multivariable data mining techniques which come under two primary categories, machine learning strategies and statistical based approaches. Typically proteomic studies can produce hundreds or thousands of variables, p, per observation, n, depending on the analytical platform or method employed to generate the data. Many classification methods are limited by an n≪p constraint, and as such, require pre-treatment to reduce the dimensionality prior to classification. Recently machine learning techniques have gained popularity in the field for their ability to successfully classify unknown samples. One limitation of such methods is the lack of a functional model allowing meaningful interpretation of results in terms of the features used for classification. This is a problem that might be solved using a statistical model-based approach where not only is the importance of the individual protein explicit, they are combined into a readily interpretable classification rule without relying on a black box approach. Here we incorporate statistical dimension reduction techniques Partial Least Squares (PLS) and Principal Components Analysis (PCA) followed by both statistical and machine learning classification methods, and compared them to a popular machine learning technique, Support Vector Machines (SVM). Both PLS and SVM demonstrate strong utility for proteomic classification problems.

TU‐EE‐A1‐04: Dimension Reduction Analysis of Dose Volume Histogram And Its Potential Application In Predicting Normal Tissue Complication Probability

Purpose: Radiation pneumonitis (RP) is a major concern for patients receiving radiotherapy for lung cancer. The present study assesses the possibility of using multiple dose‐volume‐histogram (DVH) based metrics to predict the likelihood of grade ⩾ 2 RP. MATERIALS AND METHODS: The lung DVH and clinical outcome data from 235 patients were studied. Two linear and four nonlinear statistical dimension reduction analysis methods were applied to the lung DVH to map the data from the original feature space into a 2D or 3D manifold. Then, the question of whether the lung DVH could uniquely predict the likelihood of grade ⩾ 2 RP was mapped to the feasibility of separating the populations with and without RP in the 2D/3D manifold. Results: None of the statistical dimension reduction techniques which preserve the local geometric properties of the original DVH curves was able to clearly separate the patients with and without grade ⩾ 2 RP in the 2D/3D manifold. Among the techniques tested, the Local Tangent Space Alignment (LTSA) performed the best. It could almost reduce the original DVH data into a one dimension manifold. Unfortunately the order the LTSA assigned to the lung DVH curves did show clear correlation with patient RP grades. Conclusions: The dimension reduction analysis like LTSA which preserve the distance information between DVH curves can be useful in characterizing the complexity of patient DVH data from a lung toxicity study. The lack of clear segmentation between the grade ⩾ 2 RP patients and other patients in the dimension‐reduced manifold indicates that using lung DVH data only can not generate a satisfactory result in predicting the occurrence of grade ⩾ 2 RP among the lung cancer patients after 3D‐CRT radiotherapy treatment.This work was partially funded by NIH grants R01 CA69579 and R01 CA115748.

High-Frequency Market Risk Scenarii By Independent Component Analysis: Method and Application

The literature on risk has focused in the last years on the use of intra-day data for better measurement of financial risk (see Dacorogna et al., 2001), asset pricing and asset allocation (see Bollerslev and Zhang, 2003). By extracting the common factors from the high-frequency series, it is also possible to formulate stress tests for market risk. The possibility of reducing the number of scenarii through the use of statistical dimension reduction methods is proposed in Loretan (1997), using a Principal Component Analysis. A loss in information may be entailed by the linear filter of the PCA when high-frequency data is considered, as non-linearities and non-gaussianities are specific features of this type of data (see for instance Voit, 2003). The Independent Component Analysis (see Hyvarinen et al., 2001), as mentioned by Back and Weigend (1997) in a financial context, is more appropriate when non-linearity and non-normality are at stake. Using high-frequency data on the French Stock Market, we evaluate this technique for generating scenario for accurate Value-at-Risk computations. Various methods for specifying stress scenarii are discussed, compared to other published results (see Giot and Laurent, 2004), and classical tests of rejection (Kupiec, 1995; Christoffersen and Pelletier, 2003) are presented

Approximate importance sampling Monte Carlo for data assimilation

Importance sampling Monte Carlo offers powerful approaches to approximating Bayesian updating in sequential problems. Specific classes of such approaches are known as particle filters. These procedures rely on the simulation of samples or ensembles of the unknown quantities and the calculation of associated weights for the ensemble members. As time evolves and/or when applied in high-dimensional settings, such as those of interest in many data assimilation problems, these weights typically display undesirable features. The key difficulty involves a collapse toward approximate distributions concentrating virtually all of their probability on an implausibly few ensemble members. After reviewing ensembling, Monte Carlo, importance sampling and particle filters, we present some approximations intended to moderate the problem of collapsing weights. The motivations for these suggestions are combinations of (i) the idea that key dynamical behavior in many systems actually takes place on a low dimensional manifold, and (ii) notions of statistical dimension reduction. We illustrate our suggestions in a problem of inference for ocean surface winds and atmospheric pressure. Real observational data are used.

Dimension reduction and spatiotemporal regression: Applications to neuroimaging

One method for characterizing spatiotemporal variation in brain activity levels is based on the use of statistical dimension reduction. This reduction finds temporal components in data that best preserve the spatiotemporal regression structure. The method does this by suppressing more prominent waveforms that do not vary in a spatially predictable pattern.

Using principal component analysis and self-organizing map to estimate the physical quality of cathode copper

The growing interest in utilising multivariable statistical dimension reduction techniques, PCA and PLS, and neural networks in process monitoring and analysis has resulted in a number of successful industrial applications. This paper describes a process study on the effects of the chemical quality of the anodes on the physical quality of produced cathodes at a copper electrorefining plant through PCA, SOM and a combination of these two techniques. The clustering of anode analysis data over time was compared with the physical quality data of the cathodes.

Damage identification using multivariate statistics: Kernel discriminant analysis

This paper is part of a series which illustrates how modern methods of multivariate statistics can be used to solve, or illuminate, damage identification problems. The technique discussed here is Kernel Discriminant Analysis (KDA), which can be used to assign damage classifications to measured data vectors. The data discussed is experimental data from a ball bearing system in an undamaged state and in four damage states. The classifiers are trained on the data after an initial pre-processing stage and also after a further statistical dimension reduction. The results from KDA are compared with a benchmark statistical method and with a neural network classifier.