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Principal components analysis (PCA) is one of the foremost multivariate methods utilized in marketing and business research for data reduction, latent variable modeling, multicollinearity resolution, etc. However, while its optimal properties make PCA solutions unique, interpreting the results of such analyses can be problematic. A plethora of rotation methods are available for such interpretive uses, but there is no theory as to which rotation method should be applied in any given social science problem. In addition, different rotational procedures typically render different interpretive results. The paper aims to introduce restricted PCA (RPCA), which attempts to optimally derive latent components whose coefficients are integer‐constrained (e.g.: {−1,0,1}, {0,1}, etc.).

The paper presents two algorithms for deriving efficient solutions for RPCA: an augmented branch and bound algorithm for sequential extraction, and a combinatorial optimization procedure for simultaneous extraction of these constrained components. The paper then contrasts the traditional PCA‐derived solution with those obtained from both proposed RPCA procedures with respect to a published data set of psychographic variables collected from potential buyers of the Dodge Viper sports car.

This constraint results in solutions which are easily interpretable with no need for rotation. In addition, the proposed procedure can enhance data reduction efforts since fewer raw variables define each derived component.

The paper provides two algorithms for estimating RPCA solutions from empirical data.

This paper seeks to present an integrated principal component analysis (PCA) data envelopment analysis (DEA) framework for assessment and ranking of manufacturing systems based on equipment performance indicators.

The integrated framework discussed in this paper is based on PCA and DEA. The validity of the integrated model is further verified and validated by numerical taxonomy (NT) methods.

The results of the integrated PCA DEA framework show the ranking of sectors and weak and strong points of each sector with regard to equipment and machinery. Moreover, a non‐parametric correlation method, namely, Spearman correlation experiment shows high level of correlation among the findings of PCA, DEA and NT. Furthermore, it identifies which indicators have major impacts on the performance of manufacturing sectors.

To achieve the objectives of this study, a comprehensive study was conducted to locate all economic and technical indicators which influence equipment performance. These indicators are related to equipment productivity, efficiency, effectiveness and profitability. Standard factors such as down time, time to repair, mean time between failure, operating time, value added and production value were considered as shaping factors. The manufacturing sectors are selected according to the format of International Standard for Industrial Classification.

The modeling approach of this paper could be used for ranking and analysis of other sectors in particular or countries in general.

Portfolio optimization is the process of making an investment decision on a set of assets to realize high returns with low risk. It has three major stages: asset selection, asset weighting and asset management. Asset selection is an important phase because it influences asset allocation and ultimately affects the returns of a portfolio. Today, there is an increase in the number of listings on a stock exchange. Therefore, it is important for an investor to screen and select stocks for investment. This study focuses on the first stage of the portfolio optimization problem, namely, asset selection. The purpose of this study is to evaluate and select profitable stocks quoted on National Stock Exchange (NSE) for portfolio optimization.

Financial ratios are considered as the input and output parameters for evaluating the financial performance of the firms. This study adopts a hybrid principal component analysis (PCA) and data envelopment analysis (DEA) approach to evaluate the efficiency of the firms. Based on the efficiency scores, the firms are selected for the investment process.

The model helps to determine the relative efficiencies of the firms. The efficient firms are considered to be the potential stocks for investment. It helps the investors to screen the stocks from a large number of stocks quoted on NSE.

One of the limitations of the standard DEA model is that it fails to discriminate the firms when the number of input and output parameters are larger than the number of firms. To overcome this problem, either a parameter can be ignored or weight-restricted DEA can be applied. When an input/output parameter is dropped, the information in that variable is lost. Weight-restricted DEA model uses expert opinion for measuring the relative importance of input and output parameters. Expert opinion is subjective and might be biased. The PCA-DEA model helps to identify the efficient firms by improving the discriminatory power of standard DEA without any loss of information and without the need for expert opinion, which might be biased.

Asset selection is an important stage in the investment process. Selection of stocks based on the efficiency score is an easier option available to the investors. But the misclassification of firms either due to biased expert opinion or discrimination inability of DEA can be costly to an investor. The PCA-DEA model overcomes both these limitations. Investors can select the potential candidates for asset allocation based on the efficiency scores obtained using the PCA-DEA model. Further, the relative efficiencies obtained can help the firms to benchmark their performance against the best performing firms within their industry.

This paper is one of few papers to adopt the PCA-DEA framework to select stocks in the Indian stock market.

The purpose of this paper is to propose a gait analysis technique that aims to identify differences and similarities in gait performance between three different assistive devices (ADs).

Two feature reduction techniques, linear principal component analysis (PCA) and nonlinear kernel-PCA (KPCA), are expanded to provide a comparison of the spatio-temporal, symmetrical indexes and postural control parameters among the three different ADs. Then, a multiclass support vector machine (MSVM) with different approaches is designed to evaluate the potential of PCA and KPCA to extract relevant gait features that can differentiate between ADs.

Results demonstrated that symmetrical indexes and postural control parameters are better suited to provide useful information about the different gait patterns that total knee arthroplasty (TKA) patients present when walking with different ADs. The combination of KPCA and MSVM with discriminant functions (MSVM DF) resulted in a noticeably improved performance. Such combination demonstrated that, with symmetric indexes and postural control parameters, it is possible to extract with high-accuracy nonlinear gait features for automatic classification of gait patterns with ADs.

The information obtained with the proposed technique could be used to identify benefits and limitations of ADs on the rehabilitation process and to evaluate the benefit of their use in TKA patients.

The purpose of this paper is to present an integrated algorithm composed of data envelopment analysis (DEA), corrected ordinary least squares (COLS) and principal component analysis (PCA) to estimate efficiency scores of electricity distribution units.

Several DEA and COLS models are prescribed and their results are verified and validated by the algorithm. To calculate efficiency scores, three standard internal consistency conditions between DEA and COLS results are checked by the algorithm. If these conditions are satisfied, DEA is chosen as the superior model because it could be used for optimization as well. Otherwise, the geometric mean of DEA and COLS model is used as the final efficiency scores.

The algorithm of this paper may be easily applied to decision‐making units because of its robustness (combined DEA‐COLS input and output) and validity gained through PCA.

The integrated approach has several unique features which are: verification and validation mechanism by PCA, consideration of internal consistency conditions between DEA and COLS and consolidation of DEA and COLS for improved ranking given consistency conditions are violated.

Most quality management researchers make inadequate use of statistical techniques, especially multivariate statistical methods. Applies two multivariate analysis techniques, principal component analysis (PCA) and correspondence analysis (CA), to analyse potential barriers to total quality management (TQM) implementation in Hong Kong’s service and manufacturing industries. Describes and demonstrates the applicability of these techniques as analysis tools for quality researchers and practitioners. Conducts PCA on a set of survey data and produces four orthogonal dimensions to potential barriers to TQM implementation, then applies CA in order to corroborate the findings of PCA. In addition, CA provides a simultaneous graphical representation of the data organized under different categories which shows how the potential barriers relate to one another and to the different types of industry.

This paper extends the authors’ previous research work investigating resilience for municipal infrastructure from an asset management perspective. Therefore, this paper aims to formulate a pavement resilience index while incorporating asset management and the associated resilience indicators from the authors’ previous research work.

This paper introduces a set of holistic-based key indicators that reflect municipal infrastructure resiliency. Thenceforth, the indicators were integrated using the weighted sum mean method to form the proposed resilience index. Resilience indicators weights were determined using principal components analysis (PCA) via IBM SPSS®. The developed framework for the PCA was built based on an optimization model output to generate the required weights for the desired resilience index. The output optimization data were adjusted using the standardization method before performing PCA.

This paper offers a mathematical approach to generating a resilience index for municipal infrastructure. The statistical tests conducted throughout the study showed a high significance level. Therefore, using PCA was proper for the resilience indicators data. The proposed framework is beneficial for asset management experts, where introducing the proposed index will provide ease of use to decision-makers regarding pavement network maintenance planning.

The resilience indicators used need to be updated beyond what is mentioned in this paper to include asset redundancy and structural asset capacity. Using clustering as a validation tool is an excellent opportunity for other researchers to examine the resilience index for each pavement corridor individually pertaining to the resulting clusters.

This paper provides a unique example of integrating resilience and asset management concepts and serves as a vital step toward a comprehensive integration approach between the two concepts. The used PCA framework offers dynamic resilience indicators weights and, therefore, a dynamic resilience index. Resiliency is a dynamic feature for infrastructure systems. It differs during their life cycle with the change in maintenance and rehabilitation plans, systems retrofit and the occurring disruptive events throughout their life cycle. Therefore, the PCA technique was the preferred method used where it is data-based oriented and eliminates the subjectivity while driving indicators weights.

The purpose of this paper is to present results of shape analysis of female torso shape using the discrete cosine transform (DCT) from a three-dimensional (3D) whole body scan database.

Torso shape is a central part of body shape and difficult to describe by linear measurements. In order to analyze body shape variation within a population the authors employed a DCT-based shape description method to compresses a dense 3D body scan surface into a small vector that preserves shape and removes size. The DCT-based shape descriptors of torso surfaces are further fed to principal component analysis (PCA) that decompose shape variation into constituent shape components. A visualization program was developed to observe principal components of torso shape and interpret their meanings.

Extreme shapes of the first ten principal components summarize major shape variations and identify shapes that are difficult to capture with traditional anthropometric measurements. PCA results also help to find and retrieve similar shapes from a population-level database.

Using the DCT for PCA of torso shape is a unique and original approach. It provides a basis for the description and classification of torso shape in 3D and the results from the shape analysis are potentially useful for designers of clothing and personal protective equipment.

Heart diseases have become one of the most causes of death among Egyptians. With 500 deaths per 100,000 occurring annually in Egypt, it has been noticed that medical data faces a high-dimensional problem that leads to a decrease in the classification accuracy of heart data. So the purpose of this study is to improve the classification accuracy of heart disease data for helping doctors efficiently diagnose heart disease by using a hybrid classification technique.

This paper used a new approach based on the integration between dimensionality reduction techniques as multiple correspondence analysis (MCA) and principal component analysis (PCA) with fuzzy c means (FCM) then with both of multilayer perceptron (MLP) and radial basis function networks (RBFN) which separate patients into different categories based on their diagnosis results in this paper, a comparative study of the performance performed including six structures such as MLP, RBFN, MLP via FCM–MCA, MLP via FCM–PCA, RBFN via FCM–MCA and RBFN via FCM–PCA to reach to the best classifier.

The results show that the MLP via FCM–MCA classifier structure has the highest ratio of classification accuracy and has the best performance superior to other methods; and that Smoking was the most factor causing heart disease.

This paper shows the importance of integrating statistical methods in increasing the classification accuracy of heart disease data.

This chapter presents and discusses various steps to ensure empirical reliability and theoretical validity in the construction of competence scales in graduate surveys. The development of a scale to assess demands of the teacher profession and related abilities in graduates for a German tracer study project serves as an example. Confirmatory factor analysis (CFA), principal component analysis (PCA) and Cronbach’s coefficient alpha are employed to test the reliability of the scale. Differing results illustrate how the method applied influences decisions in the process of developing a scale. Our findings show that multidimensionality can only be tested appropriately by CFA; PCA renders no feasible or similar results to CFA depending on the predetermination of the number of factors; Cronbach’s alpha produces misleading results as the prerequisite assumption of unidimensionality is violated by the data.