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Given finite i.i.d. samples in a Hilbert space with zero mean and trace-class covariance operator Σ , the problem of recovering the spectral projectors of Σ naturally arises in many applications. In this paper, we consider the problem of finding distributional approximations of the spectral projectors of the empirical covariance operator Σ ^ , and offer a dimension-free framework where the complexity is characterized by the so-called relative rank of Σ . In this setting, novel quantitative limit theorems and bootstrap approximations are presented subject to mild conditions in terms of moments and spectral decay. In many cases, these even improve upon existing results in a Gaussian setting. [ABSTRACT FROM AUTHOR]

Unsupervised learning methods are well established in the area of anomaly detection and achieve state of the art performances on outlier datasets. Outliers play a significant role, since they bear the potential to distort the predictions of a machine learning algorithm on a given dataset. Especially among PCA-based methods, outliers have an additional destructive potential regarding the result: they may not only distort the orientation and translation of the principal components, they also make it more complicated to detect outliers. To address this problem, we propose the robust outlier detection algorithm CoMadOut, which satisfies two required properties: (1) being robust towards outliers and (2) detecting them. Our CoMadOut outlier detection variants using comedian PCA define, dependent on its variant, an inlier region with a robust noise margin by measures of in-distribution (variant CMO) and optimized scores by measures of out-of-distribution (variants CMO*), e.g. kurtosis-weighting by CMO+k. These measures allow distribution based outlier scoring for each principal component, and thus, an appropriate alignment of the degree of outlierness between normal and abnormal instances. Experiments comparing CoMadOut with traditional, deep and other comparable robust outlier detection methods showed that the performance of the introduced CoMadOut approach is competitive to well established methods related to average precision (AP), area under the precision recall curve (AUPRC) and area under the receiver operating characteristic (AUROC) curve. In summary our approach can be seen as a robust alternative for outlier detection tasks. [ABSTRACT FROM AUTHOR]

We study a class of Approximate Message Passing (AMP) algorithms for symmetric and rectangular spiked random matrix models with orthogonally invariant noise. The AMP iterates have fixed dimension |$K \geq 1$|⁠ , a multivariate non-linearity is applied in each AMP iteration, and the algorithm is spectrally initialized with |$K$| super-critical sample eigenvectors. We derive the forms of the Onsager debiasing coefficients and corresponding AMP state evolution, which depend on the free cumulants of the noise spectral distribution. This extends previous results for such models with |$K=1$| and an independent initialization. Applying this approach to Bayesian principal components analysis, we introduce a Bayes-OAMP algorithm that uses as its non-linearity the posterior mean conditional on all preceding AMP iterates. We describe a practical implementation of this algorithm, where all debiasing and state evolution parameters are estimated from the observed data, and we illustrate the accuracy and stability of this approach in simulations. [ABSTRACT FROM AUTHOR]

In this paper, we provide an alternative trend (time)-dependent risk measure to Ruttiens' accrued returns variability (Ruttiens in Comput Econ 41:407–424, 2013). We propose to adjust the calculation procedure to achieve an alternative risk measure. Our modification eliminates static mean component and it is based on the deviation of squared dispersions, which reflects the trend (time factor) precisely. Moreover, we also present a new perspective on dependency measures and we apply a PCA to a new correlation matrix in order to determine a parametric and nonparametric return approximation. In addition, the two-phase portfolio selection strategy is considered, where the mean–variance portfolio selection strategies represent the first optimization. The second one is the minimization of deviations from their trend leading to identical mean and final wealth. Finally, an empirical analysis verify the property and benefit of portfolio selection strategies based on these trend-dependent measures. In particular, the ex-post results show that applying the modified measure allows us to reduce the risk with respect to the trend of several portfolio strategies. [ABSTRACT FROM AUTHOR]

This paper studies factor modeling for a vector of time series with long-memory properties to investigate how outliers affect the identification of the number of factors and also proposes a robust method to reduce their impact. The number of factors is estimated using an eigenvalue analysis for a non-negative definite matrix introduced by Lam et al. (2011). Two estimators are proposed; the first is based on the classical sample covariance function, and the second uses a robust covariance function estimate. In both cases, it is shown that the eigenvalues estimates have similar convergence rates. Empirical simulations support both estimators for multivariate stationary long-memory time series and show that the robust method is preferable when the data is contaminated with additive outliers. Time series of daily log returns are used as an example of application. In addition to abrupt observations, exchange rates exhibit non-stationarity properties with long memory parameters greater than one. Then we use semi-parametric long memory estimators to estimate the fractional parameters of the series. The number of factors was estimated using the classical and robust approaches. Due to the influence of the abrupt observations, these tools suggested a different number of factors to model the data. The robust method suggested two factors, while the classical approach indicated only one factor. [ABSTRACT FROM AUTHOR]

Sparse principal component analysis (SPCA) is a popular tool for dimensionality reduction in high-dimensional data. However, there is still a lack of theoretically justified Bayesian SPCA methods that can scale well computationally. One of the major challenges in Bayesian SPCA is selecting an appropriate prior for the loadings matrix, considering that principal components are mutually orthogonal. We propose a novel parameter-expanded coordinate ascent variational inference (PX-CAVI) algorithm. This algorithm utilizes a spike and slab prior, which incorporates parameter expansion to cope with the orthogonality constraint. Besides comparing to two popular SPCA approaches, we introduce the PX-EM algorithm as an EM analogue to the PX-CAVI algorithm for comparison. Through extensive numerical simulations, we demonstrate that the PX-CAVI algorithm outperforms these SPCA approaches, showcasing its superiority in terms of performance. We study the posterior contraction rate of the variational posterior, providing a novel contribution to the existing literature. The PX-CAVI algorithm is then applied to study a lung cancer gene expression dataset. The R package VBsparsePCA with an implementation of the algorithm is available on the Comprehensive R Archive Network (CRAN). [ABSTRACT FROM AUTHOR]

The pollution of surface water and groundwater is a real public health problem that is currently receiving particular attention throughout the world. The use of water for food or hygiene purposes requires excellent physicochemical and microbiological quality. Well water is used for many purposes by the inhabitants of M'pody, a village in the Anyama district of Côte d'Ivoire. In this village, an epidemic of diarrhoea was detected in January 2020. This epidemic claimed sixty-nine (69) victims. This study aims to evaluate well water quality controls using the methods of principal component analysis (PCA), correspondence factorial analysis (CFA), analysis of variance (ANOVA) and self-organizing map (SOM) algorithm. The parameters studied were, turbidity (Tur), conductivity (Cond), hydrogen potential (pH), temperature (T), nitrate ( N O 3 - ), nitrite ( N O 2 - ), ammonium ( N H 4 + ), phosphates ( P O 4 3 - ), chlorides (C l -) , total hydrotimetric degree (DHT), sulfates ( S O 4 2 - ), bicarbonate ( H C O 3 - ), total alkalinity contents (TAC), escherichia coli (E.coli), thermotolerant coliforms (CTH) and enterococcus faecalis (E.faecalis). Data were collected from seventy-two (72) wells in the village during four campaigns in 2020. Physicochemical parameters were determined by electrochemical and spectrophotometric methods. Microbiological analysis was carried out using membrane filtration technique. Descriptive statistics revealed that Tur, Cond, pH and T parameters did not meet world health organization (WHO, 2017) standards. However, the parameters N O 3 - , N O 2 - , N H 4 + , P O 4 3 - , C l - , DHT, TAC, S O 4 2 - and H C O 3 - comply with WHO standards. The results of bacteriological analyzes confirm the presence in very significant numbers of indicators of faecal contamination (CTH, E.coli and E.faecalis) in all wells. The logical explanations for faecal pollution would come from the infiltration of septic tanks located near the wells and the run-off of waste water carrying human and animal faecal matter. The diarrhea epidemic would therefore be caused by the consumption of this polluted water. PCA, FCA and hierarchical cluster analysis (HCA) were jointly employed to identify the structure of wells and deduce the principal factors controlling the parameters of these well waters. ANOVA revealed the effect of human-induced activities as the main factors influencing the physicochemical and microbiological parameters of the studied well waters. Further studies should focus on multivariate statistical techniques for effective forecasting and monitoring of emerging pollution for improved water quality. [ABSTRACT FROM AUTHOR]

Two important lines of research come together in this paper: entrepreneurship and corporate social responsibility (CSR). Both stand out for their ability to contribute to sustainable development and generate competitive and social advantages. This study combined both approaches under the concept of CSR entrepreneurship (CSRE). A scale was developed to assess corporate socially responsible entrepreneurs' traits in corporate contexts (i.e., CSRE-s). This quantitative measurement instrument was initially composed of 84 items, which were subjected to various validity and reliability tests. Exploratory factor and confirmatory factor analyses were conducted to identify the most significant determinant variables of individuals engaging in CSRE. The validated CSRE-s indicates that the corporate socially responsible entrepreneurship construct involves 6 entrepreneurship factors and 3 CSR dimensions—environmental, social, and economic—with 2 factors each (i.e., 6 factors), assessed by a total of 76 items. This research's main contribution is the identification of CSRE features in entrepreneurs that together constitute an original, unique, and innovative framework for a sustainable development approach to entrepreneurship. The proposed conceptual model can be used to ensure the CSR values validated for the CSRE-s are incorporated into entrepreneurial training programs (i.e., universities), the public sector's policies promoting entrepreneurship, and strategic business plans for expansion via entrepreneurship. The CSRE-s can be used to strengthen these three areas simultaneously, which should provide social advantages to all stakeholders via the sustainable management of entrepreneurial projects. [ABSTRACT FROM AUTHOR]

Increasingly, automatic face recognition algorithms have become necessary with the development and extensive use of face recognition technology, particularly in the era of machine learning and artificial intelligence. However, the presence of unconstrained environmental conditions degrades the quality of acquired face images and may deteriorate the performance of many classical face recognition algorithms. Due to this backdrop, many researchers have given considerable attention to image restoration and enhancement mechanisms, but with minimal focus on occlusion-related and multiple-constrained problems. Although occlusion robust face recognition modules, via sparse representation have been explored, they require a large number of features to achieve correct computations and to maximize robustness to occlusions. Therefore, such an approach may become deficient in the presence of random occlusions of relatively moderate magnitude. This study assesses the robustness of Principal Component Analysis and Singular Value Decomposition using Discrete Wavelet Transformation for preprocessing and city block distance for classification (DWT-PCA/SVD-L1) face recognition module to image degradations due to random occlusions of varying magnitudes (10% and 20%) in test images acquired with varying expressions. Numerical evaluation of the performance of the DWT-PCA/SVD-L1 face recognition module showed that the use of the de-occluded faces for recognition enhanced significantly the performance of the study recognition module at each level (10% and 20%) of occlusion. The algorithm attained the highest recognition rate of 85.94% and 78.65% at 10% and 20% occlusions respectively, when the MICE de-occluded face images were used for recognition. With the exception of Entropy where MICE de-occluded face images attained the highest average value, the MICE and RegEM result in images of similar quality as measured by their Absolute mean brightness error (AMBE) and peak signal to noise ratio (PSNR). The study therefore recommends MICE as a suitable imputation mechanism for de-occlusion of face images acquired under varying expressions. [ABSTRACT FROM AUTHOR]

Currently, there is no solid criterion for judging the quality of the estimators in factor analysis. This paper presents a new evaluation method for exploratory factor analysis that pinpoints an appropriate number of factors along with the best method for factor extraction. The proposed technique consists of two steps: testing the normality of the residuals from the fitted model via the Shapiro-Wilk test and using an empirical quantified index to judge the quality of the factor model. Examples are presented to demonstrate how the method is implemented and to verify its effectiveness. [ABSTRACT FROM AUTHOR]

To efficiently estimate the central subspace in sufficient dimension reduction, response discretization via slicing its range is one of the most used methodologies when inverse regression-based methods are applied. However, existing slicing schemes are almost all ad hoc and not widely accepted. Thus, how to define data-driven schemes with certain optimal properties is a longstanding problem in this field. The research described herewith is then two-fold. First, we introduce a likelihood-ratio-based framework for dimension reduction, subsuming the popularly used methods including the sliced inverse regression, the sliced average variance estimation and the likelihood acquired direction. Second, we propose a regularized log likelihood-ratio criterion to obtain a data-driven slicing scheme and derive the asymptotic properties of the estimators. A simulation study is carried out to examine the performance of the proposed method and that of existing methods. A data set concerning concrete compressive strength is also analyzed for illustration and comparison. [ABSTRACT FROM AUTHOR]

The customer-oriented and situational nature of e-commerce requires companies to build up service capabilities. However, few scholars have studied this capability systematically. Most scholars see it as a ‘black box’ and give different 'black box' elements depending on the purpose of the study. So, in the context of e-commerce, what should a company's service capabilities include? How are they formed? What impact do they have on a firm's competitive advantage? How can service capabilities be established and improved? Based on the above background and questions, this paper investigates the service capabilities of e-commerce platforms by applying customer value theory in conjunction with the background characteristics of e-commerce transactions. Through case studies, a conceptual model of e-commerce service capability is proposed and its formation mechanism is studied. On this basis, the paper investigates how to measure e-commerce service capability. The aim is to provide theoretical guidance for enterprises' capability planning on e-commerce platforms and to facilitate the transformation from ‘commodity management’ to ‘capability management’. A combination of probability sampling and non-probability sampling was used to select the sample by distributing questionnaires to manufacturing companies in Taizhou, Hangzhou and Shaoxing, Zhejiang Province. For the mail survey, this study uses a snowball method to select the sample. This paper constructs service capability measurement indexes for e-commerce enterprises based on customer's perception of the transaction process, and uses dynamic factor analysis method to analyze enterprises' e-commerce strategic capability, e-commerce management capability and e-commerce technical resources, thus bringing constructive suggestions for the improvement of e-commerce service capability. The findings show that these three competencies are key components of e-business capabilities and together determine the establishment, cultivation and maintenance of an enterprise's e-business capabilities. Enterprises need to focus on these three areas and continuously modify and improve them to ultimately acquire e-business service capabilities.