Nonlinear Principal Component Analysis Research Articles

Exploiting neural PCA and Fisher discriminate analysis for FDI system

The major goal of this paper is the description of a fault detection and isolation system. Such a system is geared to the complex processes through the combination of the neural networks, Fisher discriminate analysis and the principal component analysis. The corner stone of this work is the application of a self-associative neural network to the nonlinear PCA for fault detection by starting with a various measurement multivariable matrix stemming from a complex industrial process. FDA and PLS are, then, used to identify the directions of the detected faults through the classification of the groups with and without faults. To isolate these faults is to recognize the variables that are the cause of these faults. This is attained by calculating the contribution; in other words, the variables having the largest contribution with regard to the others are considered defective. This statistical approach is authenticated on a pastry production process and gives good results. By comparing FDI with other methods, we can perceive that our approach gives more reliable results.

Constrained Statistical Modelling of Knee Flexion From Multi-Pose Magnetic Resonance Imaging.

Reconstruction of the anterior cruciate ligament (ACL) through arthroscopy is one of the most common procedures in orthopaedics. It requires accurate alignment and drilling of the tibial and femoral tunnels through which the ligament graft is attached. Although commercial computer-assisted navigation systems exist to guide the placement of these tunnels, most of them are limited to a fixed pose without due consideration of dynamic factors involved in different knee flexion angles. This paper presents a new model for intraoperative guidance of arthroscopic ACL reconstruction with reduced error particularly in the ligament attachment area. The method uses 3D preoperative data at different flexion angles to build a subject-specific statistical model of knee pose. To circumvent the problem of limited training samples and ensure physically meaningful pose instantiation, homogeneous transformations between different poses and local-deformation finite element modelling are used to enlarge the training set. Subsequently, an anatomical geodesic flexion analysis is performed to extract the subject-specific flexion characteristics. The advantages of the method were also tested by detailed comparison to standard Principal Component Analysis (PCA), nonlinear PCA without training set enlargement, and other state-of-the-art articulated joint modelling methods. The method yielded sub-millimetre accuracy, demonstrating its potential clinical value.

Comparative evaluations of multivariate methods in spatial clustering of precipitation using GPCC V7 gridded data set: application to the Northern Territory of Australia

This study intends to evaluate whether or not there is the meaningful preference between performances of four multivariate methods of principle component analysis (PCA), factor analysis (FA), independent component analysis (ICA) and nonlinear principle component analysis based on autoassociative neural network (NLPCA-ANN) in spatial clustering of the seasonal and annual precipitation in the Northern Territory of Australia. Monthly precipitation’s gridded data of Global Precipitation Climate Centre (GPCC) version 7 from January 1901 until December 2013 was used in this research, and two homogeneity tests of H index and Cronbach’s alpha (α) test were employed for examining the accuracy of the derived clusters. The results showed that NLPCA-ICA, at the annual scale, and ICA, at the seasonal scale, present marginally more accurate clustering compared to others. Therefore, solely relying on the multivariate methods for spatial precipitation clustering in areas with complex climate and topographic conditions is not reasonable and it is quite necessary to take advantages of other advance statistical methods to refine the outcome of multivariate methods as well.

Çok Boyutlu Sağkalım Verilerinde Denetimli Temel Bileşenler Analizine Alternatif Bir Boyut İndirgeme Yaklaşımı

Objective: This study aims at comparing the performances of supervised principal component analysis (SPCA) which is used for dimension reduction and an alternatively proposed approach of nonlinear principal component analysis using artificial neural networks performed by gene selection with survival tree (survival tree based NLPCA- NN). Material and Methods: Gene expression data set from Rosenwald et al.(2002) pertaining to 240 patients with diffuse large B-cell lymphoma (DLBCL) is used. While Cox scores are used for determining important genes from high dimensional gene expression data in SPCA, in survival tree based NLPCA-NN approach, importance values of the survival tree are used. Important genes according to the Cox scores are reduced to three principal components by singular value decomposition. Important genes determined by the survival tree are taken as input variables in neural networks and reduced to three principal components. The performances of SPCA and survival tree based NLPCA-NN are compared by using Cox regression models (CRM). C index is calculated to compare obtained Cox regression models. Results: According to Cox scores, 121 genes are determined; according to importance values of survival tree 114 genes are determined. The percentages of variances explained by SPCA and survival tree based NLPCA-NN were 18.2% and 35.1% respectively. Harrell?s C indexes are calculated as 0.726 for CRM-1, 0.687 for CRM-2. Conclusion: As a result, while SPCA takes only the linear relationships into consideration, survival tree based NLPCA-NN also takes non-linear relationships into account and has more variance explanation and NLPCA-NN can be evaluated as an alternative method to SPCA.

FAMILY CHARACTERISTICS AND GOVERNANCE OF SMALL AND MEDIUM-SIZED FAMILY FIRMS

The purpose of this paper is to study the influence of family characteristics on the governance of small and medium-sized family firms. The study presents and tests a theoretical model resorting to data on 151 Portuguese SMEs. The study uses nonlinear principal component analysis by alternating least squares, bivariate analysis and cluster analysis. Family characteristics influence governance mechanisms and family firms form clusters based on family characteristics and governance mechanisms. The results reveal that family characteristics are a source of heterogeneity among family firms which corroborates the criticism on family firms' homogeneity assumption. The identification of clusters of firms constitutes a reference for family firms' definition of governance models. The originality of the paper relies on the analysis of specific family characteristics and its importance as a source of family firms' heterogeneity is proven. This study opens new insights on family firms' governance research and may be extended to other family characteristics and overall implications on performance.

Assessing regional sustainable development through an integration of nonlinear principal component analysis and Gram Schmidt orthogonalization

The regional sustainable development level (SDL), sustainability of regional development (SRD) and system coordination (SC) make up the triangular truss of regional sustainable development assessment, but it is debated how should traditional practice best weight and calculate the whole sustainable development system level. The Bohai Rim, covering three provinces and two municipalities in China, lies in a region that is sensitive to profound conflict between socioeconomic development and environment pollution in the process of sustainable development. Considering the defects of traditional models and the multidimensionality of regional sustainability issues, we proposed an integrated model of nonlinear principal component analysis and Gram Schmidt orthogonalization and presented a novel regional sustainable development assessment method and framework from three perspectives for the society–economy–environment system of the Bohai Rim region. The results show that: (a) the integration of nonlinear principal component analysis and Gram Schmidt orthogonalization can well remedy the defects of traditional methods and provide a more objective conceptual framework; (b) the sustainability of regional development and system coordination models graphically demonstrate the essence and connotation of a dynamic sustainable development system; (c) the empirical study demonstrated that the Bohai Rim region has experienced a distinct development period in which the SRD experienced a steady decline and the SDL and SC generally increased; (d) the coordination ability can be improved by a decline in the environmental sustainability, which reveals the importance of environment subsystem optimization; and (e) the weight distribution of variables demonstrates that the most significant factors affecting sustainable development are the indicators from the dimensions of people's standard of living, economic structure and environmental pollution. This study enriches the sustainable development assessment theory and methodology, and lays the foundation for further sustainable development research in the Bohai Rim region.

Being alone and expectations lost: a critical realist study of maternal depression in South Western Sydney.

The study reported here is part of a critical realist multilevel study. It seeks to identify and explain complex perinatal contextual social and psychosocial mechanisms that may influence the developmental origins of health and disease, with a focus on the role of postnatal depression. The aims of the greater study are to: (1) describe the phenomenon of postnatal depression in South Western Sydney; and (2) identify mechanisms that would add to our understanding of the psycho-social causes of maternal depression. This paper will move beyond our previous quantitative descriptions of individual-level predictors of depressive symptoms by seeking the views of local mothers and practitioners, to explain the mechanisms that might be involved. The study was set in South Western Sydney, New South Wales, Australia. An Explanatory Theory Building Method was used. The previously reported quantitative study was a non-linear principal component analysis and logistic regression study of 15,389 months delivering in 2002 and 2003. This intensive qualitative study used open coding of interviews, of seven practitioners and three naturally occurring mothers groups, to enable maximum emergence. The theoretical concepts identified were: attachment and nurturing, infant temperament, unplanned pregnancy and sole parenthood, support for mothers, access to services, stress, financial hardship, isolation and marginalisation, mothers’ “loss of control” and “power”, and expectations and dreams. Being alone and expectations lost emerged as possible triggers of stress and depression for mothers. These findings might also apply to others who have their dreams shattered during life’s transitions. In these situations social and cultural context can either nurture and support or marginalise and isolate. The challenge for policy and practice is to support mothers and their partners during the transition to parenthood within a challenging social and material context.

Beliefs as Self-Sustaining Networks: Drawing Parallels Between Networks of Ecosystems and Adults' Predictions.

In this paper, we argue that beliefs share common properties with the self-sustaining networks of complex systems. Matching experiences are said to couple with each other into a mutually reinforcing network. The goal of the current paper is to spell out and develop these ideas, using our understanding of ecosystems as a guide. In Part 1 of the paper, we provide theoretical considerations relevant to this new conceptualization of beliefs, including the theoretical overlap between energy and meaning. In Part 2, we discuss the implications of this new conceptualization on our understanding of belief emergence and belief change. Finally, in Part 3, we provide an analytical mapping between beliefs and the self-sustaining networks of ecosystems, namely by applying to behavioral data a measure developed for ecosystem networks. Specifically, average accuracies were subjected to analyses of uncertainty (H) and average mutual information. The ratio between these two values yields degree of order, a measure of how organized the self-sustained network is. Degree of order was tracked over time and compared to the amount of explained variance returned by a categorical non-linear principal components analysis. Finding high correspondence between the two measures of order, together with the theoretical groundwork discussed in Parts 1 and 2, lends preliminary validity to our theory that beliefs have important similarities to the structural characteristics of self-sustaining networks.

Multi-resolution analysis techniques and nonlinear PCA for hybrid pansharpening applications

Hyperspectral images have a higher spectral resolution (i.e., a larger number of bands covering the electromagnetic spectrum), but a lower spatial resolution with respect to multispectral or panchromatic acquisitions. For increasing the capabilities of the data in terms of utilization and interpretation, hyperspectral images having both high spectral and spatial resolution are desired. This can be achieved by combining the hyperspectral image with a high spatial resolution panchromatic image. These techniques are generally known as pansharpening and can be divided into component substitution (CS) and multi-resolution analysis (MRA) based methods. In general, the CS methods result in fused images having high spatial quality but the fused images suffer from spectral distortions. On the other hand, images obtained using MRA techniques are not as sharp as CS methods but they are spectrally consistent. Both substitution and filtering approaches are considered adequate when applied to multispectral and PAN images, but have many drawbacks when the low-resolution image is a hyperspectral image. Thus, one of the main challenges in hyperspectral pansharpening is to improve the spatial resolution while preserving as much as possible of the original spectral information. An effective solution to these problems has been found in the use of hybrid approaches, combining the better spatial information of CS and the more accurate spectral information of MRA techniques. In general, in a hybrid approach a CS technique is used to project the original data into a low dimensionality space. Thus, the PAN image is fused with one or more features by means of MRA approach. Finally the inverse projection is used to obtain the enhanced image in the original data space. These methods, permit to effectively enhance the spatial resolution of the hyperspectral image without relevant spectral distortions and on the same time to reduce the computational load of the entire process. In particular, in this paper we focus our attention on the use of Nonlinear Principal Component Analysis (NLPCA) for the projection of the image into a low dimensionality feature space. However, if on one hand the NLPCA has been proved to better represent the intrinsic information of hyperspectral images in the feature space, on the other hand an analysis of the impact of different fusion techniques applied to the nonlinear principal components in order to define the optimal framework for the hybrid pansharpening has not been carried out yet. More in particular, in this paper we analyze the overall impact of several widely used MRA pansharpening algorithms applied in the nonlinear feature space. The results obtained on both synthetic and real data demonstrate that an accurate selection of the pansharpening method can lead to an effective improvement of the enhanced hyperspectral image in terms of spectral quality and spatial consistency, as well as a strong reduction in the computational time.

Linear and Non-Linear Approaches for Statistical Seasonal Rainfall Forecast in the Sirba Watershed Region (SAHEL)

Since the 90s, several studies were conducted to evaluate the predictability of the Sahelian rainy season and propose seasonal rainfall forecasts to help stakeholders to take the adequate decisions to adapt with the predicted situation. Unfortunately, two decades later, the forecasting skills remains low and forecasts have a limited value for decision making while the population is still suffering from rainfall interannual variability: this shows the limit of commonly used predictors and forecast approaches for this region. Thus, this paper developed and tested new predictors and new approaches to predict the upcoming seasonal rainfall amount over the Sirba watershed. Predictors selected through a linear correlation analysis were further processed using combined linear methods to identify those having high predictive power. Seasonal rainfall was forecasted using a set of linear and non-linear models. An average lag time up to eight months was obtained for all models. It is found that the combined linear methods performed better than non-linear, possibly because non-linear models require larger and better datasets for calibration. The R2, Nash and Hit rate score are respectively 0.53, 0.52, and 68% for the combined linear approach; and 0.46, 0.45, 61% for non-linear principal component analysis.

Damage and nonlinearities detection in wind turbine blades based on strain field pattern recognition. FBGs, OBR and strain gauges comparison

A 13.5m wind turbine blade prototype was designed and made of glass fiber and vinylester resin doped with carbon nanofibers. The blade was manufactured using Light RTM (Resin Transfer Molding) as a monocoque structure with a PVC foam core.Within the presented work, a methodology for instrumenting the blade with Fiber Optic Sensors (FOS) embedded into the structure during the manufacturing process was developed. Two different FOS technologies for strain sensing were embedded into the blade: Fiber Bragg Gratings (FBGs) and a plain fiber optic for distributed sensing using an Optical Backscatter Reflectometer (OBR). Besides the FOS, traditional electrical extensometers were bonded to the surface of the blade.By using Hierarchical nonlinear principal component analysis (h-NLPCA) it was possible to perform a pattern recognition technique based on the strain field inferred from the measurements acquired by different sensors. Defects and nonlinearities could be detected during the certification testing of the blades, avoiding the premature failure of the structure.Several static tests were conducted, including a test campaign with known artificial damages induced into the structure and the sensitivity of the technique was evaluated. The results showed that every damages could be detected by using different sensing techniques.

Dimensionality Reduction via Regression in Hyperspectral Imagery

This paper introduces a new unsupervised method for dimensionality reduction via regression (DRR). The algorithm belongs to the family of invertible transforms that generalize Principal Component Analysis (PCA) by using curvilinear instead of linear features. DRR identifies the nonlinear features through multivariate regression to ensure the reduction in redundancy between he PCA coefficients, the reduction of the variance of the scores, and the reduction in the reconstruction error. More importantly, unlike other nonlinear dimensionality reduction methods, the invertibility, volume-preservation, and straightforward out-of-sample extension, makes DRR interpretable and easy to apply. The properties of DRR enable learning a more broader class of data manifolds than the recently proposed Non-linear Principal Components Analysis (NLPCA) and Principal Polynomial Analysis (PPA). We illustrate the performance of the representation in reducing the dimensionality of remote sensing data. In particular, we tackle two common problems: processing very high dimensional spectral information such as in hyperspectral image sounding data, and dealing with spatial-spectral image patches of multispectral images. Both settings pose collinearity and ill-determination problems. Evaluation of the expressive power of the features is assessed in terms of truncation error, estimating atmospheric variables, and surface land cover classification error. Results show that DRR outperforms linear PCA and recently proposed invertible extensions based on neural networks (NLPCA) and univariate regressions (PPA).

Hybrid neural network predictor for distributed parameter system based on nonlinear dimension reduction

In this study, a hybrid neural network predictor is proposed to predict spatiotemporal dynamics of the nonlinear distributed parameter systems (DPSs) with unwanted disturbance or slow set point changes. First, a nonlinear principal component analysis (NL-PCA) network is designed to transform the high-dimensional spatiotemporal data into a low-dimensional time domain, which can better represent the nonlinearity of the system compared to the linear time/space separation method. Then the hybrid NN models are built to identify the low-dimensional temporal data. To capture the spatiotemporal dynamics of DPS, the four-step recursive algorithm is used to obtain the time-varying weights of the model, while the parameters of NN model does not need to online update. The simulations demonstrated show that the proposed approach can achieve a good performance on prediction with system slow time-varying dynamics.

Abstract 2423: Signaling pathway profiling in multiple myeloma

Abstract Multiple myeloma (MM) is an incurable malignancy of terminally differentiated B cells. The disease develops from preclinical stages, i.e. MGUS/SMM, to symptomatic MM and eventually becomes refractory to therapy. Recent data indicate relevant clusters of mutational hotspots within signaling pathways, yet only very limited data is available on actual signaling profiles. Therefore, we aimed to characterize the activation of five oncogenic signaling pathways (RAS/RAF/MEK/ERK, JAK-STAT, NF-κB, PI3K/AKT and cMYC) in primary MM biopsies and to correlate the data with disease stage and clinical outcome. We used immunohistochemistry to assess key activation markers of respective signaling pathways in a discovery cohort (DC) of patients with SMM/MGUS (n = 32), symptomatic MM (n = 195) and refractory MM (n = 50). Furthermore, an independent validation cohort (VC, n = 84) of newly diagnosed MM, enrolled in two clinical trials, was employed. Activation scores included signal intensity as well as the percentage of positive versus total tumor cells per sample to account for potential clonal heterogeneity. A non-linear principal component analysis was applied to integrate signaling scores per pathway and sample. Overall, NF-κB was activated in 90% of cases; ERK or AKT in 45%, MYC and STAT3 activation in 44% and 27%, respectively. At diagnosis, strong activation of single pathways was found in a mutually exclusive pattern. In refractory MM, the signaling pathways were more frequently activated, except for NF-κB (NF-κB, MYC, AKT p< 0.001; ERK p = 0.002; STAT3 p = 0.008). Moreover, simultaneous activation of multiple pathways was detectable in 72% of refractory MM compared to 38.5% of MM and only 9.4% of SMM/MGUS. In the VC, MYC and STAT3 activation was associated with a higher ISS score (p = 0.05 and p = 0.0011, respectively). In addition, activated STAT3 correlated with shorter overall survival (HR 2.97, p = 0.020) and progression-free survival (HR 2.31, p = 0.026), MYC activation with shorter overall survival (HR 2.41, p = 0.028). Furthermore, pathway activation clustering revealed a prognostic hierarchy with isolated NF- κB activation being favorable; ERK or AKT activation being neutral and MYC or STAT3 activation being indicative for poor outcome. To conclude, this is the first systematic analysis of oncogenic signaling patterns on primary MM samples. Our data reveal a mutually exclusive landscape of most strongly activated pathways in newly diagnosed MM and proof to be of prognostic significance, while simultaneous pathway activation appears to be associated with disease progression. Citation Format: Jing Xu, Thomas Hielscher, Nicola Lehners, Elena Ellert, Anthony D. Ho, Peter Schirmacher, Hartmut Goldschmidt, Mindaugas Andrulis, Marc-Steffen Raab. Signaling pathway profiling in multiple myeloma. [abstract]. In: Proceedings of the 106th Annual Meeting of the American Association for Cancer Research; 2015 Apr 18-22; Philadelphia, PA. Philadelphia (PA): AACR; Cancer Res 2015;75(15 Suppl):Abstract nr 2423. doi:10.1158/1538-7445.AM2015-2423

Kernel PCA Part 1: Polynomials without the Kernels

T his is the first of two columns that will attempt to describe kernel PCA. This is a computationally efficient way of carrying out a nonlinear principal component analysis. The computationally efficient bit using the kernels requires some quite fancy mathematics, which I will attempt to explain in part 2, but for one kernel, the polynomial one, it is possible to get effectively the same results in a much simpler way, and this is what will be done here.

Descendants of Hardship: Prevalence, Drivers and Scarring Effects of Social Exclusion in Childhood

The social exclusion of children is problematic for two reasons. Young people typically inherit their marginal position from their family, and therefore cannot be held responsible for their hardship themselves; and social exclusion in childhood may affect their wellbeing and subsequent development, possibly leading to a “scarring effect” in later life. In this contribution we develop an instrument for measuring social exclusion among children. Social exclusion is regarded as a theoretical construct with four sub-dimensions: material deprivation, limited social participation, inadequate access to social rights, and a lack of normative integration. First we analyse data from a survey of 2,200 Dutch children, which contains a large set of social exclusion items. We applied nonlinear principal components analysis in order to construct a multidimensional scale. Measured in this way, the prevalence of social exclusion among children is 4.5%. Boys and children living in large families are more likely to experience social exclusion than girls and children with few siblings. The parental level of education and dependency on social security benefits are also important driving factors of childhood social exclusion. Subsequently we investigate the scarring effect. Longitudinal administrative income and household data covering 25 years were combined with a new survey of just under 1,000 Dutch adults, a third of whom were poor as a child. The survey assessed their past and current degree of social exclusion, and their health and psychosocial development, educational career, past family circumstances, etc. In an absolute sense scarring turns out to have been limited during this period: a very large majority of those who were poor or excluded as a child are above the threshold values in adult life. However, the “descendants of hardship” are still more likely to be socially excluded as adults than people who grew up in more favourable conditions. A causal analysis suggests that low educational achievements are the main mediator of scarring risks.

Examining the relationship between organizational coaching and workplace counterproductive behaviours in the United Arab Emirates

Purpose– The purpose of this study is to establish both the validity of Western theories within the Middle East, namely, the United Arab Emirates (UAE), and to further improve and extend our understanding of the effect of organisational coaching on counterproductive behaviours, such as bullying and alienation.Design/methodology/approach– A sample size of 656 participants from 29 organisations and 14 different industries was employed. A research model was proposed, refined and tested through a quantitative paradigm using one dimension nonlinear principal components analysis, linear structural equation modelling (SEM) and MANOVA.Findings– The correlation analysis results show non-significant negative correlations between coaching and all of the organisational counterproductive behaviour dimensions but not certainty. It was found that a significant weak relationship exists between most of the mediator dimensions, while a strong relationship exists between job alienation and workplace bullying. Results of the linear SEM provide support that coaching is related to certainty. Furthermore, the results reveal that certainty mediates a significant link between coaching and organisational counterproductive work behaviours (job alienation and bullying).Originality/value– The study is considered the first in the UAE to investigate organisational counterproductive work behaviours (bullying and job alienation). The main contribution of this study is to quantify the relationship between organisational coaching and bullying and job alienation mediated by organisational climate dimensions.

Uptake of agri-environmental schemes in the Less-Favoured Areas of Greece: The role of corruption and farmers’ responses to the financial crisis

Vine-growing in the Less-Favoured Areas of Greece is facing multiple challenges that might lead to its abandonment. In an attempt to maintain rural populations, Rural Development Schemes have been created that offer the opportunity to rural households to maintain or expand their farming businesses including vine-growing. This paper stems from a study that used data from a cross-sectional survey of 204 farmers to investigate how farming systems and farmers’ perception of corruption, amongst other socio-economic factors, affected their decisions to continue vine-growing through participation in Rural Development Schemes, in three remote Less-Favoured Areas of Greece. The Theory of Planned Behaviour was used to frame the research problem with the assumption being that an individual’s intention to participate in a Scheme is based on their prior beliefs about it. Data from the survey were reduced and simplified by the use of non-linear principal component analysis. The ensuing variables were used in selectivity corrected ordered probit models to reveal farmers’ attitudes towards viticulture and rural development. It was found that economic factors, perceived corruption and farmers’ attitudes were significant determinants on whether to participate in the Schemes. The research findings highlight the important role of perceived corruption and the need for policies that facilitate farmers’ access to decision making centres.

The benefits and challenges of large-scale deployment of electronic voting systems: University student views from across different subject groups

Electronic Voting System (EVS) is a classroom technology that provides a means to increase students' engagement, attention and attendance. The purpose of this paper is to provide a deeper insight into students' views on the benefits and challenges of EVS in the context of a large-scale institutional deployment and across different subject areas in higher education.The data were collected from an online survey of 590 students across eleven academic schools at a UK university.The non-linear principal component analysis of 32 question items from the survey showed that learning benefits, classroom-related benefits, usability and student-centered challenges are four distinctive dimensions in student's perceptions of the use of EVS. The non-parametric group comparison tests suggested that there are significant differences in learning benefits and challenges across different subject groups. However, the disparity appears to be related more to the way the EVS was used and the experience of students with it, rather than resulting from disciplinary differences. Content analysis of open questions revealed that summative use and staff competencies are the main issues related to EVS use by students. Finally, despite the overwhelming perception of the ease of use, it was found that usability could be an issue for students when EVS was used for summative assessment.The implications of the study are: for practitioners, it underlines the importance of the focus on formative benefits of EVS as only then and regardless of disciplinary differences, can the promised rewards of the technology be gained; for institutions, it outlines some of the new challenges specific to the large-scale institutional implementation, judged through the lens of students' experience; for researchers, it provides an overview of the literature on large-scale deployment of EVS and it suggests some new areas for research on the use of EVS in higher education.

On-line monitoring of batch processes using generalized additive kernel principal component analysis

Based on analyzing the special structure of three-way array and generalizing the concept of additive kernels, this paper proposes the generalized additive kernel principal component analysis (GAKPCA) method for on-line monitoring of batch processes. The proposed method is a special nonlinear principal component analysis (PCA) method which can handle the nonlinear relationships between different monitoring variables and/or time intervals. It inherits the good properties of traditional multiway PCA (MPCA) method for on-line monitoring, and solves some problems that exist in traditional multiway kernel PCA (MKPCA) method. For example, based on the decomposition of batch samples in the feature space, the total squared prediction error (SPE) statistic of an entire batch can be divided into K components corresponding to K time intervals respectively, and its score vectors can be directly estimated on-line by the least squares approach without filling the unknown observations. As a special case, when the Gaussian kernel is used as the kernel function at each time interval, the proposed method is connected with the concept of correntropy which can bring robustness to our method. The experimental results on a fed-batch penicillin fermentation process demonstrate the validity of the proposed GAKPCA-based on-line monitoring method.