Ability Of Principal Component Analysis Research Articles

A new IPCA-CPSO-BP Model for Predicting Gas Emission in Underground Coal Mines

Gas has become the primary factor restricting the safe and efficient production of coal mines. Gas emission prediction model is very important for mine gas emission prediction and gas disaster prevention. The improved principal component analysis (IPCA) was used to reduce the dimension of 13 influencing factors of gas emission, and the CPSO-BP neural network prediction model was built with MATLAB software to predict the absolute gas emission of Zhongtai Mining.The results show that the cumulative contribution rate of principal components is not less than 95%, and the number of principal components after improvement is reduced from the original 6 to 3, which effectively solves the problem of excessive principal components and data redundancy caused by the correlation difference between various influencing factors and gas emission amount. At the same time, the optimized particle swarm optimization algorithm alleviates the trouble that the particle swarm optimization algorithm is prone to fall into the local optimal solution. By coupling the improved particle swarm optimization algorithm with BP neural network, the problem of BP neural network's over-dependence on the initial value of weights and thresholds is solved, and the optimal initial weights and thresholds are provided for BP neural network, improving the accuracy of model prediction results. The average relative error of the original BP neural network is 1.6638%, the normalized mean square error is 0.3155, and the regression correlation index is 0.8157. The IPCA-CPSO-BP prediction model decreased to 0.5749%, 0.1143 and 0.9758, respectively. IPCA improves the data dimensionality reduction ability of principal component analysis, IPCA-CPSO-BP enhances the stability of particle swarm optimization algorithm, and significantly improves the prediction accuracy of BP model. The prediction trend is highly consistent with the actual value, which verifies the reliability of the model and provides strong data support for mine gas prevention and control.

Voxelwise Principal Component Analysis of Dynamic [S-Methyl-11C]Methionine PET Data in Glioma Patients.

Simple SummaryRecent works on dynamic amino acid positron emission tomography (PET) imaging of gliomas have highlighted characteristic behaviors of time-activity curves (TACs) extracted from the whole tumor w.r.t. the grade, genotype, and outcome. However, gliomas are known to be highly heterogeneous tumors. Here, we aim at highlighting similar dynamic behaviors at the voxel level within the tumor volume in [S-methyl-11C]methionine PET data of 33 glioma patients using principal component analysis (PCA). The PCA model was derived from TACs of 20 patients and subsequently applied to 13 other patients in whom our approach was shown to outperform classical pharmacokinetic modeling to this end. Our parameter-free approach provides additional parametric maps from dynamic methionine PET scans with little modification of the routine protocol and no arterial sampling. This early methodological work paves the way for various clinical studies on glioma heterogeneity with applications for treatment planning and response evaluation.Recent works have demonstrated the added value of dynamic amino acid positron emission tomography (PET) for glioma grading and genotyping, biopsy targeting, and recurrence diagnosis. However, most of these studies are based on hand-crafted qualitative or semi-quantitative features extracted from the mean time activity curve within predefined volumes. Voxelwise dynamic PET data analysis could instead provide a better insight into intra-tumor heterogeneity of gliomas. In this work, we investigate the ability of principal component analysis (PCA) to extract relevant quantitative features from a large number of motion-corrected [S-methyl-11C]methionine ([11C]MET) PET frames. We first demonstrate the robustness of our methodology to noise by means of numerical simulations. We then build a PCA model from dynamic [11C]MET acquisitions of 20 glioma patients. In a distinct cohort of 13 glioma patients, we compare the parametric maps derived from our PCA model to these provided by the classical one-compartment pharmacokinetic model (1TCM). We show that our PCA model outperforms the 1TCM to distinguish characteristic dynamic uptake behaviors within the tumor while being less computationally expensive and not requiring arterial sampling. Such methodology could be valuable to assess the tumor aggressiveness locally with applications for treatment planning and response evaluation. This work further supports the added value of dynamic over static [11C]MET PET in gliomas.

The identification of long-lived Southern Hemisphere flow events using archetypes and principal components

AbstractFrom time to time atmospheric flows become organized and form coherent long-lived structures. Such structures could be propagating, quasi-stationary, or recur in place. We investigate the ability of Principal Components Analysis (PCA) and Archetypal Analysis (AA) to identify long-lived events, excluding propagating forms. Our analysis is carried out on the Southern Hemisphere mid-tropospheric flow represented by geopotential height at 500hPa (Z500). The leading basis patterns of Z500 for PCA and AA are similar and describe structures representing (or similar to) the Southern Annular Mode (SAM) and Pacific South American (PSA) pattern. Long-lived events are identified here from sequences of 8 days or longer where the same basis pattern dominates for PCA or AA. AA identifies more long-lived events than PCA using this approach. The most commonly occurring long-lived event for both AA and PCA is the annular SAM-like pattern. The second most commonly occurring event is the PSA-like Pacific wavetrain for both AA and PCA. For AA the flow at any given time is approximated as weighted contributions from each basis pattern, which lends itself to metrics for discriminating among basis patterns. These show that the longest long-lived events are in general better expressed than shorter events. Case studies of long-lived events featuring a blocking structure and an annular structure show that both PCA and AA can identify and discriminate the dominant basis pattern that most closely resembles the flow event.

Target Recognition of SAR Images Based on SVM and KSRC.

A synthetic aperture radar (SAR) target recognition method combining linear and nonlinear feature extraction and classifiers is proposed. The principal component analysis (PCA) and kernel PCA (KPCA) are used to extract feature vectors of the original SAR image, respectively, which are classical and reliable feature extraction algorithms. In addition, KPCA can effectively make up for the weak linear description ability of PCA. Afterwards, support vector machine (SVM) and kernel sparse representation-based classification (KSRC) are used to classify the KPCA and PCA feature vectors, respectively. Similar to the idea of feature extraction, KSRC mainly introduces kernel functions to improve the processing and classification capabilities of nonlinear data. Through the combination of linear and nonlinear features and classifiers, the internal data structure of SAR images and the correspondence between test and training samples can be better investigated. In the experiment, the performance of the proposed method is tested based on the MSTAR dataset. The results show the effectiveness and robustness of the proposed method.

Self-organizing profiles to characterize representative temporal settings for daylight simulations

While daylight studies vary in scale and complexity, they follow almost identical procedure that yields higher spatial and temporal dimensionality of luminance/illuminance values, which should be reduced into simpler performance metrics. Several complexities arise from depending solely on performance metrics that do not neither agree on unified thresholds, nor report luminous variations spaces might experience due to weather fluctuations. Few research attempts addressed those issues using predefined timesteps. However, they capture instantaneous performance samples of spaces to which they can only be applied, considering fractions of sky conditions that do not offer generalization. This research expands previous endeavors and presents an unprecedented approach that employs unsupervised machine learning to characterize the most representative temporal settings of given locations from widely accessible weather datasets to evaluate internal luminous conditions. The strengths of three algorithms are combined: the ability of Principal Component Analysis to reduce dimensionality, with Self-Organizing Maps and K-means to cluster the reduced data. To exemplify the proposed approach, three locations are investigated, expressing diverse sky conditions. Each of which reflected unique clustering patterns that were translated into temporal profile maps for visualization. This would provide architects and policy makers with methodology to facilitate building performance simulation and design.

Autofluorescence properties of balloon polymers used in medical applications.

.Significance: For use in medical balloons and related clinical applications, polymers are usually designed for transparency under illumination with white-light sources. However, when illuminated with ultraviolet (UV) or blue light, most of these materials autofluoresce in the visible range, which can be a concern for modalities that rely on tissue autofluorescence for diagnostic or therapeutic purposes.Aim: A search for published information on spectral properties of polymers that can be used for medical balloon manufacturing revealed a scarcity of published information on this subject. The aim of these studies was to address this gap.Approach: The autofluorescence properties of polymers used in medical balloon manufacturing were examined for their suitability for hyperspectral imaging and related applications. Excitation-emission matrices of different balloon materials were acquired within the 320- to 620-nm spectral range. In parallel, autofluorescence profiles from the 420- to 620-nm range were extracted from hyperspectral datasets of the same samples illuminated with UV light. The list of tested polymers included polyurethanes, nylon, polyethylene terephthalate (PET), polyether block amide (PEBAX), vulcanized silicone, thermoplastic elastomers with and without talc, and cyclic olefin copolymers, known by their trade name TOPAS.Results: Each type of polymer exhibited a specific pattern of autofluorescence. Polyurethanes, PET, and thermoplastic elastomers containing talc had the highest autofluorescence values, while sheets made of nylon, PEBAX, and TOPAS exhibited negligible autofluorescence. Hyperspectral imaging was used to illustrate how the choice of specific balloon material can impact the ability of principal component analysis to reveal the ablated cardiac tissue.Conclusions: The data revealed significant differences between autofluorescence profiles of the polymers and pointed to the most promising balloon materials for clinical implementation of approaches that depend on tissue autofluorescence.

Metabolome Comparison of Bioactive and Inactive Rhododendron Extracts and Identification of an Antibacterial Cannabinoid(s) from Rhododendron collettianum.

The science of metabolomics offers the possibility to measure full secondary plant metabolomes with limited experimental effort to allow identification of metabolome differences using principal component analysis (PCA) and partial least squares discriminant analysis (PLS-DA) of liquid chromatography mass spectrometry (LC-MS) data. To demonstrate a bioinformatics driven hypothesis generator for identification of biologically active compounds in plant crude extracts, which is validated by activity guided fractionation. Crude extracts of Rhododendron leaves were tested for their antibacterial activity using agar diffusion and minimum inhibitory concentration assays. Extracts were profiled by LC-MS. PCA and PLS-DA were used for differentiation of bioactive and inactive extracts and their metabolites. Preparative-high performance liquid chromatography (HPLC) and nuclear magnetic resonance (NMR) spectroscopy were used for separation and structure elucidation of pure compound(s) respectively. An antibacterial Rhododendron collettianum was compared to a series of inactive extracts. Three metabolites were found to distinguish R. collettianum from other species indicating the ability of PCA and PLS-DA to suggest potential bioactive substances. An activity-guided fractionation of R. collettianum extracts was carried out and cannabiorcichromenic acid (CCA) was identified as antibacterial compound thereby validating the PCA and PLS-DA generated hypothesis. Four mammalian cell lines were used to estimate possible cytotoxicity of CCA. It was shown that bioinformatics tools facilitate early stage identification of a biologically active compound(s) using LC-MS data, which reduce complexity and number of separation steps in bioactive screening. Copyright © 2017 John Wiley & Sons, Ltd.

Principal component analysis applied to study of carbon steel electrochemical corrosion

Voltammetric techniques (open circuit potential, linear polarisation resistance and cyclic voltammetry) have been applied to study the corrosion of carbon steel in water. The study has been performed in aqueous solutions for pH ranging between 7 and 12 in the presence of chlorides, sulphates, carbonates, nitrites and nitrates. Principal component analysis (PCA) was performed with the cyclic voltammetric data. Values of corrosion potential and corrosion current obtained with traditional methods are compared to the conclusions arisen by the PCA. These results show the ability of PCA for the evaluation and diagnosis of corrosion processes and not only that, it leads to the possibility of using steel working electrodes as ion sensors.

A comparison of Normalised Difference Snow Index (NDSI) and Normalised Difference Principal Component Snow Index (NDPCSI) techniques in distinguishing snow from related land cover types

Snow is a common global meteorological phenomenon known to be a critical component of the hydrological cycle and an environmental hazard. In South Africa, snow is commonly limited to the country’s higher grounds and is considered one of the most destructive natural hazards. As a result, mapping of snow cover is an important process in catchment management and hazard mitigation. However, generating snow maps using survey techniques is often expensive, tedious and time consuming. Within the South African context, field surveys are therefore not ideal for the often highly dynamic snow covers. As an alternative, thematic cover–types based on remotely sensed data-sets are becoming popular. In this study we hypothesise that the reduced dimensionality using Principal Components Analysis (PCA) in concert Normalized Difference Snow Index (NDSI) is valuable for improving the accuracy of snow cover maps. Using the recently launched 11 spectral band Landsat 8 dataset, we propose a new technique that combines the principal component imager generated using PCA with commonly used NDSI, referred to as Normalised Difference Principal Component Snow Index (NDPCSI) to improve snow mapping accuracy. Results show that both NDPCSI and NDSI with high classification accuracies of 84.9% and 76.8% respectively, were effective in mapping snow. Results from the study also indicate that NDSI was sensitive to water bodies found on lower grounds within the study area while the PCA was able to de-correlate snow from water bodies and shadows. Although the NDSI and NDPCSI produced comparable results, the NDPCSI was capable of mapping snow from other related land covers with better accuracy. The superiority of the NDPCSI can particularly be attributed to the ability of principal component analysis to de-correlate snow from water bodies and shadows. The accuracy of both techniques was evaluated using a higher spatial resolution Landsat 8 panchromatic band and Moderate Resolution Imaging Spectroradiometer (MODIS) data acquired on the same day. The findings suggest that NDPCSI is a viable alternative in mapping snow especially in heterogeneous landscape that includes water bodies.

Investigating the Responses of Cronobacter sakazakii to Garlic-Drived Organosulfur Compounds: a Systematic Study of Pathogenic-Bacterium Injury by Use of High-Throughput Whole-Transcriptome Sequencing and Confocal Micro-Raman Spectroscopy

We present the results of a study using high-throughput whole-transcriptome sequencing (RNA-seq) and vibrational spectroscopy to characterize and fingerprint pathogenic-bacterium injury under conditions of unfavorable stress. Two garlic-derived organosulfur compounds were found to be highly effective antimicrobial compounds against Cronobacter sakazakii, a leading pathogen associated with invasive infection of infants and causing meningitis, necrotizing entercolitis, and bacteremia. RNA-seq shows changes in gene expression patterns and transcriptomic response, while confocal micro-Raman spectroscopy characterizes macromolecular changes in the bacterial cell resulting from this chemical stress. RNA-seq analyses showed that the bacterial response to ajoene differed from the response to diallyl sulfide. Specifically, ajoene caused downregulation of motility-related genes, while diallyl sulfide treatment caused an increased expression of cell wall synthesis genes. Confocal micro-Raman spectroscopy revealed that the two compounds appear to have the same phase I antimicrobial mechanism of binding to thiol-containing proteins/enzymes in bacterial cells generating a disulfide stretching band but different phase II antimicrobial mechanisms, showing alterations in the secondary structures of proteins in two different ways. Diallyl sulfide primarily altered the α-helix and β-sheet, as reflected in changes in amide I, while ajoene altered the structures containing phenylalanine and tyrosine. Bayesian probability analysis validated the ability of principal component analysis to differentiate treated and control C. sakazakii cells. Scanning electron microscopy confirmed cell injury, showing significant morphological variations in cells following treatments by these two compounds. Findings from this study aid in the development of effective intervention strategies to reduce the risk of C. sakazakii contamination in the food production environment and on food contact surfaces, reducing the risks to susceptible consumers.

Extracting the Underlying Physiological Determinants of Resource-Based Trade-Offs: A Principal Components Approach

The relationship between traits that compete for resources is influenced by variance in the acquisition and allocation of resources. The difficulty of accurately measuring these underlying physiological processes has hampered studies of resource-based trade-offs. Here, we explore the ability of principal components analysis (PCA) to extract axes corresponding to acquisition and allocation in a bivariate trade-off by comparing these axes to estimates obtained using physiological measurements. We validate the method using simulations and then test it using empirical data for the well-characterized trade-off between flight capability and reproduction in female sand crickets, Gryllus firmus. We find a high correspondence between our physiological estimates and the estimates obtained using PCA. Our results demonstrate that PCA provides a robust and efficient method for estimating acquisition and allocation directly from the traits involved in a resource-based trade-off.

Improved Classification of Orthosiphon stamineus by Data Fusion of Electronic Nose and Tongue Sensors

An improved classification of Orthosiphon stamineus using a data fusion technique is presented. Five different commercial sources along with freshly prepared samples were discriminated using an electronic nose (e-nose) and an electronic tongue (e-tongue). Samples from the different commercial brands were evaluated by the e-tongue and then followed by the e-nose. Applying Principal Component Analysis (PCA) separately on the respective e-tongue and e-nose data, only five distinct groups were projected. However, by employing a low level data fusion technique, six distinct groupings were achieved. Hence, this technique can enhance the ability of PCA to analyze the complex samples of Orthosiphon stamineus. Linear Discriminant Analysis (LDA) was then used to further validate and classify the samples. It was found that the LDA performance was also improved when the responses from the e-nose and e-tongue were fused together.

Early warning of hazard for pipelines by acoustic recognition using principal component analysis and one-class support vector machines

This paper proposes a method for early warning of hazard for pipelines. Many pipelines transport dangerous contents so that any damage incurred might lead to catastrophic consequences. However, most of these damages are usually a result of surrounding third-party activities, mainly the constructions. In order to prevent accidents and disasters, detection of potential hazards from third-party activities is indispensable. This paper focuses on recognizing the running of construction machines because they indicate the activity of the constructions. Acoustic information is applied for the recognition and a novel pipeline monitoring approach is proposed. Principal Component Analysis (PCA) is applied. The obtained Eigenvalues are regarded as the special signature and thus used for building feature vectors. One-class Support Vector Machine (SVM) is used for the classifier. The denoising ability of PCA can make it robust to noise interference, while the powerful classifying ability of SVM can provide good recognition results. Some related issues such as standardization are also studied and discussed. On-site experiments are conducted and results prove the effectiveness of the proposed early warning method. Thus the possible hazards can be prevented and the integrity of pipelines can be ensured.

Impact-acoustics-based health monitoring of tile-wall bonding integrity using principal component analysis

The use of the acoustic features extracted from the impact sounds for bonding integrity assessment has been extensively investigated. Nonetheless, considering the practical implementation of tile-wall non-destructive evaluation (NDE), the traditional defects classification method based directly on frequency-domain features has been of limited application because of the overlapping feature patterns corresponding to different classes whenever there is physical surface irregularity. The purpose of this paper is to explore the clustering and classification ability of principal component analysis (PCA) as applied to the impact-acoustics signature in tile-wall inspection with a view to mitigating the adverse influence of surface non-uniformity. A clustering analysis with signature acquired on sample slabs shows that impact-acoustics signatures of different bonding quality and different surface roughness are well separated into different clusters when using the first two principal components obtained. By adopting as inputs the feature vectors extracted with PCA applied, a multilayer back-propagation artificial neural network (ANN) classifier is developed for automatic health monitoring and defects classification of tile-walls. The inspection results obtained experimentally on the prepared sample slabs are presented and discussed, confirming the utility of the proposed method, particularly in dealing with tile surface irregularity.

Determination of Femoral Artery Occlusion Using Principal Component Analysis of Doppler Signals

The aim of this study is to scrutinize the ability of principal component analysis (PCA) over power spectral densities (PSD) for common femoral artery blood flow study. Doppler femoral artery signals of patients with occluded arteries and of healthy subjects were recorded. Then, power spectral densities of these signals were obtained using the Welch method. To clearly determine the difference between the groups of occluded patients and healthy subjects, PCA was implemented with patients and healthy matrices derived from PSD. The basic differences between the healthy and occluded patients were acquired with 1st principal component. The use of PCA of physiological waveforms is presented as a powerful method likely to be incorporated into future medical signal processing.

Differentiating lifting technique between those who develop low back pain and those who do not

Background. No research to date has been able to discriminate differences in lifting technique for healthy individuals who eventually develop low back pain compared to those that do not while employed in a manual materials handling industry. The purpose of this study was to demonstrate the ability of principal component analysis to identify differences in lifting technique. Methods. Principal component analysis was applied to sixteen kinematic and kinetic waveforms describing the two-dimensional motion of the trunk and load. The principal component scores for each variable were used as the dependent measures in a one-way ANOVA to determine group differences. Findings. Significant group differences ( P < 0.05) were found for five of the principal component scores capturing associated kinematic waveform patterns related to the control and placement of the box on the shelf, and associated kinetic waveform patterns related to the relative timing of extension moment generation in the sacral and thoracic regions. A related waveform pattern for trunk compression was also found. Interpretation. Due to the coordinated movements involved in tasks such as lifting, differences among clinical populations have been difficult to demonstrate empirically. We were able to identify different characteristics in lifting kinematics and kinetics prior to the development of low back pain. Principal component analysis was able to identify important biomechanical differences where traditional analyses failed. This is the first study to identify such lifting differences prior to the development of low back pain.

Intrinsic, Observed, and Retrieved Properties of Interstellar Turbulence

We generate synthetic observations of three-dimensional, self-gravitating MHD simulations of the interstellar medium (ISM) to evaluate the ability of principal component analysis (PCA) to measure the scale dependence of turbulent velocity fluctuations in molecular clouds. Scaling exponents, α, observationally obtained from the coupled characteristic scales for line profile variability in velocity, δv, and in space, L, where δv ∝ Lα, are compared with the intrinsic scaling exponents of the MHD velocity fields. We determine the approximate structure function order at which PCA operates in order to then verify a previously established calibration of the PCA method. We also analyze the statistical properties of projected velocity line centroid fields, including effects of intermittent velocity fluctuations, density inhomogeneity, and opacity, and examine the relationship of the projected two-dimensional statistics to the intrinsic three-dimensional statistics. Using PCA, we infer steep three-dimensional energy spectra in the molecular ISM, generally steeper than can be accounted for by Kolmogorov turbulence or possibly even shock-dominated turbulence.

Detecting stable clusters using principal component analysis.

Clustering is one of the most commonly used tools in the analysis of gene expression data (1, 2) . The usage in grouping genes is based on the premise that co-expression is a result of co-regulation. It is thus a preliminary step in extracting gene networks and inference of gene function (3, 4) . Clustering of experiments can be used to discover novel phenotypic aspects of cells and tissues (3, 5, 6) , including sensitivity to drugs (7) , and can also detect artifacts of experimental conditions (8) . Clustering and its applications in biology are presented in greater detail in the chapter by Zhao and Karypis (see also (9) ). While we focus on gene expression data in this chapter, the methodology presented here is applicable for other types of data as well. Clustering is a form of unsupervised learning, i.e. no information on the class variable is assumed, and the objective is to find the “natural” groups in the data. However, most clustering algorithms generate a clustering even if the data has no inherent cluster structure, so external validation tools are required. Given a set of partitions of the data into an increasing number of clusters (e.g. by a hierarchical clustering algorithm, or k-means), such a validation tool will tell the user the number of clusters in the data (if any). Many methods have been proposed in the literature to address this problem (10–15) . Recent studies have shown the advantages of sampling-based methods (12, 14) . These methods are based on the idea that when a partition has captured the structure in the data, this partition should be stable with respect to perturbation of the data. Bittner et al. (16) used a similar approach to validate clusters representing gene expression of melanoma patients. The emergence of cluster structure depends on several choices: data representation and normalization, the choice of a similarity measure and clustering algorithm. In this chapter we extend the stability-based validation of cluster structure, and propose stability as a figure of merit that is useful for comparing clustering solutions, thus helping in making these choices. We use this framework to demonstrate the ability of Principal Component Analysis (PCA) to extract features relevant to the cluster structure. We use stability as a tool for simultaneously choosing the number of principal components and the number of clusters; we compare the performance of different similarity measures and normalization schemes. The approach is demonstrated through a case study of yeast gene expression data from Eisen et al. (1) . For yeast, a functional classification of a large number of genes is known, and we use this classification for validating the results produced by clustering. A method for comparing clustering solutions specifically applicable to gene expression data was introduced in (17) . However, it cannot be used to choose the number of clusters, and is not directly applicable in choosing the number of principal components. The results of clustering are easily corrupted by the addition of noise: even a few

Is principal components analysis necessary to characterise dietary behaviour in studies of diet and disease?

To assess the relative ability of principal components analysis (PCA)-derived dietary patterns to correctly identify cases and controls compared with other methods of characterising food intake. Participants in this study were 232 endometrial cancer cases and 639 controls from the Western New York Diet Study, 1986-1991, frequency-matched to cases on age and county of residence. Usual intake in the year preceding interview of 190 foods and beverages was collected during a personal interview using a detailed food-frequency questionnaire. Principal components analysis identified two major dietary patterns which we labelled 'healthy' and 'high fat'. Classification on disease status was assessed with separate discriminant analyses (DAs) for four different characterisation schemes: stepwise DA of 168 food items to identify the subset of foods that best discriminated between cases and controls; foods associated with each PCA-derived dietary pattern; fruits and vegetables (47 items); and stepwise DA of USDA-defined food groups (fresh fruit, canned/frozen fruit, raw vegetables, cooked vegetables, red meat, poultry, fish and seafood, processed meats, snacks and sweets, grain products, dairy, and fats). In general, classification of disease status was somewhat better among cases (54.7% to 67.7%) than controls (54.0% to 63.1%). Correct classification was highest for fruits and vegetables (67.7% and 62.9%, respectively) but comparable to that of the other schemes (49.5% to 66.8%). Our results suggest that the use of principal components analysis to characterise dietary behaviour may not provide substantial advantages over more commonly used, less sophisticated methods of characterising diet.

Application of PCA and FA in electron spectroscopy. II. The minimum energy shift of factors that can be resolved in a set of noisy spectra

This paper shows how signal-to-noise ratio, shift, shape and contributions from the factors present in a set of spectra are related to one another from the point of view of the ability of principal component analysis (PCA) to detect the presence of the factors. In the derived relationship a coefficient with a value dependent on the number of parameters appears. Values of this coefficient for a particular criterion for detection of the factors and for four selected factor shapes have been found from the results obtained for simulated sets of spectra of known properties. Consequently, a simple formula for evaluation of the minimum shift between factors (δ min ) that ensures the presence of both factors can be proposed. This paper also proves that δ min can be lowered when the spectra are recorded in derivative form, and that further lowering of δ min can be obtained when PCA is applied to the set of spectra after rejection of their less informative parts. As an illustration of the latter effect, δ min values of 0.125 and 0.035 eV, respectively, are obtained for a set of derivative Auger MNN spectra.