Outer Product Analysis Research Articles

Feasibility of using Vis-NIR spectroscopy and PXRF spectrometry to estimate regional soil cadmium concentration

Conventionally, soil cadmium (Cd) measurements in the laboratory are expensive and time-consuming, involving complex processes of sample preparation and chemical analysis. This study aimed to identify the feasibility of using sensor data of visible near-infrared reflectance (Vis-NIR) spectroscopy and portable X-ray fluorescence spectrometry (PXRF) to estimate regional soil Cd concentration in a time- and cost-saving manner. The sensor data of Vis-NIR and PXRF, and Cd concentrations of 128 surface soils from Yunnan Province, China, were measured. Outer-product analysis (OPA) was used for synthesizing the sensor data and Granger-Ramanathan averaging (GRA) was applied to fuse the model results. Artificial neural network (ANN) models were built using Vis-NIR data, PXRF data, and OPA data, respectively. Results showed that: (1) ANN model based on PXRF data performed better than that based on Vis-NIR data for soil Cd estimation; (2) Fusion methods of both OPA and GRA had higher predictive power (R2) = 0.89, ratios of performance to interquartile range (RPIQ) = 4.14, and lower root mean squared error (RMSE) = 0.06, in ANN model based on OPA fusion; R2 = 0.88, RMSE = 0.06, and RPIQ = 3.53 in GRA model) than those based on either Vis-NIR data or PXRF data. In conclusion, there exists a great potential for the combination of OPA fusion and ANN to estimate soil Cd concentration rapidly and accurately.

Rapid Estimation of Soil Pb Concentration Based on Spectral Feature Screening and Multi-Strategy Spectral Fusion.

Traditional methods for obtaining soil heavy metal content are expensive, inefficient, and limited in monitoring range. In order to meet the needs of soil environmental quality evaluation and health status assessment, visible near-infrared spectroscopy and XRF spectroscopy for monitoring heavy metal content in soil have attracted much attention, because of their rapid, nondestructive, economical, and environmentally friendly features. The use of either of these spectra alone cannot meet the accuracy requirements of traditional measurements, while the synergistic use of the two spectra can further improve the accuracy of monitoring heavy metal lead content in soil. Therefore, this study applied various spectral transformations and preprocessing to vis-NIR and XRF spectra; used the whale optimization algorithm (WOA) and competitive adaptive re-weighted sampling (CARS) algorithms to identify feature spectra; designed a combination variable model (CVM) based on multi-layer spectral data fusion, which improved the spectral preprocessing and spectral feature screening process to increase the efficiency of spectral fusion; and established a quantitative model for soil Pb concentration using partial least squares regression (PLSR). The estimation performance of three spectral fusion strategies, CVM, outer-product analysis (OPA), and Granger-Ramanathan averaging (GRA), was discussed. The results showed that the accuracy and efficiency of the CARS algorithm in the fused spectra estimation model were superior to those of the WOA algorithm, with an average coefficient of determination (R2) value of 0.9226 and an average root mean square error (RMSE) of 0.1984. The accuracy of the estimation models established, based on the different spectral types, to predict the Pb content of the soil was ranked as follows: the CVM model > the XRF spectral model > the vis-NIR spectral model. Within the CVM fusion strategy, the estimation model based on CARS and PLSR (CARS_D1+D2) performed the best, with R2 and RMSE values of 0.9546 and 0.2035, respectively. Among the three spectral fusion strategies, CVM had the highest accuracy, OPA had the smallest errors, and GRA showed a more balanced performance. This study provides technical means for on-site rapid estimation of Pb content based on multi-source spectral fusion and lays the foundation for subsequent research on dynamic, real-time, and large-scale quantitative monitoring of soil heavy metal pollution using high-spectral remote sensing images.

Optimised use of data fusion and memory‐based learning with an Austrian soil library for predictions with infrared data

AbstractInfrared spectroscopy in the visible to near‐infrared (vis–NIR) and mid‐infrared (MIR) regions is a well‐established approach for the prediction of soil properties. Different data fusion and training approaches exist, and the optimal procedures are yet undefined and may depend on the heterogeneity present in the set and on the considered scale. The objectives were to test the usefulness of partial least squares regressions (PLSRs) for soil organic carbon (SOC), total carbon (Ct), total nitrogen (Nt) and pH using vis–NIR and MIR spectroscopy for an independent validation after standard calibration (use of a general PLSR model) or using memory‐based learning (MBL) with and without spiking for a national spectral database. Data fusion approaches were simple concatenation of spectra, outer product analysis (OPA) and model averaging. In total, 481 soils from an Austrian forest soil archive were measured in the vis–NIR and MIR regions, and regressions were calculated. Fivefold calibration‐validation approaches were carried out with a region‐related split of spectra to implement independent validations with n ranging from 47 to 99 soils in different folds. MIR predictions were generally superior over vis–NIR predictions. For all properties, optimal predictions were obtained with data fusion, with OPA and spectra concatenation outperforming model averaging. The greatest robustness of performance was found for OPA and MBL with spiking with R2 ≥ 0.77 (N), 0.85 (SOC), 0.86 (pH) and 0.88 (Ct) in the validations of all folds. Overall, the results indicate that the combination of OPA for vis–NIR and MIR spectra with MBL and spiking has a high potential to accurately estimate properties when using large‐scale soil spectral libraries as reference data. However, the reduction of cost‐effectiveness using two spectrometers needs to be weighed against the potential increase in accuracy compared to a single MIR spectroscopy approach.

Coal seam in-situ inorganic analysis based on least angle regression and competitive adaptive reweighted sampling algorithm by XRF–visNIR fusion

The fusion of X-ray fluorescence spectroscopy (XRF) and visible near infrared spectroscopy (visNIR) has been widely used in geological exploration. The outer product analysis (OPA) has a good effect in the fusion. The dimension of the spectral matrix obtained by OPA is large, and the Competitive Adaptive Reweighted Sampling (CARS) cannot cover the whole spectrum. As a result, the selected variables by the method are inconsistent each time. In this paper, a new feature variable screening method is proposed, which uses the Least Angle Regression (LAR) to select the high dimensional spectral matrix first, and then uses CARS to complete the secondary selection of the spectral matrix, forming the LAR-CARS algorithm. The purpose is to make the sampling method cover all the spectral data. XRF and visNIR tests were carried out on three cores in two boreholes, and a cross-validation set, validation set and a test set were established by combining the results of wavelength dispersion X-ray fluorescence spectrometer and ITRAX Core scanner in the laboratory. The quantitative model was established with the Extreme Gradient Boosting (XGBoost) and LAR-CARS was compared to these other algorithms (LAR, Successive Projections Algorithm, Monte Carlo uninformative variables elimination and CARS). The results showed that the RMSEP values of the models established by the LAR-CARS for six rock-forming elements (Si, Al, K, Ca, Fe, Ti) were relatively small, and the RPD ranges from 1.424 to 2.514. All these results show that the high-dimensional matrix formed by XRF and visNIR integration combined with LAR-CARS can be used for quantitative analysis of rock forming elements in in-situ coal seam cores, and the analysis results can be used as the basis for judging lithology. The research will provide necessary technical support for digital mine construction.

Improving soil organic matter estimation accuracy by combining optimal spectral preprocessing and feature selection methods based on pXRF and vis-NIR data fusion

Rapid and accurate estimation of soil organic matter (SOM) content is of great significance for agricultural production and carbon stock estimation. Visible-near-infrared spectroscopy (Vis-NIR) and portable X-ray fluorescence spectroscopy (pXRF), with the fast, low-cost, and environmental friendly characteristics, can realize the rapid large-scale detection of SOM. However, due to the heterogeneity and complexity of soil, estimation of SOM using a single sensor often leads to high uncertainty in result. Multi-sensor data fusion is one of the approaches to solve this problem, but suitable spectral preprocessing methods and data fusion methods still need further research. In this study, 500 soil samples were collected from two watersheds with large differences in soil parent material, soil type, and climate in the Xinjiang Uygur Autonomous Region of China. The effects of different spectral preprocessing methods for vis-NIR and pXRF spectra on SOM estimation were compared, and the effects of five feature selection methods on single sensor estimation and three different multi-sensor fusion estimations were evaluated. The results showed that vis-NIR spectrum was better than pXRF spectrum for SOM estimation, and the 1.6th-order derivative and baseline correction were the optimal preprocessing method for vis-NIR and pXRF spectra (Beam 3), respectively. Feature selection could improve the accuracy of the single sensor and multi-sensor fusion estimations. The competitive adaptive reweighted sampling (CARS) method was the optimal feature selection method for single sensor estimation and Granger–Ramanathan averaging (GRA) fusion estimation, and the variable importance in projection (VIP) was the optimal feature selection method for direct concatenation and outer-product analysis fusion estimation. In general, the optimal SOM estimation (RMSEp = 3.59 g kg−1, LCCCp = 0.84, RPIQp = 2.67) could be achieved based on CARS feature selection method and GRA fusion. This study proves that the combination of spectral preprocessing and feature selection can effectively improve the accuracy of the single sensor and multi-sensor fusion estimations. Especially, the multi-sensor fusion estimation has higher accuracy than the single sensor estimation. This study will provide a reference for the application of proximal soil sensing.

Iron Ore Tailing Composition Estimation Using Fused Visible–Near Infrared and Thermal Infrared Spectra by Outer Product Analysis

Iron ore tailings are mainly composed of SiO2 and iron, whose content determines the potential reuse strategy of the tailings. Compared with the traditional wet chemistry approach, spectroscopy has proven its superior effectiveness in characterizing and predicting minerals, such as iron oxides, clay, and SiO2. This study aims to estimate the content of SiO2 and TFe in iron ore tailings based on visible–near infrared (VIS–NIR, 350–2500 nm) and thermal infrared (TIR, 8–14 μm) spectroscopy. The outer product analysis (OPA) method is used to combine VIS–NIR and TIR spectral domains, from which an outer product matrix of fusion data can be generated. The study area is the iron ore tailing dam from Waitoushan, which is one of the super-large iron deposits in the Anshan–Benxi iron cluster of northeastern China. The spectral analysis results demonstrated the following: (1) The reflectance feature at 1163–2499 nm in the VIS–NIR range correlates with TFe and the emissivity feature at 8–9.4 and 10.7–12 μm in the TIR range correlates with SiO2. (2) Compared with the original absorbance spectra, the correlation coefficients of fusion spectra improve from 0.66 to 0.87 for TFe and from 0.64 to 0.84 for SiO2. (3) The partial least squares regression, random forest (RF), and extreme learning machine exploiting particle swarm optimization modeling methods are established for SiO2 and TFe estimation. The prediction accuracy results indicate that the prediction model with OPA-fused spectra performs significantly better than with individual VIS–NIR and TIR spectra. The RF model with input-fused spectra provides the highest accuracy with the coefficients of determination of 0.95 and 0.91, root mean square errors of 0.97% and 0.96%, and ratios of performance to interquartile distance of 6.49 and 2.31 for SiO2 and TFe content estimation, respectively. These outcomes provide a theoretical basis and technical support for tailing composition estimation using spectroscopy.

Fusion of visible near‐infrared and mid‐infrared data for modelling key soil‐forming processes in loess soils

AbstractPedogenic weathering of aeolian materials plays an essential role in global nutrient and carbon cycling. A quick and effective approach for temporally high‐resolution and spatially large‐scale pedogenic investigations has long been needed. Here, we used visible and near‐infrared, mid‐infrared and sensor‐fused data to predict pedogenesis‐related soil properties (i.e., grain‐size distribution, clay‐mineral properties and geochemical ratios) in a thick loess sequence in central China. Sensor fusion was achieved at three different levels: (1) direct combination of spectral parameters (low‐level fusion; Fusionpara); (2) combination of spectral features selected by principal component analysis (middle‐level fusion; FusionPCA) and (3) fusion using outer product analysis (high‐level fusion; FusionOPA). Sensor‐fusion generally improves the model predictions for all soil properties, with increases in the values of the model efficiency coefficient (MEC) of 8% and the performance‐to‐interquartile range of 12%. Whole‐soil properties are optimally predicted with the Fusionpara dataset using the random forest algorithm, yielding a mean MEC of 0.85. Spectral parameters D2200/D1900 and AS2200 are demonstrated as promising new pedogenic proxies, with higher values indicating more intense hydrolysis during pedogenesis. Spectral proxies along the loess sequence suggest that intense soil formation occurred during warm and humid interglacial periods when the East Asian summer monsoon intensified. The sensor‐fusion technique improved model performance for assessing mineral transformations and chemical weathering intensity, providing a quick and efficient means of interpreting pedogenic evolution, especially in the case of spatially large‐scale soil investigations.Highlights Fusion of VNIR and MIR spectra to model loess pedogenesis. Spectral modeling provides a robust surrogate for pedogenic evolution studies. Sensor fusion improves the performance of chemometric models. Sensor‐fusion models can reconstruct loess pedogenesis.

Data Fusion of XRF and Vis-NIR Using Outer Product Analysis, Granger–Ramanathan, and Least Squares for Prediction of Key Soil Attributes

Visible-near-infrared (vis-NIR) and X-ray fluorescence (XRF) are key technologies becoming pervasive in proximal soil sensing (PSS), whose fusion holds promising potential to improve the estimation accuracy of soil attributes. In this paper, we examine different data fusion methods for the prediction of key soil fertility attributes including pH, organic carbon (OC), magnesium (Mg), and calcium (Ca). To this end, the vis-NIR and XRF spectra of 267 soil samples were collected from nine fields in Belgium, from which the soil samples of six fields were used for calibration of the single-sensor and data fusion models while the validation was performed on the remaining three fields. The first fusion method was the outer product analysis (OPA), for which the outer product (OP) of the two spectra is computed, flattened, and then subjected to partial least squares (PLS) regression model. Two versions of OPA were evaluated: (i) OPA-FS in which the full spectra were used as input; and (ii) OPA-SS in which selected spectral ranges were used as input. In addition, we examined the potential of least squares (LS) and Granger–Ramanathan (GR) analyses for the fusion of the predictions provided by the single-sensor PLS models. Results demonstrate that the prediction performance of the single-sensor PLS models is improved by GR in addition to the LS fusion method for all soil attributes since it accounts for residuals. Resorting to LS, the largest improvements compared to the single-sensor models were obtained, respectively, for Mg (residual prediction deviation (RPD) = 4.08, coefficient of determination (R2) = 0.94, ratio of performance of inter-quantile (RPIQ) = 1.64, root mean square error (RMSE) = 4.57 mg/100 g), OC (RPD = 1.79, R2 = 0.69, RPIQ = 2.82, RMSE = 0.16%), pH (RPD = 1.61, R2 = 0.61, RPIQ = 3.06, RMSE = 0.29), and Ca (RPD = 3.33, R2 = 0.91, RPIQ = 1, RMSE = 207.48 mg/100 g). OPA-FS and OPA-SS outperformed the individual, GR, and LS models for pH only, while OPA-FS was effective in improving the individual sensor models for Mg as well. The results of this study suggest LS as a robust fusion method in improving the prediction accuracy for all the studied soil attributes.

Rapid Determination of Soil Class Based on Visible-Near Infrared, Mid-Infrared Spectroscopy and Data Fusion

Wise soil management requires detailed soil information, but conventional soil class mapping in a rather coarse spatial resolution cannot meet the demand for precision agriculture. With the advantages of non-destructiveness, rapid cost-efficiency, and labor savings, the spectroscopic technique has proved its high potential for success in soil classification. Previous studies mainly focused on predicting soil classes using a single sensor. In this study, we attempted to compare the predictive ability of visible near infrared (vis-NIR) spectra, mid-infrared (MIR) spectra, and their fused spectra for soil classification. A total of 146 soil profiles were collected from Zhejiang, China, and the soil properties and spectra were measured by their genetic horizons. Along with easy-to-measure auxiliary soil information (soil organic matter, soil texture, color and pH), four spectral data, including vis-NIR, MIR, their simple combination (vis-NIR-MIR), and outer product analysis (OPA) fused spectra, were used for soil classification using a multiple objectives mixed support vector machine model. The independent validation results showed that the classification model using MIR (accuracy of 64.5%) was slightly better than that using vis-NIR (accuracy of 64.2%). The predictive model built on vis-NIR-MIR did not improve the classification accuracy, having the lowest accuracy of 61.1%, which likely resulted from an over-fitting problem. The model based on OPA fused spectra performed best with an accuracy of 68.4%. Our results prove the potential of fusing vis-NIR and MIR using OPA for improving prediction ability for soil classification.

Data fusion for the measurement of potentially toxic elements in soil using portable spectrometers

Soil contamination posed by potentially toxic elements is becoming more serious under continuously development of industrialization and the abuse of fertilizers and pesticides. The investigation of soil potentially toxic elements is therefore urgently needed to ensure human and other organisms’ health. In this study, we investigated the feasibility of the separate and combined use of portable X-ray fluorescence (pXRF) and visible near-infrared reflectance (vis-NIR) sensors for measuring eight potentially toxic elements in soil. Low-level fusion was achieved by the direct combination of the pXRF and vis-NIR spectra; middle-level fusion was achieved by the combination of selected bands of the pXRF and vis-NIR spectra using the Boruta feature selection algorithm; and high-level fusion was conducted by outer-product analysis (OPA) and Granger–Ramanathan averaging (GRA). The estimation accuracy for the eight considered elements were in the following order: Zn > Cu > Ni > Cr > As > Cd > Pb > Hg. The measurement for Cu and Zn could be achieved by pXRF spectra alone with Lin’s concordance correlation coefficient (LCCC) values of 0.96 and 0.98, and ratio of performance to interquartile distance (RPIQ) values of 2.36 and 2.69, respectively. The measurement of Ni had the highest model performance for high-level fusion GRA with LCCC of 0.89 and RPIQ of 3.42. The measurements of Cr using middle- and high-level fusion were similar, with LCCC of 0.86 and RPIQ of 2.97. The best estimation accuracy for As, Cd, and Pb were obtained by high-level fusion using OPA, with LCCC >0.72 and RPIQ >1.2. However, Hg measurement by these techniques failed, having an unacceptable performance of LCCC <0.20 and RPIQ <0.75. These results confirm the effectiveness of using portable spectrometers to determine the contents of several potentially toxic elements in soils.

Convolutional neural network for simultaneous prediction of several soil properties using visible/near-infrared, mid-infrared, and their combined spectra

No single instrument can characterize all soil properties because soil is a complex material. With the advancement of technology, laboratories have become equipped with various spectrometers. By fusing output from different spectrometers, better prediction outcomes are expected than using any single spectrometer alone. In this study, model performance from a single spectrometer (visible-near-infrared spectroscopy, vis-NIR or mid-infrared spectroscopy, MIR) was compared to the combined spectrometers (vis-NIR and MIR). We selected a total of 14,594 samples from the Kellogg Soil Survey Laboratory (KSSL) database that had both vis-NIR and MIR spectra along with measurements of sand, clay, total C (TC) content, organic C (OC) content, cation exchange capacity (CEC), and pH. The dataset was randomly split into 75% training (n = 10,946) and the remaining (n = 3,648) as a test set. Prediction models were constructed with partial least squares regression (PLSR) and Cubist tree model. Additionally, we explored the use of a deep learning model, the convolutional neural network (CNN). We investigated various ways to feed spectral data to the CNN, either as one-dimensional (1D) data (as a spectrum) or as two-dimensional (2D) data (as a spectrogram). Compared to the PLSR model, we found that the CNN model provides an average improvement prediction of 33–42% using vis-NIR and 30–43% using MIR spectral data input. The relative accuracy improvement of CNN, when compared to the Cubist regression tree model, ranged between 22 and 36% with vis-NIR and 16–27% with MIR spectral data input. Various methods to fuse the vis-NIR and MIR spectral data were explored. We compared the performance of spectral concatenation (for PLSR and Cubist model), two-channel input method, and outer product analysis (OPA) method (for CNN model). We found that the performance of two-channel 1D CNN model was the best (R2 = 0.95–0.98) followed closely by the OPA with CNN (R2 = 0.93–0.98), Cubist model with spectral concatenation (R2 = 0.91–0.97), two-channel 2D CNN model (R2 = 0.90–0.95) and PLSR with spectral concatenation (R2 = 0.87–0.95). Chemometric analysis of spectroscopy data relied on spectral pre-processing methods: such as spectral trimming, baseline correction, smoothing, and normalization before being fed into the model. CNN achieved higher performance than the PLSR and Cubist model without utilizing the pre-processed spectral data. We also found that the predictions using the CNN model retained similar correlations to the actual values in comparison to other models. By doing sensitivity analysis, we identified the important spectral wavelengths variables used by the CNN model to predict various soil properties. CNN is an effective model for modelling soil properties from a large spectral library.

X-ray fluorescence and visible near infrared sensor fusion for predicting soil chromium content

Anthropogenic activities, such as sewage irrigation and application of pesticides and fertilizers, are the main cause of chromium (Cr) contamination in agricultural soils. Cr contamination reduces soil quality and threatens environmental and human health. Conventional Cr measurement methods, although accurate, involve complex sample processing steps and sophisticated laboratory analysis, which are time-consuming, costly, and often environmentally unfriendly. X-ray fluorescence (XRF) and visible near-infrared (vis–NIR) spectroscopy have been recognized as alternatives to measure soil heavy metal contamination in a cheap, fast, non-destructive, and environmentally conscious manner. In this study, 301 paddy soil samples from Fuyang, Zhejiang Province, China were used to explore the feasibility and effectiveness of XRF and vis–NIR spectra separately and in combination for estimating the soil Cr content. Two strategies, including outer-product analysis (OPA) and Granger–Ramanathan averaging (GRA), were used to combine the spectra and spectral models, respectively, from the two instruments (sensor fusion). Partial least-squares regression (PLSR) was used to train the models using a single sensor (XRF or vis-NIR spectra) and OPA fused spectra. Fifty boot straps were used to assess the uncertainty of the predictions for the aforementioned models. The results indicated that XRF spectra performed better than vis–NIR spectra for predictions of Cr content, with a Lin's concordance correlation coefficient (ρc) of 0.83, a root mean square error (RMSE) of 8.80, and a ratio of prediction derivation (RPD) of 1.75. Sensor fusion by OPA gave the highest prediction accuracy with a ρc of 0.90, RMSE of 6.80, and RPD of 2.30. The sensor fusion by GRA gave similar results with a ρc of 0.88, RMSE of 7.40, and RPD of 2.13. The predictions using both methods (OPA and GRA) were acceptable when considering the standard deviation of differences (SDD = 4.23). This suggests that OPA and the GRA sensor fusion methods are efficient and accurate for rapid measurement of Cr and provide a way forward for using these technologies for fast, sensor-based soil characterization.

Spectral fusion by Outer Product Analysis (OPA) to improve predictions of soil organic C

Soil organic carbon (C) is an important indicator of agricultural and environmental quality. It improves soil fertility and helps to mitigate greenhouse gas emissions. Soil spectroscopy with either vis–NIR (350–2500 nm) or mid-IR (4000–400 cm−1) spectra have been used successfully to predict organic C concentrations in soil. However, research to improve predictions of soil organic C by simply combining vis–NIR and mid-IR spectra to model them together has been unsuccessful. Here we use the Outer Product Analysis (OPA) to fuse vis–NIR and mid-IR spectra by bringing them into a common spectral domain. Using the fused data, we derived models to predict soil organic C and compared its predictions to those derived with vis–NIR and mid-IR models separately. We analyzed 1259 tropical soil samples from surface and subsurface layers across agricultural areas in Central Brazil. Soil organic C contents were determined by a modified Walkley-Black method, and vis–NIR and mid-IR reflectance spectra were obtained with a FieldSpec Pro and a Nicolet 6700 Fourier Transformed Infrared (FT-IR), respectively. Reflectances were log-transformed into absorbances. The mean content of soil organic C was 9.14 g kg−1 (SD = 5.64 g kg−1). The OPA algorithm was used to emphasize co-evolutions of each spectral domain into the same one by multiplying the absorbances from both sets of spectra to produce a matrix with all possible products between them. Support Vector Machine with linear kernel function was used for the spectroscopic modeling. Predictions of soil organic C using vis–NIR, mid-IR, and fused spectra were statistically compared by the Tukey's test using the coefficient of determination (R2), root mean squared error (RMSE), and ratio of performance to interquartile distance (RPIQ). Absorbances in vis–NIR and mid-IR were emphasized in the common spectral domain presenting stronger correlations with soil organic C than individual ranges. Soil organic C predictions with the OPA fused spectra were significantly better (R2 = 0.81, RMSE = 2.42 g kg−1, and RPIQ = 2.87) than those with vis–NIR (R2 = 0.69, RMSE = 3.38 g kg−1, and RPIQ = 2.08) or mid-IR spectra (R2 = 0.77, RMSE = 2.90 g kg−1, and RPIQ = 2.43). Fusing vis–NIR and mid-IR spectra by OPA improves predictions of soil organic C.

Rapid Non-destructive Detection of Spoilage of Intact Chicken Breast Muscle Using Near-infrared and Fourier Transform Mid-infrared Spectroscopy and Multivariate Statistics

Near-infrared (NIR) transflectance and Fourier transform-infrared (FT-IR) attenuated total reflectance spectra of intact chicken breast muscle packed under aerobic conditions and stored at 4° for 14 days were collected and investigated for their potential use in rapid non-destructive detection of spoilage. Multiplicative scatter correction-transformed NIR and standard normal variate-transformed FT-IR spectra were analysed using principal component analysis (PCA), partial least-squares discriminant analysis (PLS2-DA) and outer product analysis (OPA). PCA and PLS2-DA regression failed to completely discriminate between days 0 and 4 samples (total viable count (TVC) days 0 and 4 = 5.23 and 6.75 log10 cfu g−1) which had bacterial loads smaller than the accepted levels (8 log10 cfu g−1) of sensory spoilage detection but classified correctly days 8 and 14 samples (TVC days 8 and 14 = 9.61 and 10.37 log10 cfu g−1). OPA performed on both NIR and FT-IR datasets revealed several correlations that highlight the effect of proteolysis in influencing the spectra. These correlations indicate that increase in free amino acids and peptides could be the main factor in the discrimination of intact chicken breast muscle. This investigation suggests that NIR and FT-IR spectroscopy can become useful, rapid, non-destructive tools for spoilage detection.

Outer Product Analysis Applied to near Infrared and Mid Infrared Spectra to Study a Spanish Protected Denomination of Origin Cheese

Near infrared to mid infrared (NIR–MIR) spectroscopy correlation analysis was applied to test its feasibility in understanding the contribution of the absorption bands related to cheese components for the characterisation of protected denomination of origin (PDO) products. The influence of sample presentation on spectral response was also investigated. Idiazabal cheese, a Spanish PDO cheese, was used as a model. Acidity, expressed as pH, dry matter, fat and total nitrogen content were evaluated in duplicate. The NIR–MIR interactions were analysed by outer product analysis. This study allowed the identification of the main absorption bands associated with fat, protein and water, by using the correlations between constituents in the two studied domains. Confirming preliminary results, it was highlighted that quantitative determination is influenced by sample presentation mode.

Sugars as a Perturbation of the Water Matrix

Near infrared (NIR) and nuclear magnetic resonance (NMR) spectroscopy studies were performed to determine the behaviour of water during an osmotic process of apple spheres in concentrated sugar solutions. The osmotic dehydration is a process of water removal from cellular structures through immersion in a hypertonic solution. Relationships between sugars and water were studied using both two-dimensional correlation, calculated on NIR spectra recorded during the process, and NIR–NMR outer product analysis (OPA). We found that there was a shift of 7nm towards higher wavelengths in the maximum absorbance of the first overtone range of the water O–H stretching, due to the increase of hydrogen bonds implicated in the binding of the sugars progressively increasing in concentration during water removal. The absorptions detected by two-dimensional correlation, using processing time as the dynamic variable, belong to the elements which have more OH free as indicated from the outer product analysis, i.e. free water at 1936 nm followed by bonded water at 1393 nm and 1518 nm and sugars at 2131 nm, respectively.

Principal component transform — Outer product analysis in the PCA context

Outer product analysis is a method that permits the combination of two spectral domains with the aim of emphasizing co-evolutions of spectral regions. This data fusion technique consists in the product of all combinations of the variables that define each spectral domain. The main issue concerning the application of this technique is the very wide data matrix obtained which can be very hard to handle with multivariate techniques such as PCA or PLS, due to computer resources constraints. The present work presents an alternative way to perform outer product analysis in the PCA context without incurring into high demands on computational resources. This works shows that by decomposing each spectral domain with PCA and performing the outer product on the recovered scores, one can obtain the same results as if one calculated the outer product in the original variable space, but using much less computational resources. The results show that this approach will make possible to apply outer product analysis to very wide domains.

Infrared spectroscopy and outer product analysis for quantification of fat, nitrogen, and moisture of cocoa powder

The combination of the near infrared (NIR) and Fourier-transform infrared (FTIR) absorbance spectra (1100–2500 nm and 4000–600 cm −1) of 100 cocoa powder samples was used to build calibration models for the determination of the content of fat, nitrogen, and moisture. The samples that comprised the dataset had an average composition of 13.51% of fat, 3.77% nitrogen, and 3.98% moisture. The fat content ranged from 2.42 to 22.00%, the nitrogen from 0.88 to 4.48%, and moisture from 1.60 to 7.80%. For NIR, the relative root mean square error of cross-validation (RMSECV) was 7.0% ( R 2 = 0.96) for fat, 1.7% ( R 2 = 0.98) for nitrogen, and 5.2% ( R 2 = 0.94) for moisture. For FTIR, the relative RMSECV was 10.4% ( R 2 = 0.94) for fat and 3.9% ( R 2 = 0.95) for nitrogen. However, for moisture, it was not possible to build a calibration model with suitable predictability. The combination of the NIR and FTIR domains (data fusion) by outer product analysis PLS1 allowed to predict these parameters and to characterise frequencies in one domain based on the information of the other domain. This work allows to conclude that the second derivative of NIR is the recommended procedure to quantify fat, nitrogen, and moisture content in cocoa powders by infrared spectroscopy.

Enhanced multivariate analysis by correlation scaling and fusion of LC/MS and 1H NMR data

A method to enhance the multivariate data interpretation of, for instance, metabolic profiles is presented. This was done by correlation scaling of 1H NMR data by the time pattern of drug metabolite peaks identified by LC/MS, followed by parallel factor analysis (PARAFAC). The variables responsible for the discrimination between the dosed and control rats in this model were then eliminated in both data sets. Next, an additional PARAFAC analysis was performed with both LC/MS and 1H NMR data, fused by outer product analysis (OPA), to obtain sufficient class separation. The loadings from this second PARAFAC analysis showed new peaks discriminating between the classes. The time trajectories of these peaks did not agree with the drug metabolites and were detected as possible candidates for markers. These data analyses were also compared with the PARAFAC analysis of raw data, which showed very much the same loading peaks as for the correlation-scaled data, although the intensities differed. Elimination of the variables correlated with the drug metabolites was therefore necessary to be able to select the peaks which were not drug metabolites and which discriminated between the classes. 1 1 A copy of the Matlab program files used in this work may be obtained from the authors.

Image processing of outer-product matrices – A new way to classify samples: Examples using visible/NIR/MIR spectral data

A chemometric analysis has been developed to emphasise the discrimination power of spectroscopic techniques such as near infrared, mid-infrared and visible spectroscopy. The combination of two spectral domains using outer product analysis (OPA) leads to the calculation of an outer product (OP) matrix. The representation of this matrix is called the “analytical fingerprint” of the samples and their classification is performed in the following steps. First, two different techniques are tested by subtracting the images one-by-one and the sum of all the elements of the resulting difference matrix gives a scalar, characteristic of the distance between the two images. Combining chemical analysis with image processing techniques provides an original approach to study butters and margarines in relation to their fat content. Best results were obtained with the OP matrix built from NIR and visible signals following the use of city-block distance and average linkage. Samples were arranged in four groups: 100%, 82–75%, 70–59% and 38–25% w/w fat. The cophenetic correlation coefficient (validity of the cluster information generated by the linkage function) associated with these spectral data has a value of 0.973. Similar results were obtained using Ward's algorithm which generated four groups and a cophenetic correlation coefficient equal to 0.959.