A Simplified Algorithm of PLS Regression

This paper describes a simplified algorithm of PLS regression, which can obviously reduce the computation of some parameters and simplify the computing procedure. Moreover, the new optimistic rule of this method provides a new explanation to the result of PLS regression.

PARTIAL LEAST-SQUARES(PLS)REGRESSION AND SPECTROPHOTOMETRY AS APPLIED TO THE ANALYSIS OF MULTICOMPONENT MIXTURES

The UV absorption spectra of o-naphthol,α-naphthylamine,2,7-dihydroxy naphthalene,2,4-dimethoxy ben- zaldehyde and methyl salicylate,overlap severely;therefore it is impossible to determine them in mixtures by traditional spectrophotometric methods.In this paper,the partial least-squares(PLS)regression is applied to the simultaneous determination of these compounds in mixtures by UV spectrophtometry without any pretreatment of the samples.Ten synthetic mixture samples are analyzed by the proposed method.The mean recoveries are 99.4%,996%,100.2%,99.3% and 99.1%,and the relative standard deviations(RSD) are 1.87%,1.98%,1.94%,0.960% and 0.672%,respectively.

Latent Structure Linear Regression

A short review is given of standard regression analysis. It is shown that the results presented by program packages are not always reliable. Here is presented a general framework for linear regression that includes most linear regression methods based on linear algebra. The H-principle of mathematical modelling is presented. It uses the analogy between the modelling task and measurement situation in quantum mechanics. The principle states that the modelling task should be carried out in steps where at each step an optimal balance should be determined between the value of the objective function, the fit, and the associated precision. H-methods are different methods to carry out the modelling task based on recommendations of the H-principle. They have been applied to different types of data. In general, they provide better predictions than linear regression methods in the literature.

Improved Water Network Macroscopic Model Utilising Auto-Control Adjusting Valve by PLS

In order to overcome the low precision and weak applicability problems of the current municipal water network state simulation model, the water network structure is studied. Since the telemetry system has been applied increasingly in the water network, and in order to reflect the network operational condition more accurately, a new water network macroscopic model is developed by taking the auto-control adjusting valve opening state into consideration. Then for highly correlated or collinear independent variables in the model, the partial least squares (PLS) regression method provides a model solution which can distinguish between the system information and the noisy data. Finally, a hypothetical water network is introduced for validating the model. The simulation results show that the relative error is less than 5.2%, indicating that the model is efficient and feasible, and has better generalization performance.

Correlation Analysis between Quality Characteristics and Fruit Mineral Element Contents in 'Fuji' Apples

[Objective] The aims were to explore the relationship between the contents of fruit mineral elements and quality features of the ＇Fuji＇ apple, screen major mineral elements of the fruit affecting fruit quality features, and set up optimum proposals of fruit mineral elements for good fruit qualities, so as to provide a theoretical basis for the reasonable orchard soil and foliar fertilizer applications to increase fruit quality and reduce the physiological diseases related to the ＇Fuji＇ apple. [Methods] The fruit mineral elements and quality indicators of ＇Fuji＂ apples were in- vestigated and analyzed, which were collected from the 153 commercial apple or- chards of ＂Fuji＇ apple located in 51 counties. The variable importance for projection （VlP） of partial least squares regression （PLS） method was used to analyze the model effect and weight analysis impact of the fruit mineral element contents to fruit quality, screen out major factors of fruit mineral elements influencing the different fruit qualities, and set up the regression equation of the fruit qualities and major fruit mineral elements. Linear programming was used to obtain optimum proposals of the fruit mineral elements to achieve good ＇Fuji＇ apple qualities. [Results] The mineral elements content and quality characteristics in ＂Fuji＇ apple fruit had great differences in the different produce regions in which the maximum content of nitro- gen, iron, zinc and boron in the ＇Fuji＇ fruit were12.06, 6.17, 7.7, and 10.08 times greater than the minimum respectively, and the differences for titratable acid and the SSC/TA ratio were 2.33 and 2.16 times respectively. The correlation analysis between the fruit mineral element contents and qualities showed that the nitrogen content of fruit had a significantly negative correlation with the soluble solid content, SSC/TA ratio and red color area, while the calcium and iron contents in the fruit were in significantly positive correlation with the soluble solid content and SSC/TA ratio. The model effect and weight analysis showed that the content of nitrogen and iron in the fruit had a greater influence on the integral fruit quality, followed by phosphorus, potassium and calcium. The variable importance for projection （VlP） technology of PLS found that the mean fruit weight was primarily affected by nitro- gen, phosphorus and potassium, and the soluble solid was primarily affected by ni- trogen, calcium and iron, while the red color area was primarily affected by nitro- gen, potassium, calcium, iron and zinc. The regression equation between fruit quality and mineral element contents showed that the mean fruit weight had a greater pos- itive effect coefficient with the content of phosphorus and potassium, and a greater negative effect coefficient with the content of nitrogen in the fruit. Moreover, the sol- uble solid had the largest negative effect coefficient with nitrogen and largest posi- tive effect coefficient with calcium and iron in the fruit. [Conclusion] The maximum content of soluble solid and titratable acid were 1.5 times more than the minimum, and nitrogen, iron, zinc and boron were 6 times more than in the ＇Fuji＇ apple fruit in the different produce regions. Therefore, it is a key technological measure to improve the overall qualities of the ＂Fuji＇ apple by decreasing the content of nitrogen, and increasing the contents of iron, phosphorus, potassium and calcium in the fruit.

In vivo prediction of intramuscular fat in pigs using computed tomography

One hundred and four pure-bred Norwegian Duroc boars were CT (computed tomography) scanned to predict the in vivo intramuscular fat percentage in the loin. The animals were slaughtered and the loin was cut commercially. A muscle sample of the m. Longissimus dorsi was sampled and analyzed by the use of near-infrared spectroscopy. Data from CT images were collected using an in-house MATLAB script. Calibration models were made using PLS (partial least square) regression, containing independent data from CT images and dependent data from near-infrared spectroscopy. The data set used for calibration was a subset of 72 animals. The calibration models were validated using a subset of 32 animals. Scaling of independent data and filtering using median filtering were tested to improve predictions. The results showed that CT is not a feasible method for in vivo prediction of intramuscular content in swine.

Land Suitability Evaluation for Agricultural Cropland in Mongolia Using the Spatial MCDM Method and AHP Based GIS

The purpose of this study was to prepare a cropland suitability map of Mongolia based on comprehensive landscape principles, including topography, soil properties, vegetation, climate and socio-economic factors. The primary goal was to create a more accurate map to estimate vegetation criteria (above ground biomass AGB), soil organic matter, soil texture, and the hydrothermal coefficient using Landsat 8 satellite imagery. The analysis used Landsat 8 imagery from the 2016 summer season with a resolution of 30 meters, time series MODIS vegetation products (MOD13, MOD15, MOD17) averaged over 16 days from June to August 2000-2016, an SRTM DEM with a resolution of 30 meters, and a field survey of measured biomass and soil data. In total, 6 main factors were classified and quality evaluation criteria were developed for 17 criteria, each with 5 levels. In this research the spatial MCDM (multi-criteria decision-making) method and AHP based GIS were applied. This was developed for each criteria layer’s value by multiplying parameters for each factor obtained from the pair comparison matrix by the weight addition, and by the suitable evaluation of several criteria factors affecting cropland. General accuracy was 88%, while PLS and RF regressions were 82.3% and 92.8%, respectively.

Determination of drug,excipients and coating distribution in pharmaceutical tablets using NIR-CI

The growing interest of the pharmaceutical industry in Near Infrared-Chemical Imaging (NIR-CI) is a result of its high usefulness for quality control analyses of drugs throughout their production process (particularly of its non-destructive nature and expeditious data acquisition).In this work,the concentration and distribution of the major and minor components of pharmaceutical tablets are determined and the spatial distribution from the internal and external sides has been obtained.In addition,the same NIR-CI allowed the coating thickness and its surface distribution to be quantified.Images were processed to extract the target data and calibration models constructed using the Partial Least Squares (PLS) algorithms.The concentrations of Active Pharmaceutical Ingredient (API) and excipients obtained for uncoated cores were essentially identical to the nominal values of the pharmaceutical formulation.But the predictive ability of the calibration models applied to the coated tablets decreased as the coating thickness increased.

Retrieval of Total Suspended Matters Using Field Spectral Data in Shitoukoumen Reservoir,Jilin Province,Northeast China

From August to October in 2006,three times of field spectral measurements with a Field Spec FR spectroradiometer(Analytical Spectral Devices,Inc.,USA) were carried out in Shitoukoumen Reservoir,Jilin Province,Northeast China. Owing to the serious soil and water loss in the upstream,reflectance curves of the reservoir were characterized by high concentrations of total suspended matter(TSM) . Extending the spectral analysis to 1200nm in the near-infrared band,this research revealed an obvious reflectance peak around 1070nm which was caused by the strong backscattering of high TSM. The method of partial least squares(PLS) regression was applied to retrieving the TSM. Reflectance in two spectral bands,i.e.,675-948nm and 1029-1105nm,were used as variables to develop PLS models. Traditional linear regression,first derivative model and logarithmic model were also used for the comparison of different models. Results showed that the PLS model based on Rrs(675) -Rrs(948) gave out best results with high precision and stability. Although the PLS model based on Rrs(1029) -Rrs(1105) did not have an outstanding performance due to lots of noise,the reflectance peak in the near-infrared band was an important TSM feature and its efficient exploitation would have a considerable significance in TSM remote sensing.

Spatio-temporal variation of Fraction of Photosynthetically Active Radiation absorbed by vegetation in the Hengduan Mountains, China

The Fraction of Absorbed Photosynthetically Active Radiation(FPAR) is an important indicator of the primary productivity of vegetation. FPAR is often used to estimate the assimilation of carbon dioxide in vegetation. Based on MOD15 A2 H/FPAR data product, the temporal and spatial variation characteristics and variation trend of FPAR in different vegetation types in 2001 to 2018 were analyzed in the Hengduan Mountains. The response of FPAR to climate change was investigated by using Pearson correlation analytical method and partial least squares regression analysis. Results showed that the FPAR in Hengduan Mountains presented an increasing trend with time. Spatially, it was high in the south and low in the north, and it also showed obvious vertical zonality by elevation gradient.The vegetation FPAR was found to be positively correlated with air temperature and sunshine duration but negatively correlated with precipitation. Partial least squares regression analysis showed that the influence of sunshine duration on vegetation FPAR in Hengduan Mountains was stronger than that of air temperature and precipitation.

Prediction of salmon (Salmo salar) quality during refrigeration storage based on dielectric properties

Dielectric properties are validated to be correlated with the changes of food quality during 4℃ storage,thus it could be used as predictive indicators for the quality parameters of salmon(Salmo salar)during cold storage.An open-ended coaxial detection method was used to determine the dielectric properties(dielectric constantε'and dielectric lossε")of salmon at the frequency range of 20-2500 MHz,and to explore the relationship between dielectric properties and volatile base nitrogen(TVB-N),thiobarbituric acid reactants(TBARS),total viable counts(TVC),pH and K-value in salmon fillets during storage for 7 d.Results showed that the TVB-N,TBARS,TVC and K-value of salmon increased linearly with the increase of storage time,and the pH decreased firstly and increased subsequently.Also,the dielectric properties(ε'andε")decreased with the increase of frequency,and increased with the increase of storage time.During 7 d storage,ε"increased the most at the frequency of 27.12 and 40.68 MHz,while at the frequency of 915 MHz and 2450 MHz,the increase ofε"was smaller.Results analyzed by Pearson correlation analysis showed that significant correlation(p<0.01)was found betweenε"and TVB-N and TBARS at the frequency of 27.12,40.68,100.00,300 and 915 MHz.The results of the partial least square(PLS)model showed that all the determination coefficients(R2pred)were over 0.900.Especially for TBARS,the R2pred of PLS-ε'and PLS-ε"were 0.913 and 0.920,respectively,and the root mean square error of prediction(RMSEP)were 0.041 and 0.039,respectively.However,the highest R2pred for PLS-ε'and PLS-ε"both occurred in TVB-N.Also,the predicted values against measured values of TVB-N,TBARS and TVC of salmon presented a good linear relationship.The linear coefficient R2 of TVB-N,TBARS and TVC for PLS-ε'were 0.937,0.910 and 0.917 respectively,and 0.942,0.917 and 0.933 respectively for PLS-ε".The results demonstrated the dielectric properties combined with PLS analysis can be used as a rapid and non-destructive method to predict quality parameters of salmon during 4℃ storage and could be further applied to other aquatic products.

Volatile profile analysis and quality prediction of Longjing tea(Camellia sinensis) by HS-SPME/GC-MS

This study aimed to analyze the volatile chemical profile of Longjing tea, and further develop a prediction model for aroma quality of Longjing tea based on potent odorants. A total of 21 Longjing samples were analyzed by headspace solid phase microextraction (HS-SPME) coupled with gas chromatography-mass spectrometry (GC-MS).Pearson's linear correlation analysis and partial least square (PLS) regression were applied to investigate the relationship between sensory aroma scores and the volatile compounds. Results showed that 60 volatile compound scould be commonly detected in this famous green tea. Terpenes and esters were two major groups characterized,representing 33.89% and 15.53% of the total peak area respectively. Ten compounds were determined to contribute significantly to the perceived aroma quality of Longjing tea, especially linalool (0.701), nonanal (0.738), (Z)-3-hexenyl hexanoate (-0.785), and β-ionone (-0.763). On the basis of these 10 compounds, a model (correlation coefficient of89.4% and cross-validated correlation coefficient of 80.4%) was constructed to predict the aroma quality of Longjingtea. Summarily, this study has provided a novel option for quality prediction of green tea based on HS-SPME/GC-MStechnique.

Real time monitoring of bioreactor mAb IgG3 cell culture process dynamics via Fourier transform infrared spectroscopy： Implications for enabling cell culture process analytical technology

Compared to small molecule process analytical technology （PAT） applications, biotechnology product PAT applications have certain unique challenges and opportunities. Understanding process dynamics of bioreactor cell culture process is essential to establish an appropriate process control strategy for biotechnology product PAT applications. Inline spectroscopic techniques for real time monitoring of bioreactor cell culture process have the distinct potential to develop PAT approaches in manufac- turing biotechnology drug products. However, the use of inline Fourier transform infrared （FTIR） spectroscopic techniques for bioreactor cell culture process monitoring has not been reported. In this work, real time inline FTIR Spectroscopy was applied to a lab scale bioreactor mAb IgG3 cell culture fluid biomolecular dynamic model. The technical feasibility of using FTIR Spectroscopy for real time tracking and monitoring four key cell culture metabolites （including glucose, glutamine, lactate, and ammonia） and protein yield at increasing levels of complexity （simple binary system, fully formulated media, actual bioreactor cell culture process） was evaluated via a stepwise approach. The FTIR fingerprints of the key metabolites were identified. The multivariate partial least squares （PLS） calibration models were established to correlate the process FTIR spectra with the concentrations of key metabolites and protein yield of in-process samples, either individually for each metabolite and protein or globally for all four metabolites simultaneously. Applying the 2＇ld derivative pre-processing algorithm to the FTIR spectra helps to reduce the number of PLS latent variables needed significantly and thus simplify the interpretation of the PLS models. The validated PLS models show promise in predicting the concentration profiles of glucose, glutamine, lactate, and ammonia and protein yield over the course of the bioreactor cell culture process. Therefore, this work demonstrated the technical feasibility of real time monitoring of the bioreactor cell culture process via FTIR spectroscopy. Its implications for enabling cell culture PAT were discussed.