Estimation of the Microbiological Quality of Meat Using Rapid and Non-Invasive Spectroscopic Sensors

Spectroscopic methods in tandem with machine learning methodologies have attracted considerable research interest for the estimation of food quality. The objective of this study was the evaluation of Fourier transform infrared (FTIR) spectroscopy and multispectral imaging (MSI) coupled with appropriate machine learning regression algorithms for assessing meat microbiological quality. For this purpose, minced pork patties were stored aerobically and under modified atmosphere packaging (MAP) conditions, at isothermal and dynamic temperature conditions. At regular time intervals during storage, samples were subjected to (i) microbiological analysis, (ii) FTIR measurements and (iii) MSI acquisition. The collected FTIR data were processed by feature extraction methods to reduce dimensionality, and subsequently Support Vector Machines (SVM) regression models were trained using spectral features (FTIR and MSI) to estimate microbiological quality of meat (microbial population). The regression models were evaluated with different experimental replicates using distinct meat batches. The performance of the models was evaluated in terms of correlation coefficient (r), root mean square error (RMSE), mean absolute error (MAE) and residual prediction deviation (RPD). The RMSE values for the microbial population estimation models using FTIR were 1.268 and 1.024 for aerobic and MAP storage, respectively. The performance in terms of RMSE for the MSI-based models was 1.144 for aerobic and 0.923 for MAP storage, while the combination of FTIR and MSI spectra resulted in models with RMSE equal to 1.146 for aerobic and 0.886 for MAP storage. The experimental results demonstrated the potential of estimating the microbiological quality of minced pork meat from spectroscopic data.


I. INTRODUCTION
In the current Food Safety approach, a wide range of audits and inspections are applied to evaluate the quality or safety of raw or processed materials and food products [1]. This is largely based on good design of processes, products and procedures, where the end or finished product testing is considered to be the control measure of the production process. In the case of microbiological food safety, specific The associate editor coordinating the review of this manuscript and approving it for publication was Shuihua Wang . microbiological analyses should be performed. In specific, microbiological analyses can be implemented with conventional microbiology approaches (e.g., colony counting methods) or molecular techniques that are considered more reliable and accurate [2], [3]. Chemical analyses are also used to monitor safety and quality of foods. These analyses have certain disadvantages, as they are (i) time-consuming in providing retrospective results, (ii) costly, (iii) some require high-tech molecular tools and thus, experienced and specialized personnel and commonly (iv) destructive to test products, limiting thus their potential to be used on-, in-or at-line [4], [5]. Due to these disadvantages, such analysis approaches cannot sufficiently guarantee consumer protection, since 100% inspection and sampling are technically, financially and logistically impossible.
In recent years, novel spectroscopic techniques have been used for assessing the quality and/or adulteration or other fraudulent practices of certain foods including raw meats and fish. Such techniques are based on visible/infrared (VIS/IR), Raman [6], nuclear magnetic resonance (NMR) spectroscopies and spectral imaging [7], [8]. Although the currently available data should allow for significant improvements in food chain traceability and food safety, such improvements have not been sufficiently fulfilled yet. Actually, novel spectroscopic techniques are not yet scientifically sound and foodspecific data are not readily available for producers and food chain actors [9]- [14].
In this context, the potential use of spectroscopybased sensors, in tandem with machine learning regression algorithms, in the estimation of microbial populations was investigated. The objective of this study was to evaluate the potential of spectral data for developing models that will allow accurate estimation of the microbial populations of minced pork samples. The spectral data evaluated for this purpose were Fourier transform infrared (FTIR) spectroscopy and multispectral imaging (MSI) data, while different parameters were taken into account in model development. Specifically, the collected pairs of data (spectroscopic measurements of each meat sample and the corresponding microbiological analyses results) utilized for model development and evaluation corresponded to (a) independent experimental replicates involving distinct meat batches (accounting for both experimental and biological variability) and (b) different packaging conditions (aerobic storage, modified atmosphere packaging). Moreover, with reference to the FTIR data, different feature extraction approaches were applied in order to extract useful information (due to the high dimensionality of the FTIR feature space compared to the number of samples).

II. EXPERIMENTAL DESIGN A. PREPARATION OF MEAT SAMPLES AND STORAGE CONDITIONS
Minced pork was purchased from a local butchery in Athens, Greece and transported to the laboratory with minimal delay, i.e. within 30 min. Minced pork patties (ca. 100g each) were prepared and placed onto styrofoam trays (duplicate samples (two patties) were placed in each tray). The described procedure was repeated eight times and the experiments were chronically independent (eight experimental replicates). Four replicates were stored aerobically (AIR) and four replicates under modified atmosphere packaging (MAP) conditions. Data derived from experimental replicates 1 and 2 have been previously published [15]. Samples stored aerobically were wrapped with cling film, while samples packed under modified atmosphere packaging conditions were enclosed in plastic packages (length: 25cm, width: 25cm, thickness: 90µm, permeability of ca. 25, 90, 6 cm 3 m −2 day −1 bar −1 (1 bar = 105Pa), at 20 • C and 50% RH for CO 2 , O 2 and N 2 , respectively) and flushed with 80%O 2 and 20%CO 2 using a HenkoVac 1900Machine (Howden Food Equipment BV, The Netherlands). The applied high-oxygen MAP conditions were selected so as the red colour of minced pork to be preserved and the microbiological shelf life to be extended [16]. Samples were stored at three different isothermal conditions, namely 4, 8 and 12 • C and under dynamic temperature conditions (periodic temperature changes (4-8-12 • C) every 8h) in high-precision (±0.5 • C) programmable incubators (MIR-153, Sanyo Electric Co., Osaka, Japan) for a maximum time period of 15 days (i.e. during storage at 4 • C under MAP storage). Duplicate samples were analyzed at 10-h or 14-h intervals until 110h, while after 110h samples were analyzed at 24-h intervals, until pronounced spoilage was observed. The incubation temperatures were recorded at 15-min intervals throughout storage using electronic temperature-monitoring devices (COX TRACER R , Cox Technologies Inc., Belmont, NC, USA). Meat samples corresponding to independent experimental replicates were evaluated in the context of this study, with duplicate samples (originating from different 100g portions) being analyzed at the defined time intervals for every storage condition (i.e. packaging and temperature). The sampling points (time intervals) were selected so as different microbiological quality levels of minced meat, corresponding to various microbial concentrations from low (fresh meat) to high populations (spoiled meat), to be covered; in this sense, the proposed methodology should allow for the development of an efficient meat quality assessment approach that is applicable in real-life setups such as food quality inspections in restaurants, butcheries and groceries where the storage conditions and time are unknown. The assessment of food quality and more specifically of microbiological quality is a rather difficult and complex task for food commodities, such as minced pork. A number of intrinsic (pH, a w , chemical composition, Eh, food structure) and extrinsic (temperature, humidity, gaseous condition of packaging) factors influence the rate of food deterioration, loss of freshness and loss of quality across the food chain e.g. during the storage of the product from farm to fork. Among the intrinsic/extrinsic factors mentioned above, temperature is the most detrimental one. For this reason, in food science the simulation of conditions followed in the present study (i.e. different temperature and storage conditions) is essential. The more samples analyzed in different storage conditions the better the microbial modeling is. The applied analytical procedures included: (i) microbiological analysis, (ii) FTIR spectroscopy measurements and (iii) MSI acquisition. A total of 903 samples were analyzed in the course of this study, with 456 and 447 samples corresponding to storage under AIR and MAP conditions, respectively.

B. MICROBIOLOGICAL ANALYSIS
Minced pork patties were analyzed microbiologically on the day of arrival to the laboratory (time-zero) and at regular VOLUME 8, 2020 time intervals during storage as described in section II. A. For the purpose of microbiological analysis, 25-g minced pork portions were transferred aseptically to 400-ml sterile stomacher bags (Seward Medical, London, United Kingdom) containing 225 ml of quarter-strength Ringer's solution (Lab M Limited, Lancashire, United Kingdom) and homogenized in a Stomacher apparatus (Lab Blender 400, Seward Medical) for 60 sec at room temperature. Appropriate serial decimal dilutions in Ringer's solution were surface plated on tryptic glucose yeast agar (Plate Count Agar; Biolife, Milan, Italy) and incubated at 25 • C for 72h, for the enumeration of total mesophiles (total viable counts, TVC). The obtained microbiological data were converted to log (colony forming units) per gram of meat (log CFU/g).

1) AIR STORAGE
The evolution of TVC of minced pork stored aerobically at 4 • C, 8 • C, dynamic temperatures and 12 • C for replicates 1, 2, 3 and 4 is illustrated in Fig. 1 (a), (b), (c) and (d), respectively. The initial TVC in minced pork ranged from 3.00 to 3.86 log CFU/g (Fig. 1), a concentration which is in accordance with the range of 2.0 to 4.2 log CFU/g reported in the scientific literature [17], [18]. Similar microbial growth trends were observed among independent replicates, with replicate 1 being associated with lower values of microbial counts compared to the other replicates in most sampling times, an observation that is most likely related to the better initial microbiological quality of meat ( Fig. 1). It has been demonstrated that excessive quality deterioration of minced meat during aerobic storage, including off-odours' development and slime production, is evident when TVC is 7-8 log CFU/g [19], [20]. Mean (± standard deviation, n = 8) TVC of samples reached 7-8 log CFU/g at 4 • C in 158h (7.63 ± 0.79 log CFU/g), at 8 • C in 96h (7.93 ± 0.48 log CFU/g), at dynamic temperatures in 96h (7.66 ± 0.43 log CFU/g) and at 12 • C in 62h (7.57 ± 0.32 log CFU/g). The microbial growth recorded at 8 • C was similar with that recorded at dynamic temperature conditions. The microbial groups that contributed mainly to the spoilage of minced pork were Pseudomonas spp., Brochothrix thermosphacta and lactic acid bacteria, with Pseudomonas spp. constituting the dominant spoilage microorganisms (data not shown), findings that are in agreement with those previously reported in the scientific literature [21].

2) MAP STORAGE
The initial microbial populations in the minced pork samples corresponding to the four experimental replicates of MAP storage were generally higher compared to those recorded for the samples stored under AIR conditions. Indeed, the initial TVC in minced pork stored under MAP conditions ranged from 3.66 to 5.30 log CFU/g. The evolution of TVC during storage at 4 • C, 8 • C, dynamic temperatures and 12 • C under MAP conditions for replicates 1, 2, 3 and 4 is illustrated in Fig. 2 (a), (b), (c) and (d), respectively. Since the initial microbiological quality of minced pork corresponding to replicates 1 and 2 was higher (i.e. lower initial microbial populations) compared to replicates 3 and 4, the duration of the applied storage in the latter case was shorter (Fig. 2). Similarly to the observations made under AIR storage conditions, the microbial evolution recorded during MAP storage at 8 • C was comparable with that recorded at dynamic temperature conditions. Overall, the shelf life of minced pork did not appear to be considerably extended during MAP storage as compared to AIR storage under the conditions of this study, most likely due to the relatively high initial microbial population of the minced pork samples as mentioned above. The main spoilage bacteria expected to contribute to quality deterioration of minced pork during storage under MAP conditions are in decreasing order Br. thermosphacta, lactic acid bacteria and Pseudomonas spp. [21].

C. FTIR SPECTROSCOPY
FTIR spectral data were collected using a ZnSe 45 • HATR (Horizontal Attenuated Total Reflectance) crystal (PIKE Technologies, Madison, Wisconsin, United States) and an FTIR-6200 JASCO spectrometer (Jasco Corp., Tokyo, Japan) equipped with a standard sample chamber, a triglycine sulphate (TGS) detector and a Ge/KBr beam splitter. The crystal used has a refractive index of 2.4 and a depth of penetration of 2.0 µm at 1000 cm −1 . Using the Spectra Manager TM software version 2 (Jasco Corp.), spectra were collected over the wavenumber range of 4000 to 400 cm −1 , by accumulating 100 scans with a resolution of 4 cm −1 within a period of 2 min. Prior to the measurements of the tested samples, reference spectra were acquired using the cleaned blank (no added sample) crystal. Small portions of minced meat were placed on the crystal and measurements were performed. After each measurement, the crystal's surface was cleaned, first with detergent and distilled water and then with analytical grade acetone and dried using lint-free tissue. The FTIR spectra that were ultimately used in further analyses were in the approximate wavenumber range of 1800 to 900 cm −1 [22], consisting of 934 wavenumbers.

D. IMAGE ACQUISITION
Multispectral imaging data from portions (ca. 70g) of the minced pork samples were acquired using the VideometerLab system, originally developed by the Technical University of Denmark [23] and according to procedures that have been described in detail previously [24]. In brief, this instrument acquires multispectral images in 18 different, non-uniformly distributed wavelengths ranging from 405 to 970 nm (i.e. 405, 430, 450, 470, 505, 565, 590, 630, 645, 660, 850, 870, 890, 910, 920, 940, 950 and 970 nm). Prior to image acquisition, the system was subjected to a light set up procedure known as ''autolight'' and calibration. Each minced meat sample was placed in a Petri dish and the latter was placed inside an Ulbricht sphere, in which the camera is top-mounted and the corresponding multispectral image of the product's surface was taken.
The collected images were segmented using the accompanying software (version 2.12.39) of the VideometerLab system so as to remove information related to the background (i.e. Petri dish, fat). Specifically, first the contrast between the sample material and the other irrelevant objects was maximized, in order to enable a threshold operation. Then, Canonical Discriminant Analysis (CDA) was employed as a supervised transformation method so as to divide the image into regions of interest. In this way a segmented image was produced, where the region of interest was used to extract the spectral data. After the segmentation process of each image, the mean reflectance spectrum (i.e. mean intensity of pixels within the informative area) along with the corresponding standard deviation values were calculated. The MSI data that ultimately were used in further analyses were 18 mean reflectance values and 18 standard deviations, constructing a 36-dimentional feature vector representation for each MSI image, without using 2-dimensional image features.
The proposed framework is based on offline training and online operation (test phase) for the estimation of microbial population of meat using spectroscopic data (FTIR, MSI). The methodology is generalized and can be expanded by using or adding other spectroscopic techniques (e.g. Raman). The experimental design and methodology applied on minced pork samples in the framework of the present study is illustrated in Fig. 3.

III. DATA ANALYSIS
Data (spectra, microbial populations) were collected and Support Vector Machines (SVM) regression models were developed for each sensor and packaging condition (FTIR_AIR, MSI_AIR, FTIR_MAP, MSI_MAP) and evaluated. Spectral data (FTIR, MSI) were used as input variables (X) and TVC as output (target) variables (Y). In the case of FTIR, where the number of variables is greater than the number of samples [25], different dimensionality reduction methods were applied (Principal Component Analysis, Partial Least Squares, ReliefF, Descriptive statistics, Autoencoders).
The acquired FTIR variables were used as X variables. The training of the models was performed using three replicates, while the fourth replicate was used to evaluate the SVM regression models. A 4-fold cross validation experimental protocol was followed in order to avoid overlap between training and test replicates. The train and test sets used for the 4-fold cross validation experimental protocol are presented in Tables 1 and 2. Several well-known and widely used classifiers were evaluated and the results demonstrated that SVM offer competitive performance in most setups and was thus, selected for our analysis. Also, since SVM has good generalization ability and do not suffer from the curse of dimensionality [26], [27], it is regarded as an appropriate approach for comparison of datasets with different dimensionality. The performance of the regression models was evaluated in terms of Root Mean Square Error (RMSE). Except RMSE which was considered as the main numerical estimation metric as also in [10], [11], [12], [14], also were calculated the Mean Absolute Error (MAE), the correlation coefficient (r) and the Residual Prediction Deviation (RPD).

A. DIMENSIONALITY REDUCTION OF FTIR DATA
Several methods were used for the reduction of dimensions of the FTIR data. These methods are: (a) Principal Component Analysis (PCA), which is a method for reducing the dimensionality, but at the same time minimizing the information loss. A large number of potentially correlated factors are projected into a number of orthogonal (uncorrelated) factors (i.e. principal components) reducing thus the size of the initial dataset taking into account only X-variables [28]; (b) Partial Least Squares (PLS), an approach which, unlike PCA, constructs new factors (i.e. latent variables) that combine information about the variances of both the X-variables and Y-variables (find combinations of the predictors (Xvariables) that have a large covariance with the response (target) values (Y-variables)) and is used for data with many, noisy and collinear variables [29], [30]; (c) ReliefF is a feature ranking method, which evaluates the worth of an attribute by repeatedly sampling an instance and considering the value of the given attribute for the nearest instance of the same and different class and is able to detect conditional dependencies between attributes and to provide a unified view on the attribute estimation in regression [31] (e) Autoencoder, which is a neural network trained to replicate its input at its output. When nonlinear activation functions are used, autoencoders provide nonlinear generalizations of PCA. Training an autoencoder is unsupervised in the sense that no labeled data are needed [32]- [35].
Spectral data were processed by each of the above described methods, (a)-(e), to reduce dimensionality either by projecting them to a new lower dimensional feature space (i.e. descriptive statistics, autoencoders), or by projecting them to a new feature space with the same dimensionality and selecting a subset of the new feature space dimensions (PCA, PLS, ReliefF). All dimensionality reduction algorithms were trained using only the train sets presented in Tables 1 and 2 and the developed models for dimensionality reduction were then used to reduce the dimensionality of the corresponding test set, thus there was no overlap between train and test sets. The selection of the optimal number of features was based on the RMSE score minimization on the test datasets, except for the case of descriptive statistics in which the dimensionality was fixed to 22.

B. SUPPORT VECTOR MACHINES REGRESSION
FTIR and MSI data were used for the development of SVM regression models. Data were mapped non-linearly into a higher dimensional feature space, so as a maximal separating VOLUME 8, 2020 hyper-plane to be constructed. Radial Basis Function (RBF) and Polykernel (POLY) were used as kernel functions and grid search was employed for finding the optimal cost (C) and gamma (γ ) parameters, with the parameters being selected according to best performance of each test set [36]. Spectral data (FTIR, MSI) were concatenated in an early fusion setup. As regards FTIR data, they were used after the application of dimensionality reduction.
The evaluation results (RMSE, MAE, r, RPD) on the test sets are presented in Section IV. PCA, ReliefF, Descriptive Statistics and Autoencoders were implemented in MATLAB [37], while PLS was implemented in R 3.5.1 [38] and RStudio [39], using 'pls' package [30]. For the SVM regression modelling, the WEKA 3.8 software tool was utilized for machine learning using the SMOreg function [40].

IV. RESULTS AND DISCUSSION
Spectral data obtained from FTIR spectroscopy in the range of 1800 to 900cm −1 and from MSI in the range of 405 to 970 nm were used as X-variables for the development of the regression models (estimators of microbial population). FTIR data provide an overall fingerprint of the biochemical composition of food samples, also including the metabolic activity of microorganisms and are thus used as means of microbiological quality assessment. The abovementioned region has been widely used in model development for the ultimate purpose of food quality estimation [22], [41], [42]. On the other hand, MSI data cover the visible and a part of the near-infrared red (NIR) region. There are peaks in the abovementioned regions which are associated with myoglobin oxidation (visible region), as well as with protein and moisture content (near-infrared region) [43], [44].
A. AIR STORAGE SVM models were developed and evaluated after dimensionality reduction methods (PCA, PLS, ReliefF, Descriptive statistics and Autoencoder) were applied to FTIR data of AIR storage. A visualization of the relation between the measured (via microbiological analysis) and estimated (by the model) microbial population is illustrated in the scatterplots shown in Fig. 4. As can be seen in Fig. 4, the two variables (measured and estimated population) have positive association with a slight exception for the case of Autoencoders. A moderate linear relationship can be seen in all methods with PCA, PLS and ReliefF methods presenting stronger relationship than descriptive statistics and Autoencoders, which is in agreement with the results of Table 3. The best performance of the SVM models on FTIR data was obtained using PCA and PLS methods, as shown in Table 3. In a review of the literature [14] about spectroscopic data related to food science and more specifically to microbial evaluation, it was concluded that PLS is the most frequently used method, followed by ANN, PCA and SVM methods. In more detail according to RMSE, MAE and RPD values, the best performance on the testing data sets was observed using PCA with the scores being 1.268, 1.028 and 1.759, respectively. Slightly worse performance was obtained when applying the PLS feature selection method with RMSE, MAE and RPD being 1.277, 1.050 and 1.746, respectively. r was slightly better in the case of PLS by 0.003 compared to PCA, which is not a considerable difference. The use of ReliefF method for dimensionality reduction resulted in a lower performance compared to the two aforementioned methods (r = 0.774, RMSE = 1.417, TABLE 3. Performance of microbial population estimation under AIR storage conditions using SVM regression modelling and different dimensionality reduction methods applied on the FTIR data. MAE = 1.174 and RPD = 1.574). Moreover, the Descriptive Statistics and the Autoencoder exhibited a considerably lower performance than the PCA and PLS feature selection methods, most probably due to the limited size of the training data set, which was not enough to robustly train an autoencoder and estimate descriptive statistical values. When microbial population was estimated using SVM and Descriptive Statistics, the performance metrics of r, RMSE, MAE and RPD were equal to 0.388, 2.231, 1.868 and 0.999, respectively, while in the case of Autoencoders the corresponding values were 0.177, 2.314, 2.035 and 0.964.
The relation between the measured (via microbiological analysis) and estimated microbial population by the SVM models using MSI and MSI+FTIR features is visualized in Fig. 5 and 6, respectively. As can be seen in both scatterplots, the two variables (measured and estimated population) have positive association and stronger linear relationship     compared to Fig. 4, which is in agreement with the results shown in Table 4. The performance metrics of r, RMSE, MAE and RPD (Table 4) for models developed using MSI data were estimated to be 0.859, 1.144, 0.921 and 1.949, respectively. The performance of the SVM regression models using MSI data was better compared to FTIR. Models derived from early fusion had comparable performance with models derived from MSI (r = 0.863, RMSE = 1.146, MAE = 0.937 and RPD = 1.946).
The performance (in terms of RMSE scores) of the four test sets using different dimensionality reduction methods under AIR storage is shown in Fig. 7. The highest performance, as indicated by the lowest RMSE value, was observed when 100 principal components from PCA method were used. In contrast to PCA, the best performance when using the PLS method was observed with fewer components (10 to 30 latent variables), which is in agreement with the scientific literature [30], where it has been reported that when using PLS fewer components are needed to achieve similar prediction accuracies compared to PCA. On the other hand, PCA achieved slightly better performance in terms of RMSE due to the good generalization ability of SVM which do not suffer from the curse of dimensionality [26], [27], thus making the SVM regression model not quite sensitive to dimensionality variations. In the case of ReliefF method, the RMSE was reduced and minimized when over 300 variables were used. On the other hand, RMSE values of SVM models applied to Autoencoders were stable at about 2.150 to 2.549 (Fig. 7).
Spectroscopic methods, and particularly FTIR data, have also been used in other studies for the estimation of microbial quality of meat stored under aerobic conditions. For example, in [45] minced pork was stored at different isothermal conditions, where a total of 134 samples (67 samples for training and 67 for testing) were used. In the case of this latter study, r (correlation coefficient) for train and test set was 0.895 and 0.880, respectively. In [46] beef fillets stored at different temperatures (0, 5, 10, 15 and 20 • C), models were developed using ANN, and the RMSE value for train and test set was 1.821 and 1.978, respectively, and the corresponding RMSE values for PLS modeling were 1.073 and 1.993. In the study [47], microbiological quality of goat and fallow meat was studied using PLSR, with samples being stored at 3 • C in the context of four experimental replicates (60 samples per meat type); the RMSE values estimated for external validation of models developed for fallow and goat were 0.75 and 0.74, respectively. Promising results regarding the estimation of microbiological spoilage based on FTIR data has been also reported for chicken breast [48]. Moreover, MSI data have been successfully used for the quantitative assessment of meat spoilage [49], [50], [24]. Actually, in the latter study and regarding the correlation of MSI and microbiological data, r values as high as 0.928, 0.918 and 0.783 were reported for model calibration, cross-validation and prediction, respectively. Going beyond the parameters studied in the abovementioned studies, different experimental replicates and temperature conditions were taken into account in the present study. The developed models were full-cross validated using independent experiments (corresponding to distinct meat batches) as test sets for the purpose of model optimization and method evaluation.

B. MAP STORAGE
The SVM regression models developed from data acquired during storage under MAP conditions, had comparable performance with those obtained from samples stored under AIR conditions. In Fig 8., the relation between the measured (via microbiological analysis) and estimated (by the model) microbial population is illustrated in the form of scatterplots. A moderate linear relationship can be seen in all methods with PCA, PLS and ReliefF methods presenting stronger relationship than descriptive statistics and Autoencoders, which is in agreement with the results shown in Table 5. In Table 5, r, RMSE, MAE and RPD scores when using FTIR data are shown; the best performance of the MAP models was obtained using the PLS feature selection method with r, RMSE, MAE and RPD being equal to 0.765, 1.024, 0.809 and 1.538, respectively. Models developed using the PCA and ReliefF methods were slightly worse compared to the PLS method. PCA-based models had better performance (r = 0.759, RMSE = 1.047, MAE = 0.787 and RPD = 1.504) compared to ReliefF-based models (r = 0.706, RMSE = 1.141, MAE = 0.951 and RPD = 1.381). The methods of Descriptive Statistics and Autoencoders resulted in poor model performance, similarly to the AIR storage case. RMSE scores of the SVM regression models developed using FTIR data with Descriptive Statistics and Autoencoders were equal to 1.429 and 1.563, respectively. The performance of the SVM regression models was better when MSI data concatenated with FTIR data were used as shown in Table 6. A visualization of the relation between the measured (via microbiological analysis) and estimated microbial population by the SVM models using MSI and MSI+FTIR features is provided in Fig. 9 and 10, respectively. As can be seen in both scatterplots, the two variables (measured and estimated population) have positive association and stronger linear relationship compared to Fig. 8 which is in agreement with the results shown in Table 6. In Table 6, the r,    Data fusion of spectroscopic data in tandem with data analysis has been studied for several applications related to food quality assessment and food fraud [51], [52], but only few of the conducted research studies are related to the evaluation of meat quality [53], [54].
The performance (in terms of RMSE scores) of the four test data sets using different dimensionality reduction methods under MAP storage conditions is shown in Fig. 11. Similarly, to the results observed under AIR conditions, the PCA and PLS methods outperformed all other evaluated dimensionality reduction methods. It can be seen that PCA and PLS dimensionality reduction methods exhibited a similar trend regarding the RMSE scores varying across different components (dimensions) used. It is interesting that ReliefF and Autoencoders presented similar RMSE score curves as well, however both performing significantly worse than PLS and PCA. The highest performance (i.e. the lowest RMSE score value) was observed when 10 latent variables from the PLS dimensionality reduction method were used (see Fig. 11 (c)). RMSE scores obtained using Autoencoders were almost stable, independently of the number of components used.
Although MAP is a common packaging technology for extending the shelf life of meat, the utilization of spectroscopic data for the evaluation of microbiological quality of meat under such storage conditions has not been extensively studied. Argyri et al. [22] reported findings pertinent to the development and evaluation of regression models based on FTIR spectral data and corresponding to beef samples (n = 98) stored at 5 • C and under different packaging conditions (aerobic and MAP). Different methods (i.e. PLS regression, genetic programming, genetic algorithm, ANN and SVM regression including different kernel functions) were applied, and the minimum RMSE score reported was 0.504 [22]. In another study [55], beef samples (n = 186) were stored under aerobic, MAP and active packaging conditions at temperatures from 0 to 15 • C, and an RMSE value of 0.71 was reported for cross-validation of a model correlating microbiological and FTIR spectral data. Similarly promising were the results of a more recent study [56], in which meat samples (n = 105) were stored under different packaging conditions (aerobic, MAP), and different instruments (electronic nose, HPLC, GC-MS, FTIR and MSI) and algorithms were evaluated for the prediction of meat spoilage, as this is manifested via the growth of distinct microbial groups.
The rapid assessment of meat quality is of vital importance for industries and authorities in order to ensure quality of perishable food for consumers. Conventional techniques for VOLUME 8, 2020 microbial enumeration are reliable, certified methods and commonly acceptable, but are time-consuming and laborious. For example, the result of probably the most commonly used technique (Standard Plate Count) for the enumeration of microbial populations in food are available after 48-72h. In this context, results are not directly available in order for timely corrective actions to be applied and economic losses and consumer complaints to be minimized. Hence, there is an increasing research interest in rapid and non-invasive spectroscopic techniques.
In the present study, the RMSE scores (expressing in part the performance of the developed models) estimated for FTIR were 1.268 and 1.024 for AIR and MAP storage, respectively, whereas the corresponding values for MSI were 1.144 and 0.923, while for FTIR+MSI these values were 1.146 and 0.886. Since the estimated RMSE values were, in most of the cases, within the ''acceptable'' microbiological variability (i.e. within the 1-log cfu range commonly encountered in microbiological studies due to the extensive variability characterizing biological systems), the predictive information provided by the developed models can be regarded as rather promising for future application. Indeed, as also commented previously, a sample is considered as ''correctly predicted'' from a microbiological standpoint when the difference between predicted and observed values is < 1 log cfu [57]. As demonstrated by the data collected in this study, the RMSE scores estimated for the models corresponding to MAP storage were systematically lower than those referring to AIR storage; such difference may be associated with the different organisms dominating in these two packaging conditions. It is also worth mentioning, that the application of a 4-fold cross validation experimental protocol demonstrated the differences among experimental replicates, and how extensive may the encountered biological variability be; for instance, the RMSE values estimated for the models developed in the case of FTIR+MSI and for samples stored under MAP ranged from 0.461 to 1.142 (data not shown).
Beyond biological variability, the variability related to the environmental conditions, and more specifically to storage temperature and atmosphere, was also taken into consideration in this study. Specifically, different temperature profiles, both isothermal and dynamic, were applied during storage of minced pork patties in an attempt to account for the variable temperature conditions likely to be encountered in the farm-to-fork continuum. A wide range of temperatures, varying from well-controlled refrigeration (4 • C in this study) to slightly or excessively abusive (8 or 12 • C, respectively in this study) temperatures may be observed in the food supply chain, and there is a high likelihood of food commodities being exposed to changing temperature conditions throughout distribution. In this sense, the value of the results of this study is, among others, delineated by the fact that different sources of variability are taken into account in model development, with the resulting models expected to allow for robust and realistic predictions.

V. CONCLUSION
In conclusion, a methodology for microbial population estimation in meat portions based on non-invasive spectroscopic sensors was presented. The proposed methodology is using FTIR and MSI sensors and the extracted data are processed by machine learning regression models to estimate the microbial population. The methodology can perform estimation of microbial populations in less than few minutes, in contrast to traditional microbial population analysis techniques which require 48-72h as well as food technology expert staff, thus allowing real-time food quality inspection onsite at food industries and giving the potential of inspections even in food retail and service premises (e.g., supermarkets and restaurants).
As demonstrated by the findings of the present study, FTIR and MSI data, as well as early fusion of such spectral data, appear to hold considerable potential for the estimation of the microbiological quality of meat stored under different temperature and packaging conditions. Further investigation with respect to the (inevitably encountered) biological variability and collection of more data to train machine learning models for regression can result in the development of more precise estimation models thus allowing the onsite and realtime assessment of the microbiological quality of meat and meat products.