## 2 Materials and Methods
### SIMCA Validation  
Over five years, the SIMCA prediction model was validated by _Salmonella_ serotypes, similar _Enterobacteriaceae_ family members, and other pathogenic/spoilage microbes commonly found in food products, totaling 19 microorganisms and 3421 bacterial cells after outlier removal. Table 2 describes the sample size breakdown of the _Salmonella_ spectral library and validation. Five _Salmonella_ serotypes common to foodborne disease outbreaks, namely _S. Enteritidis_ (SE), _S. Heidelberg_ (SH), _S. Infantits_ (SI), _S. Kentucky_ (SK), and _S. Typhimuriumurium_ (ST), were cultured, in addition to 14 other organisms known to be foodborne pathogens [24].  
The HMI for these samples were collected in the same manner as the calibration model. Preprocessing and outlier detection methods were also repeated. New single cell mean spectra were projected onto the _Salmonella_ calibration model's PC space, and distances towards the class's model were calculated by Equations (8)-(10), as follows:  
\[\widetilde{x}_{new}\ (1 xp)=\ \widetilde{x}_{K}+\big{(}x_{new-\ \widetilde{x}_{K}} \big{)}V_{K}V_{K}^{T} \tag{8}\]  
\[e_{new}=\ x_{new}-\widetilde{x}_{new} \tag{9}\]  
\[S_{K}=\ \sqrt{\sum_{i=1}^{p}e_{new,i}^{2}/(p-r)} \tag{10}\]  
where \(e^{2}_{new}=\) the new object's squared residual, and \(S_{K}=\) distance towards the class model and is compared to the \(S_{crit}\) value from Equation (7). Bacteria cells are labeled as _Salmonella_ if \(S_{K}<S_{crit}\). If \(S_{K}>S_{crit}\), then the bacteria cell is classified as a non-_Salmonella_ cell.  
\begin{table}
\begin{tabular}{c c c c c} \hline \multicolumn{2}{c}{**Calibration**} & \multicolumn{3}{c}{**Validation**} \\ \hline
**Microorganism** & **Reps** & **Cells** & **Microorganism** & **Reps** & **Cells** \\ \hline _Salmonella_ Enteritidis & 4 & 346 & _Campylobacter coli_ & 2 & 27 \\ _Salmonella_ Heidelberg & 4 & 388 & _Campylobacter fetus_ & 2 & 26 \\ _Salmonella_ Infantis & 3 & 282 & _Campylobacter jejuni_ & 2 & 65 \\ _Salmonella_ Javiana & 2 & 231 & _Enterobacter cloace_ & 1 & 142 \\ _Salmonella_ Kentucky & 3 & 313 & _Enterococcus faecalis_ & 3 & 157 \\ _Salmonella_ Kiambu & 2 & 279 & _Escherichia coli_ & 8 & 767 \\ _Salmonella_ Mbandanka & 2 & 274 & _Klebsiella axytoca_ & 3 & 82 \\ _Salmonella_ Montevideo & 2 & 156 & _Listeria innocua_ & 3 & 79 \\ _Salmonella_ Muenchen & 2 & 259 & _Listeria monocytogenes_ & 2 & 116 \\ _Salmonella_ Settenberg & 3 & 165 & _Macrococcus acosolyticus_ & 3 & 24 \\ _Salmonella_ Typhimuriumurium & 3 & 345 & _Paenibacillus polymyna_ & 2 & 66 \\ _Salmonella_ Typhimuriumurium-NAL & 3 & 140 & _Pseudomonas putida_ & 3 & 151 \\ _Salmonella_ Weltevreden & 2 & 137 & _Staphylococcus aureus_ & 2 & 212 \\  & & & _Staphylococcus simulans_ & 2 & 190 \\  & & & _Salmonella_ Enteritidis & 8 & 350 \\  & & & _Salmonella_ Heidelberg & 6 & 149 \\  & & & _Salmonella_ Infants & 5 & 284 \\  & & & _Salmonella_ Kentucky & 3 & 239 \\  & & & _Salmonella_ Typhimuriumurium & 8 & 295 \\ Total & 35 & 3315 & Total & 68 & 3421 \\ \hline \end{tabular}
\end{table}
Table 2: List of spectral library files used in building and validating the soft independent modeling of class analogy (SIMCA) from hyperspectral microscope images of bacterial cells.