# An Unsupervised Prediction Model for Salmonella Detection with Hyperspectral Microscopy: A Multi-Year Validation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Sample Preparation and Collection

#### 2.2. HMI Processing

_{1}and P

_{2}represent cumulative probabilities of the two groups, T = a threshold that divides the image into pixel set S

_{1}or S

_{2}, and P

_{i}= the probability of image value i. After the global thresholding was computed, the Time Series 3.0 plugin [16] was used to apply the masks to the virtual stack, calculating the mean of the pixels in each regions of interest (bacterial cell). Next, Fiji exported two comma-separated value (CSV) files, where one file represented the spectral data and one file represented the shape metrics. The two CSV files were combined into one matrix, where rows were single cells with corresponding shape and spectral data shown as columns. Circularity represents how close a shape is to a perfect circle on a scale of 0 to 1, and was computed by Equation (2), as follows:

#### 2.3. Spectral Pre-Processing

_{i}is the sample’s mean, x

_{i}is the sample’s spectra, and δ

_{i}is the sample’s standard deviation. Following SNV, outlier detection was calculated by applying a centroid-based Mahalanobis distance (MD) between two vectors, one being the individual cell’s mean spectra, and the other vector representing the class mean spectra, and was calculated by Equation (4), as follows:

_{i}= an object vector and $\overline{x}$ = the cluster centroid. From here, single cell values within ±3δ of the class mean MD were removed from the dataset, with 0.97% of the calibration data and 1.37% of the validation data being labeled as outliers and being removed.

#### 2.4. SIMCA Classification Model

_{K}= the mean centered matrix, T

_{K}(nxr) = the score matrix obtained from n objects and r selected PCs, ${V}_{K}^{T}\left(rxp\right)$ = the loading matrix obtained for r selected PCs and p variables, and ${E}_{K}\left(nxp\right)$ = the residual matrix [22]. The leave-one-out-cross-validation (LOO-CV) was an important step in the development of the prediction model, which has previously been shown to reduce the number of false outliers by inflating the within class component variances [23]. Class boundaries of the SIMCA are determined by Equation (6), as follows:

_{0}= mean distance between objects belonging to the k class model and ${e}_{ki}^{2}$ = squared residual of the kth object for the ith (latent) variable. The critical distance value is then calculated through an F-test at a specified significance level (α) by Equation (7), as follows:

#### 2.5. SIMCA Validation

^{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.

## 3. Results and Discussion

#### 3.1. Standard Normal Variant and Spectra

#### 3.2. SIMCA Calibration Model

^{2}values against the F-residuals is shown in Figure 5D.

#### 3.3. SIMCA Validation

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Flowchart of steps used to record Fiji macro for processing hyperspectral microscope images of bacteria.

**Figure 2.**Representation of data collection of hyperspectral microscope images of bacterial cells between 450 and 800 nm.

**Figure 3.**Hyperspectral microscope image of Salmonella Heidelberg at 638 nm: (

**A**) Raw image and (

**B**) cell segmentation image with extracted pixels shown in white.

**Figure 5.**Soft-independent modelling of class analogy (SIMCA) calibration diagnostics: (

**A**) PC scores 1 and 2, (

**B**) loadings for PCs 1–4, (

**C**) principal component analysis residuals, and (

**D**) scree plot of explained variance (%).

**Figure 6.**Principal component analysis projections for the validation data of (

**A**) S. Enteritidis and (

**B**) Staphylococcus aureus onto the soft-independent calibration model for unsupervised Salmonella prediction.

Microorganism | Microorganism |
---|---|

Campylobacter coli (Cc) | Salmonella Enteritidis (SE) |

Campylobacter fetus (Cf) | Salmonella Heidelberg (SH) |

Campylobacter jejuni (Cj) | Salmonella Infantis (SI) |

Enterobacter cloacae (Ecl) | Salmonella Javiana (SJ) |

Enterococcus faecalis (Ef) | Salmonella Kentucky (SKe) |

Escherichia coli (Eco) | Salmonella Kiambu (SKi) |

Klebsiella oxytoca (Ko) | Salmonella Mbandanka (SMb) |

Listeria innocua (Li) | Salmonella Montevideo (SMo) |

Listeria monocytogenes (Lm) | Salmonella Muenchen (SMu) |

Macrococcus caseolyticus (Mc) | Salmonella Seftenberg (SSe) |

Paenibacillus polymyxa (Ppo) | Salmonella Typhimurium (ST) |

Pseudomonas putida (Ppu) | Salmonella Typhimurium–NAL (STN) |

Staphylococcus aureus (Sa) | Salmonella Weltevreden (SW) |

Staphylococcus simulans (Ss) |

**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.

Calibration | Validation | ||||
---|---|---|---|---|---|

Microorganism | Reps | Cells | Microorganism | Reps | Cells |

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 cloacae | 1 | 142 |

Salmonella Kentucky | 3 | 313 | Enterococcus faecalis | 3 | 157 |

Salmonella Kiambu | 2 | 279 | Escherichia coli | 8 | 767 |

Salmonella Mbandanka | 2 | 274 | Klebsiella oxytoca | 3 | 82 |

Salmonella Montevideo | 2 | 156 | Listeria innocua | 3 | 79 |

Salmonella Muenchen | 2 | 259 | Listeria monocytogenes | 2 | 116 |

Salmonella Seftenberg | 3 | 165 | Macrococcus caseolyticus | 3 | 24 |

Salmonella Typhimurium | 3 | 345 | Paenibacillus polymyxa | 2 | 66 |

Salmonella Typhimurium-NAL | 3 | 140 | Pseudomonas putida | 3 | 151 |

Salmonella Weltevreden | 2 | 137 | Staphylococcus aureus | 2 | 212 |

Staphylococcus simulans | 2 | 190 | |||

Salmonella Enteritdis | 8 | 350 | |||

Salmonella Heidelberg | 6 | 149 | |||

Salmonella Infantis | 5 | 284 | |||

Salmonella Kentucky | 3 | 239 | |||

Salmonella Typhimurium | 8 | 295 | |||

Total | 35 | 3315 | Total | 68 | 3421 |

**Table 3.**SIMCA results for a one-class Salmonella prediction model obtained from hyperspectral microscope images of bacteria.

Salmonella | ||||
---|---|---|---|---|

Microorganism | Cells | Yes | No | Accuracy (%) |

Campylobacter coli | 27 | 6 | 21 | 77.8 |

Campylobacter fetus | 26 | 3 | 23 | 88.5 |

Campylobacter jejuni | 65 | 9 | 56 | 86.2 |

Enterobacter cloacae | 142 | 4 | 138 | 97.2 |

Enterococcus faecalis | 157 | 1 | 156 | 99.4 |

Escherichia coli | 767 | 9 | 758 | 98.8 |

Klebsiella oxytoca | 82 | 1 | 81 | 98.8 |

Listeria innocua | 79 | 9 | 70 | 88.6 |

Listeria monocytogenes | 116 | 1 | 115 | 99.1 |

Macrococcus caseolyticus | 24 | 0 | 24 | 100 |

Paenibacillus polymyxa | 66 | 6 | 60 | 90.9 |

Pseudomonas putida | 151 | 55 | 96 | 63.6 |

Staphylococcus aureus | 212 | 10 | 202 | 95.3 |

Staphylococcus simulans | 190 | 5 | 185 | 97.4 |

Salmonella Enteritdis | 350 | 343 | 7 | 98.0 |

Salmonella Heidelberg | 149 | 141 | 8 | 94.6 |

Salmonella Infantis | 284 | 277 | 7 | 97.5 |

Salmonella Kentucky | 239 | 233 | 6 | 97.5 |

Salmonella Typhimurium | 295 | 283 | 12 | 95.9 |

Total | 3421 | 1277 | 1985 | 95.4 |

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Eady, M.; Park, B.
An Unsupervised Prediction Model for *Salmonella* Detection with Hyperspectral Microscopy: A Multi-Year Validation. *Appl. Sci.* **2021**, *11*, 895.
https://doi.org/10.3390/app11030895

**AMA Style**

Eady M, Park B.
An Unsupervised Prediction Model for *Salmonella* Detection with Hyperspectral Microscopy: A Multi-Year Validation. *Applied Sciences*. 2021; 11(3):895.
https://doi.org/10.3390/app11030895

**Chicago/Turabian Style**

Eady, Matthew, and Bosoon Park.
2021. "An Unsupervised Prediction Model for *Salmonella* Detection with Hyperspectral Microscopy: A Multi-Year Validation" *Applied Sciences* 11, no. 3: 895.
https://doi.org/10.3390/app11030895