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4.3.2.2 Class Prediction Accuracies In addition to the overall accuracies, the per-class percentages of correctly classified samples for the standalone and integrated datasets of case study 4 are depicted in Figure 4-9 and Figure 4-10 respectively. In this case study, spoiled samples constitute the majority class; thus, as expected, spoiled samples obtain outstanding class accuracies throughout all classification models and experimental techniques; in the majority of cases, these class percentages were well above 90%. The class predictions of the raw standalone datasets were determined earlier, in Section 2.3.2.2. Since PCA is the first step towards data integration, the per-class accuracies of the individual PCA scores for each experimental technique are examined as follows. Based on Figure 4-9, the PCA scores of FTIR in the case of the PLS-DA ensembles increase the class accuracies of both fresh and spoiled samples, while the semi-fresh accuracies are equal to 0%. Since case study 1 is a multi-class problem, semi-fresh samples, which constitute the minority class, are extremely difficult to predict. Furthermore, in the case of linear SVMs, the application of PCA has proven to be extremely fruitful since the fresh and semi-fresh class accuracies increase by 11% and 25% respectively. On the contrary, the class predictions of spoiled samples decrease by 10%. Finally, for nonlinear (RBF) SVMs, the FTIR accuracies for all three classes increase substantially, but most importantly the class prediction of SF samples reaches the notable percentage of 31%. For the HPLC data, PLS-DA provides a strong nearly linear separation between fresh and spoiled samples with prediction rates above 90%, while the semi-fresh samples present a noteworthy accuracy of 17%. In the case of linear SVMs, the fresh and spoiled class predictions drop compared to raw HPLC, while the SF prediction rate increases by 32%; this fact justifies the decreased overall accuracy of HPLC in Figure 4-7. As far as the RBF SVMs are concerned, the class predictions follow the trend of linear SVMs. 97
Similar to FTIR, the PLS-DA ensembles for the e-nose data increase the rates of fresh and spoiled samples, while the semi-fresh accuracies are equal to 0%. Even though linear and nonlinear SVMs generate higher percentages of correctly classified samples ( ), PLS-DA demonstrates better classification accuracies for the fresh samples compared to the SVMs. Finally, in the case of linear and nonlinear (RBF) SVMs, both fresh and semi-fresh accuracies significantly decrease, while the prediction rates of the majority class approximate 100%. To summarise the previous observations, as with raw data, the highest per-class accuracies for the semi-fresh samples are recorded in the case of FTIR data when SVMs are applied. In addition, the high overall accuracies of HPLC are justified by the nearly perfect class predictions of fresh and spoiled samples, especially for the linear classifiers (PLS-DA and SVMs). Finally, based on the e-nose class predictions it is obvious that the implemented classifiers have no discriminative power to correctly classify the semi-fresh samples; it appears that the boundaries of both the linear and nonlinear classifiers are dominated by the majority class, thus resulting in outstanding class predictions for the spoiled samples. According to Section 4.3.2.1, it is obvious that e-nose is a dominant technique that strongly influences the outcome of the integration and analysis process. In the case of GPA, the class accuracies from the pairwise fusion of either FTIR or HPLC with e-nose verify this hypothesis. Based on Figure 4-10, the high fresh and semi-fresh accuracies obtained by standalone FTIR and HPLC decrease once the integration is performed, for all the different types of classifiers. Furthermore, the integrated datasets present at least 80% in the class predictions of spoiled samples. This is to be expected, not only because spoiled samples constitute the majority class, but also because the standalone e-nose data most often resulted in high percentages of correctly classified spoiled samples. For the integrated dataset of FTIR and HPLC, the overall accuracies and class predictions of both linear and nonlinear models demonstrate similar results. After the integration, the spoiled accuracies increase for all three classifiers, while the performance of fresh samples drops for the linear models (PLS-DA and linear SVMs). The most noteworthy improvement from standalone to integrated datasets for all individual classes (sensory scores) was documented for the RBF SVMs. Finally, in the integration of all three datasets, it 98
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CRANFIELD UNIVERSITY Eleni Anthippi
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ABSTRACT Muscle foods such as meat,
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TABLE OF CONTENTS ABSTRACT ........
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6.2.4 The iWebPlots package .......
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Figure 3-12 Speedup produced by the
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Figure 6-9 Sweave example for the d
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TABLE OF EQUATIONS Equation 1 Mean-
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RMSE RMSECV SSE SVD SVMs SYMBIOSIS-
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Figure 1-1 Evolution from molecular
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1.1.2.1 Fourier Transform Infrared
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1.1.3 Microbial Spoilage in Meat Sy
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The multivariate techniques applied
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1.4 Multivariate Analysis: Unsuperv
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1.4.2 Cluster Analysis Cluster anal
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1.5 Multivariate Analysis: Supervis
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In any linearly separable binary da
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Where ( ) are the Lagrange multipli
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Every kernel is characterised by a
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The “one-against-all” approach
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Furthermore, metrics such as the bi
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1.6.3 Leave-One-Out Cross-Validatio
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In such cases, the model becomes qu
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1.8 Aims and objectives The overall
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2 Development of the multivariate a
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Sensory panel scores were of the hi
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DF (Hz) 2.2.1.5 Electronic Nose (e-
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Figure 2-3 Data intersection The fi
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3. Validation Techniques In the cas
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Figure 2-4 The process of construct
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2.3 Results and Discussion 2.3.1 Pr
Page 61 and 62: (b) HPLC data (c) e-nose data Figur
Page 63 and 64: In the case of FTIR, linear classif
Page 65 and 66: 2.3.2.2 Class Prediction Accuracies
Page 67 and 68: Figure 2-7 Class prediction rates o
Page 69 and 70: The topology of the three-dimension
Page 71 and 72: Figure 2-9 Three-dimensional error
Page 73 and 74: Furthermore, a thorough comparison
Page 75 and 76: In the master/slave architecture, a
Page 77 and 78: precision of the classification acc
Page 79 and 80: Figure 3-3 The steps of the Nelder-
Page 81 and 82: 3.3 Results and Discussion 3.3.1 Li
Page 83 and 84: 3.3.2 Nonlinear Models In order to
Page 85 and 86: 9) 10) 11) 12) 13) 14) 15) 16) Figu
Page 87 and 88: As an additional visual aid, these
Page 89 and 90: a) Number of iterations b) Number o
Page 91 and 92: Figure 3-10 Comparison of the execu
Page 93 and 94: Figure 3-12 Speedup produced by the
Page 95 and 96: 4 Integration of Heterogeneous Data
Page 97 and 98: 4.2.2 Procrustes Analysis Procruste
Page 99 and 100: symmetric method since the ordering
Page 101 and 102: Figure 4-3 Steps of CPCA for the da
Page 103 and 104: 4.2.5 Data Integration and Analysis
Page 105 and 106: Figure 4-4 Data integration workflo
Page 107 and 108: a) GPA b) CPCA Figure 4-6 The conse
Page 109 and 110: accuracies as the linear models; po
Page 111: Figure 4-8 Classification Results f
Page 117 and 118: 4.3.3 Permutation Tests Even though
Page 119 and 120: Even though the interpretation of t
Page 121 and 122: Figure 4-12 Distribution plots of t
Page 123 and 124: RBF SVMs Datasets Original %CC Mean
Page 125 and 126: Figure 4-14 Boxplots representing t
Page 127 and 128: 5 Application of the multivariate a
Page 129 and 130: Figure 5-1 Mean FTIR spectra for ca
Page 131 and 132: 5.2.2.2 Fourier Transform Infrared
Page 133 and 134: 5.2.2.4 Data Overview For each expe
Page 135 and 136: 5.2.3.3 High Throughput Liquid Chro
Page 137 and 138: Figure 5-5 displays the PCA scores
Page 139 and 140: (a) GPA (b) CPCA Figure 5-6 The con
Page 141 and 142: observation confirms that indeed CP
Page 145 and 146: (a) RBF SVMs (b) PLS-DA Figure 5-9
Page 149 and 150: Figure 5-12 Execution times of the
Page 151 and 152: (a) FTIR data (b) Raman data Figure
Page 153 and 154: The classification results for the
Page 155 and 156: Figure 5-16 Class prediction rates
Page 157 and 158: (a) RBF SVMs (b) PLS-DA Figure 5-17
Page 161 and 162: Figure 5-20 Execution times of the
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(a) FTIR data (b) HPLC data 148
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(a) GPA (b) CPCA Figure 5-22 The co
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The classification results of the f
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Figure 5-24 Classification Results
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Figure 5-25 Class prediction rates
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The permutation results for the dat
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Figure 5-28 Distribution plots of t
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RBF SVMs Datasets Original %CC Mean
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Figure 5-30 Boxplots representing t
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5.4 Comparison of the individual ca
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Figure 5-32 Investigating the commo
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6 Development of improved visualisa
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6.2.2 Generating static graphs As d
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Figure 6-2 Construction process of
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6.2.2.2 Generating dynamic reports
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activity, while simultaneously the
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or disappeared (Wang et al., 2008).
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ectangles, circles and/or irregular
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In addition to the static figures g
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c) graphics package d) ggplot2 pack
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In addition to aesthetics, faceting
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Datasets FTIR HPLC e-nose PLS-DA (L
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Figure 6-10 Interactive dendrogram
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6.4 Conclusion The work reported in
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large number of individual models i
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The generated suite of tools, as pr
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In addition, the difficulty to corr
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REFERENCES Almeida, J. A. S., Barbo
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Processing., Proceedings of the 12t
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Clarke, B., Fokoué, E. and Zhang,
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spectroscopy and machine learning",
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Gower, J. C. (1975), "Generalized p
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Jardon, M. (2006), Systems Biology:
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Nicolaou, N., Xu, Y. and Goodacre,
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Shah, A. A., Barthel, D., Lukasiak,
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Vera, G., Jansen, R. and Suppi, R.
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Xu, Y. and Goodacre, R. (2012), "Mu
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