CRANFIELD UNIVERSITY Eleni Anthippi Chatzimichali ...

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4.3 Results and Discussion 4.3.1 Exploratory Data Analysis The first implemented data fusion technique involved the GPA algorithm. As illustrated in Figure 4-5, the PCA scores from each experimental technique of case study 1 expand over wide and different numerical ranges. The GPA algorithm uses the output of PCA to perform statistical shape analysis in order to minimise the dissimilarity between the initial datasets. Figure 4-5 demonstrates step-by-step the geometric transformations (translation, rotation and isotropic scaling) performed by the GPA algorithm on all three standalone datasets simultaneously. Once the shapes are fitted as closely as possible to each other, the algorithm makes use of the individual transformed matrices in order to construct the consensus. The consensus matrix, as presented in Figure 4-6, is further used as the input into a classification ensemble. Figure 4-5 The steps of GPA (shown in order from left to right) when applied on the datasets of case study 1 The two-dimensional scatterplots display the standalone datasets prior and after the application of GPA when all three experimental techniques of case study 1 are investigated simultaneously. In this case, the GPA algorithm is applied in the subspace created by the first two principal components. In order to demonstrate the differences in range of the initial datasets under study, PCA was applied on raw standalone data with no prior pre-processing. The GPA algorithm subjects all individual datasets to translation (mean-centering), rotation and isotropic scaling. In the final plot, the shapes are as similar to each other as possible. 91
a) GPA b) CPCA Figure 4-6 The consensus of the first two Principal Components based on the fusion of all three experimental techniques of case study 1 using GPA and CPCA respectively The consensus output of GPA is compared against the super-scores obtained by CPCA; in both cases, all three experimental techniques of case study 1 (FTIR, HPLC, e-nose) were used simultaneously for the data fusion. Dynamically generated 95% confidence ellipses per each class were added in the plots in order to highlight the presence of any clusters and/or outliers. Colour representation was used to identify the three classes: fresh (red colour), semi-fresh (orange colour) and spoiled (green colour). Based on the graphs, the consensus shapes do not provide any obvious discrimination between the three classification groups since the distinct classes are highly overlapping. It is apparent that the good clustering between fresh and spoiled samples as observed by standalone HPLC in Figure 2-5 was destroyed during the fusion process with the other two analytical techniques. 92
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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
Page 55 and 56: 3. Validation Techniques In the cas
Page 57 and 58: Figure 2-4 The process of construct
Page 59 and 60: 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: Figure 4-4 Data integration workflo
Page 109 and 110: accuracies as the linear models; po
Page 111 and 112: Figure 4-8 Classification Results f
Page 113 and 114: Similar to FTIR, the PLS-DA ensembl
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 147 and 148: RBF SVMs Datasets Original %CC Mean
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
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(a) RBF SVMs (b) PLS-DA Figure 5-17
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RBF SVMs Datasets Original %CC Mean
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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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