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1. Select vector as a starting point 2. Compute the block loadings ‖ ‖ 3. Compute the block scores 4. Consider the matrix [ ] 5. Compute the global loadings ‖ ‖ 6. Update the global scores 7. Iterate steps 2 - 6 until the convergence of 8. Deflate the residuals ( ) The most notable breakthrough contribution pertaining to the field of multi-block algorithms was made by Westerhuis et al. (1998), whereby it was proved that the super-scores of CPCA are identical to the scores of normal PCA when applied on the concatenated set of blocks (the super-matrix) (Qin et al., 2001; Smilde et al. 2003) (see Figure 4-3). In addition, according to Westerhuis et al. (1998) regular PCA can be also used to calculate the individual block scores and loadings. Normal PCA may be applied using a plethora of algorithms, the most popular of which is the NIPALS algorithm (see Section 1.4.1). In the context of this project, consensus PCA was primarily investigated as a data integration technique rather than for the purpose of detecting an underlying common pattern between the different blocks. The super-scores of CPCA, which constitute the consensus matrix, are used as input into the implemented classifiers. 87
4.2.5 Data Integration and Analysis Pipeline The functionality of the multivariate analysis pipeline developed in the previous chapters was further extended to incorporate data fusion techniques. As presented in Section 2.2.1, the datasets of case study 1 have been acquired from beef samples using three main experimental techniques: spectroscopy (FTIR), high performance liquid chromatography (HPLC) and electronic nose. Initially, the datasets are crossreferenced based on the samples’ names and sensory values (see Section 2.2.2). Based on this filtering, a total of 32 common samples are inserted in the data integration pipeline along with the respective sensory scores as depicted in Figure 4-4. As PCA is the first step towards data integration, the principal components of each experimental technique were also tested using the multivariate analysis pipeline. More specifically, the PCA data were analysed in a repetitive manner by increasing the number of principal components each time by one until the optimal number of PCs, responsible for the highest classification accuracy, was identified. Since PLS-DA employs the PLS algorithm for data decomposition and dimensionality reduction (Section 1.5.1), the application of PCA with this type of classifier is considered redundant. However, in order to obtain directly comparable classification results, this approach was also investigated and the outcome is presented as follows. In this work, data integration is employed using a “mid-level fusion” approach based on the methodology presented in Section 4.2.1. As a first step towards analysing the integrated datasets, unsupervised methods for dimensionality reduction and the extraction of prominent features are applied on pre-processed data. In the case of GPA, prior pre-treatment such as mean-centering and/or scaling is not a necessity since these steps are included in the algorithm. Thus, raw data are subjected to PCA, and a predefined number of Principal Components (PCs) is extracted from each dataset. The PCA scores of each instrumental technique are concatenated in a threeway data matrix, which is subjected to geometric transformations. The output of GPA consists of the average (consensus) matrix in addition to all individual transformed matrices for the given combination of experimental techniques. 88
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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
Page 51 and 52: DF (Hz) 2.2.1.5 Electronic Nose (e-
Page 53 and 54: 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: Figure 4-3 Steps of CPCA for the da
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 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
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The classification results for the
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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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