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2.2.4 Ensemble of Classifiers In an effort to enhance the overall accuracy ( ) of the classifiers, while simultaneously control the bias-variance trade-off and minimise the instances of overfitting (see Section 1.6.5), the use of ensembles of classifiers was also evaluated. 1. Selection of the Classification Model First and foremost, the selection of the classification model to be applied had to be decided upon. There is no straightforward way of determining a priori which classification algorithm is the best; the selection of a classification model or kernel function highly depends on the problem under investigation. In cases where there is very little or no knowledge about the data under study, often more than one type of classifier may need to be tested. The choice of the classifier determines the hyperparameters to be optimised. In the case of PLS-DA, we are looking for the optimum number of latent variables (LVs), whereas in the case of RBF SVMs, the hyperparameters and have to be optimised. 2. Random split For a given input dataset D, a random fraction of samples is removed and kept aside as an independent test set during the training process of the model. This selection of samples forms the dataset D test . This test set typically comprises a third of the original samples. Using a stratified holdout approach as described in Section 1.6.1, the test set consists of the same balance of sample classes as the initial dataset D. The remaining samples that are not selected, form the training set D train . Since the test set is kept aside during the whole training process, the risk of overfitting is minimised (Ramadan et al., 2006). 39
3. Validation Techniques In the case of bootstrapping, a bootstrap training set D bootTrain is created by randomly picking samples with replacement from the training dataset D train . The total size of D bootTrain is equal to the size of D train . Since bootstrapping is based on sampling with replacement, any given sample could be present multiple times within the same bootstrap training set. The remaining samples not found in the bootstrap training set make up the bootstrap test set D bootTest . Similarly, for -fold cross-validation, the initial dataset D is partitioned into mutually exclusive folds; (10-fold cross-validation) was employed according to Section 1.6.2. In each iteration, a single fold will be used to form the test set D kfoldTest , while the remaining samples constitute the D kfoldTrain . In the ultimate case of LOOCV, D loocvTest consists of a single sample, while the remaining samples form D loocvTrain . 4. Hyperparameter optimisation According to Section 1.5.2.3, nonlinear SVMs are usually considered a reasonable first choice. In the case of RBF models with bootstrapping, the SVMs are built and optimised using D bootTrain and D bootTest for different hyperparameter settings. More specifically, for each given combination of the hyperparameters and , a new SVM model is trained with D bootTrain and tested with D bootTest . The most intuitive and fairly naïve approach for parameter selection involves an exhaustive grid-search over an extensive range of hyperparameters. However, this is an extremely time-consuming and computationally intensive procedure, even if there is more than adequate processor power. Therefore, in this work, the parameter search was implemented based on the approach suggested by Hsu et al. (2003), also described in Meyer et al. (2003), in a two-step approach using a combination of a coarse and fine grid-search. Initially, the values of and increase exponentially with ranges equal to [ ] and [ ] respectively. The combination of hyperparameters that gives the highest overall classification accuracy is recorded as optimal. Once an optimal region is located on the grid, a finer grid-search is conducted in the “neighbourhood” of good parameters. 40
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CRANFIELD UNIVERSITY Eleni Anthippi
Page 3 and 4: ABSTRACT Muscle foods such as meat,
Page 5 and 6: TABLE OF CONTENTS ABSTRACT ........
Page 7 and 8: 6.2.4 The iWebPlots package .......
Page 9 and 10: Figure 3-12 Speedup produced by the
Page 11 and 12: Figure 6-9 Sweave example for the d
Page 13 and 14: TABLE OF EQUATIONS Equation 1 Mean-
Page 15 and 16: RMSE RMSECV SSE SVD SVMs SYMBIOSIS-
Page 17 and 18: Figure 1-1 Evolution from molecular
Page 19 and 20: 1.1.2.1 Fourier Transform Infrared
Page 21 and 22: 1.1.3 Microbial Spoilage in Meat Sy
Page 23 and 24: The multivariate techniques applied
Page 25 and 26: 1.4 Multivariate Analysis: Unsuperv
Page 27 and 28: 1.4.2 Cluster Analysis Cluster anal
Page 29 and 30: 1.5 Multivariate Analysis: Supervis
Page 31 and 32: In any linearly separable binary da
Page 33 and 34: Where ( ) are the Lagrange multipli
Page 35 and 36: Every kernel is characterised by a
Page 37 and 38: The “one-against-all” approach
Page 39 and 40: Furthermore, metrics such as the bi
Page 41 and 42: 1.6.3 Leave-One-Out Cross-Validatio
Page 43 and 44: In such cases, the model becomes qu
Page 45 and 46: 1.8 Aims and objectives The overall
Page 47 and 48: 2 Development of the multivariate a
Page 49 and 50: Sensory panel scores were of the hi
Page 51 and 52: DF (Hz) 2.2.1.5 Electronic Nose (e-
Page 53: Figure 2-3 Data intersection The fi
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
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Figure 4-4 Data integration workflo
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a) GPA b) CPCA Figure 4-6 The conse
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accuracies as the linear models; po
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Figure 4-8 Classification Results f
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Similar to FTIR, the PLS-DA ensembl
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Figure 4-9 Class prediction rates o
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4.3.3 Permutation Tests Even though
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Even though the interpretation of t
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Figure 4-12 Distribution plots of t
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RBF SVMs Datasets Original %CC Mean
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Figure 4-14 Boxplots representing t
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5 Application of the multivariate a
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Figure 5-1 Mean FTIR spectra for ca
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5.2.2.2 Fourier Transform Infrared
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5.2.2.4 Data Overview For each expe
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5.2.3.3 High Throughput Liquid Chro
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Figure 5-5 displays the PCA scores
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(a) GPA (b) CPCA Figure 5-6 The con
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observation confirms that indeed CP
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Figure 5-8 Class prediction rates o
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(a) RBF SVMs (b) PLS-DA Figure 5-9
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Figure 5-12 Execution times of the
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(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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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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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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