CRANFIELD UNIVERSITY Eleni Anthippi Chatzimichali ...

More documents

Recommendations

Info

1.6.2 k-fold Cross-Validation Cross-validation (Wold, 1978) is the most popular validation technique. In -fold cross-validation, the entire dataset is randomly split into mutually exclusive subsets – the folds – of approximately equal size (Kohavi, 1995; Duan et al., 2003; Izenman, 2008). The algorithm of -fold cross-validation performs iterations in total. As demonstrated in Figure 1-7, in each iteration, one subset is considered to be the test set, while the remaining folds are used to train the classifier. Therefore, each fold will be used exactly once for testing. As thoroughly described in the previous section, each test set is kept aside and should in no way be used during the development of the model (Brereton, 2006; Westerhuis et al., 2008). The total prediction rate of the classifier is calculated by averaging the individual test results over the iterations. A great advantage of -fold cross-validation is that all examples in the dataset are eventually used for both training and testing. Thus, the bias of this estimate is reduced compared to the holdout method. In general, the outcome of -fold cross-validation depends highly on the split of the initial dataset into folds. Since this partition is not canonical, it may often lead to instances of high variance, especially for large values of (Glasmachers, 2008); thus, or are most commonly applied for cross-validation (Clarke et al. 2009). Figure 1-7 k-fold Cross-Validation In -fold cross-validation, the initial dataset is partitioned into mutually exclusive folds of approximately equal size. In every run, a single fold is omitted and the remaining sets are used in the model’s training process. One can conclude that the split and the allocation of samples into the folds may easily influence the prediction rates. The figure has been extracted from http://research.cs.tamu.edu/prism/lectures/iss/iss_l13.pdf 25
1.6.3 Leave-One-Out Cross-Validation Leave-One-Out Cross-Validation (LOOCV) is the extreme version of -fold crossvalidation. In this case, is equal to , which is the total number of samples in the dataset (Duan et al., 2003). Thus, training and testing are repeated times. During each run, a single sample is used as the test set, while all the remaining samples are used in in the model’s training process as illustrated in Figure 1-8. Even though the LOOCV algorithm produces an almost unbiased estimate of the expected test error, due to its high variance it may often be leading to unreliable estimates (Efron, 1983; Kohavi, 1995; Chapelle and Vapnik, 2000; Duan et al., 2003; Glasmachers, 2008; Clarke et al. 2009). Furhermore, LOOCV is a computationally expensive and time-consuming validation method; thus, it is mainly used in cases where the input data are extremely scarce such that the computational expense is no longer a discouraging factor (Cawley et al., 2007). Figure 1-8 Leave-One-Out Cross Validation (LOOCV) The figure graphically represents the steps of leave-one-out cross-validation. In this method, the number of folds is equal to the number of initial observations. Thus, in every run, all samples but one are used for training, whereas the single sample is kept aside for testing. The figure has been extracted from http://research.cs.tamu.edu/prism/lectures/iss/iss_l13.pdf 26
Page 1 and 2: 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: Furthermore, metrics such as the bi
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 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 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 and 112:
Figure 4-8 Classification Results f
Page 113 and 114:
Similar to FTIR, the PLS-DA ensembl
Page 115 and 116:
Figure 4-9 Class prediction rates o
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 143 and 144:
Figure 5-8 Class prediction rates o
Page 145 and 146:
(a) RBF SVMs (b) PLS-DA Figure 5-9
Page 147 and 148:
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 159 and 160:
Page 161 and 162:
Figure 5-20 Execution times of the
Page 163 and 164:
(a) FTIR data (b) HPLC data 148
Page 165 and 166:
(a) GPA (b) CPCA Figure 5-22 The co
Page 167 and 168:
The classification results of the f
Page 169 and 170:
Figure 5-24 Classification Results
Page 171 and 172:
Figure 5-25 Class prediction rates
Page 173 and 174:
The permutation results for the dat
Page 175 and 176:
Figure 5-28 Distribution plots of t
Page 177 and 178:
Page 179 and 180:
Figure 5-30 Boxplots representing t
Page 181 and 182:
5.4 Comparison of the individual ca
Page 183 and 184:
Figure 5-32 Investigating the commo
Page 185 and 186:
6 Development of improved visualisa
Page 187 and 188:
6.2.2 Generating static graphs As d
Page 189 and 190:
Figure 6-2 Construction process of
Page 191 and 192:
6.2.2.2 Generating dynamic reports
Page 193 and 194:
activity, while simultaneously the
Page 195 and 196:
or disappeared (Wang et al., 2008).
Page 197 and 198:
ectangles, circles and/or irregular
Page 199 and 200:
In addition to the static figures g
Page 201 and 202:
c) graphics package d) ggplot2 pack
Page 203 and 204:
In addition to aesthetics, faceting
Page 205 and 206:
Datasets FTIR HPLC e-nose PLS-DA (L
Page 207 and 208:
Figure 6-10 Interactive dendrogram
Page 209 and 210:
6.4 Conclusion The work reported in
Page 211 and 212:
large number of individual models i
Page 213 and 214:
The generated suite of tools, as pr
Page 215 and 216:
In addition, the difficulty to corr
Page 217 and 218:
REFERENCES Almeida, J. A. S., Barbo
Page 219 and 220:
Processing., Proceedings of the 12t
Page 221 and 222:
Clarke, B., Fokoué, E. and Zhang,
Page 223 and 224:
spectroscopy and machine learning",
Page 225 and 226:
Gower, J. C. (1975), "Generalized p
Page 227 and 228:
Jardon, M. (2006), Systems Biology:
Page 229 and 230:
Nicolaou, N., Xu, Y. and Goodacre,
Page 231 and 232:
Shah, A. A., Barthel, D., Lukasiak,
Page 233 and 234:
Vera, G., Jansen, R. and Suppi, R.
Page 235:
Xu, Y. and Goodacre, R. (2012), "Mu
show all

CRANFIELD UNIVERSITY Eleni Anthippi Chatzimichali ...

Create successful ePaper yourself

Delete template?

Save as template?