European Journal of Scientific Research - EuroJournals
European Journal of Scientific Research - EuroJournals European Journal of Scientific Research - EuroJournals
430 Nooritawati Md Tahir, Aini Hussain, Salina Abdul Samad, Hafizah Husain and Mohd Yusof Jamaluddin KG rule that suggested retaining all eigenvalues > 1 results in thirty-five PCs to be considered as significant components. The PCs are as tabulated in Table 1. Table 1: The significant eigenvalues or PCs using the KG rule. Factor k 1 2 3 4 5 Eigenvalue 44.37 23.64 17.48 12.25 10.32 Factor k 6 7 8 9 10 Eigenvalue 9.37 5.77 5.64 5.21 3.89 Factor k 11 12 13 14 15 Eigenvalue 3.79 3.17 3.07 2.9 2.64 Factor k 16 17 18 19 20 Eigenvalue 2.6 2.48 2.39 2.19 2.02 Factor k 21 22 23 24 25 Eigenvalue 1.97 1.77 1.71 1.67 1.63 Factor k 26 27 28 29 30 Eigenvalue 1.57 1.42 1.35 1.28 1.26 Factor k 31 32 33 34 35 Eigenvalue 1.2 1.14 1.11 1.06 1.01 Figure 3: Percentage of the total variance accounted by each PCs or eigenvalues using Scree Test. Percent of total variance (%) 20 18 16 14 12 10 8 6 4 2 0 0 5 10 15 20 Factor No k 25 30 35 40 Further, we consider the cumulative variance rule of thumb as our feature selection basis to determine the optimum number of eigenvalues or PCs. Figure 4a depicts the overall cumulative variance of the eigenvalues of the orthogonal eigenvectors of the human posture database produced in this study. The blue solid line represents the cumulative variance whilst the dotted line represents the t threshold of 90% for selecting the optimal number of PCs to retain. As suggested in [8], a threshold t of between 80%-90% can be considered to determine factor number, k. In this case, a 90% criterion would result in k equals 70, thus suggesting that 70 PCs are required to account for more than 90% of the total variance and an 80% criterion would result in k equals 34 as depicts in Figure 4b. Consequently, all three rules of thumb provide constructive results and in this study, we rule that thirty-five PCs are adequate to represent a large part of the variance of the original human postures data set. The eigenvectors of these thirty-five PCs that we termed as eigenpostures will undergo the statistical analysis prior to classification. Accordingly, we determine the statistical significance of all the thirty-five eigenpostures of the four main postures using ANOVA. In this analysis, null hypothesis
Feature Selection Based on Statistical Analysis 431 Cumulative Variance (%) 100 90 80 70 60 50 40 30 20 10 0 20 40 60 80 100 120 140 160 180 200 Factor Number K Figure 4: Cumulative Variance Graph will be discarded for p-value near zero and suggests that at least one sample mean is significantly different from the other sample means. If the PCs are statistically significant, hence the selected PCs will undergo the MCP test. Hence, from the ANOVA test, at a significant level of α = 0.05, we anticipate that the p-values for eigenpostures 1-9, 11-13, 15-18, and 20-21 are numerically indistinguishable from zero, therefore we conclude that a total of nineteen eigenpostures or PCs are fit to undergo the MCP. As a result, the ANOVA test has lucratively reduced the feature vectors to nineteen or 54% of the initial feature extraction quantity. Table 2: Classification results using combination of three eigenpostures. (CA = Classification Accuracy) Exp No 1 2 3 4 Eigenpostures Combination / CA (%) E1, E2, E3 E1, E2, E5 E1, E3, E5 E2, E3, E5 Bending 100 100 80 85 93 88 93 78 Sitting Standing Lying (a) t between 80 & 90 % Cumulative Variance (%) 10 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 Factor Number K 98 87 88 82 95 93 95 67 In addition, the MCP test is performed to determine the number of optimized eigenpostures for classification. Using MCP and homogeneous subset test, we foresee that E1, E2, E3, and E5 are the eigenpostures that are significantly different between groups. As a result, the statistical analysis has enabled us to perform effectively the selection of only four eigenpostures as inputs to the classifier and further lessen the feature vectors to 11% of the initial feature vectors. As aforementioned, Multilayer Perceptron (MLP) is chosen as our classifier in this study. In order to develop a classification system, a combination of these significant eigenpostures of the training images will serve as inputs to the neural network. For each experiment, a combination of three eigenpostures according to the MCP and homogeneous subset tests are selected as in Table 2 respectively. For this study, 100 sets of each posture profile are used for training the ANN and another 100 sets unseen profile of each category will be the testing data. The system is trained on the training data and its performance measured on the test data. As shown in Table 2, for all four postures, using only the combination of three eigenpostures give 87% classification results for unseen images of standing and sitting apart from experiment 4. Another 100 90 80 70 60 50 40 30 20 (b) t at 80 %
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Feature Selection Based on Statistical Analysis 431<br />
Cumulative Variance (%)<br />
100<br />
90<br />
80<br />
70<br />
60<br />
50<br />
40<br />
30<br />
20<br />
10<br />
0 20 40 60 80 100 120 140 160 180 200<br />
Factor Number K<br />
Figure 4: Cumulative Variance Graph<br />
will be discarded for p-value near zero and suggests that at least one sample mean is significantly<br />
different from the other sample means. If the PCs are statistically significant, hence the selected PCs<br />
will undergo the MCP test. Hence, from the ANOVA test, at a significant level <strong>of</strong> α = 0.05, we<br />
anticipate that the p-values for eigenpostures 1-9, 11-13, 15-18, and 20-21 are numerically<br />
indistinguishable from zero, therefore we conclude that a total <strong>of</strong> nineteen eigenpostures or PCs are fit<br />
to undergo the MCP. As a result, the ANOVA test has lucratively reduced the feature vectors to<br />
nineteen or 54% <strong>of</strong> the initial feature extraction quantity.<br />
Table 2: Classification results using combination <strong>of</strong> three eigenpostures.<br />
(CA = Classification Accuracy)<br />
Exp No 1 2 3 4<br />
Eigenpostures Combination / CA (%) E1, E2, E3 E1, E2, E5 E1, E3, E5 E2, E3, E5<br />
Bending<br />
100 100 80 85<br />
93 88 93 78<br />
Sitting<br />
Standing<br />
Lying<br />
(a)<br />
t between 80 & 90 %<br />
Cumulative Variance (%)<br />
10<br />
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40<br />
Factor Number K<br />
98 87 88 82<br />
95 93 95 67<br />
In addition, the MCP test is performed to determine the number <strong>of</strong> optimized eigenpostures for<br />
classification. Using MCP and homogeneous subset test, we foresee that E1, E2, E3, and E5 are the<br />
eigenpostures that are significantly different between groups. As a result, the statistical analysis has<br />
enabled us to perform effectively the selection <strong>of</strong> only four eigenpostures as inputs to the classifier and<br />
further lessen the feature vectors to 11% <strong>of</strong> the initial feature vectors. As aforementioned, Multilayer<br />
Perceptron (MLP) is chosen as our classifier in this study. In order to develop a classification system, a<br />
combination <strong>of</strong> these significant eigenpostures <strong>of</strong> the training images will serve as inputs to the neural<br />
network.<br />
For each experiment, a combination <strong>of</strong> three eigenpostures according to the MCP and<br />
homogeneous subset tests are selected as in Table 2 respectively. For this study, 100 sets <strong>of</strong> each<br />
posture pr<strong>of</strong>ile are used for training the ANN and another 100 sets unseen pr<strong>of</strong>ile <strong>of</strong> each category will<br />
be the testing data. The system is trained on the training data and its performance measured on the test<br />
data. As shown in Table 2, for all four postures, using only the combination <strong>of</strong> three eigenpostures give<br />
87% classification results for unseen images <strong>of</strong> standing and sitting apart from experiment 4. Another<br />
100<br />
90<br />
80<br />
70<br />
60<br />
50<br />
40<br />
30<br />
20<br />
(b)<br />
t at 80 %
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