CHAPTER 4: DATA SETS AND EXPERIMENTAL RESULTS
4.1 Hyperspectral Image Dataset and Experiments
4.1.2 Experimental Designs and Results
There is one dataset (Washington DC Mall Image) applied to compare the performances of non feature extraction (NonFE), NWFE, AdaFE_CE, AdaFE_RR, and AdaFE_SI methods in our experiments. In the AdaFE_CE and AdaFE_SI, the training error from 5-fold cross validation is used to renew the weights, u is set as 5. In the AdaFE_RR, the training error from 5-fold cross validation is used to renew the weights, u is set as 5, and r is set as 0.1. We create the classifiers under each different feature space, and finally combine them to turn into a strong classifier by weighted vote method.
Table 4.1. Number of pixels for each category in the Washington DC Mall Image.
Category #(Pixels)
1 Roofs 3776
2 Roads 1982
3 Paths 737
4 Grass 2870
5 Trees 1430
6 Water 1156
7 Shadows 840
Total 12791
Figure 4.1. Washington DC Mall Image.
feature extraction (NonFE), NWFE, AdaFE_CE, AdaFE_RR, and AdaFE_SI. Table 4.2 displays the classification accuracies of testing data in cases 1, 2, and 3, respectively.
Note that the highest accuracy of each dataset (in column) is highlighted in shadow cell. The brackets show the number of extracted features.
Table 4.2. The accuracy of Case 1, Case 2, and Case 3.
Case 1 Case 2 Case 3
Methods Classifier
Washington, DC Washington, DC Washington, DC
Gaussian N/A N/A 92.3 %
NonFE
3NN 84.3 % 87.5 % 94.2 %
Gaussian 87.7 % (4) 92.0 % (4) 94.1 % (15) NWFE
3NN 88.9 % (4) 91.2 % (7) 95.1 % (8) Gaussian 89.2 % (11) 92.3 % (9) 94.1 % (13) AdaFE_CE
3NN 88.3 % (4) 91.1 % (5) 96.0 % (7) Gaussian 90.3 % (7) 93.7 % (15) 95.2 % (15) AdaFE_RR
3NN 89.2 % (4) 92.1 % (4) 95.5 % (8) Gaussian 93.1 % (8) 94.6 % (14) 95.0 % (14) AdaFE_SI
3NN 92.6 % (3) 94.3 % (7) 98.1 % (8)
The comparisons of mean accuracies between all algorithms using two different classifiers are displayed in Figures 4.2-4.7.
85%
87%
89%
91%
93%
95%
NonFE NWFE AdaFE_CE AdaFE_RR AdaFE_SI
NonFE 0%
NWFE 87.70%
AdaFE_CE 89.20%
AdaFE_RR 90.30%
AdaFE_SI 93.10%
Gaussian (Case 1)
Figure 4.2. The accuracy of five methods with Gaussian classifier for hyperspectral image classification in Case 1.
80%
83%
86%
89%
92%
95%
NonFE NWFE AdaFE_CE AdaFE_RR AdaFE_SI
NonFE 84.30%
NWFE 88.90%
AdaFE_CE 88.30%
AdaFE_RR 89.20%
AdaFE_SI 92.60%
kNN (k=3, Case 1)
90%
91%
92%
93%
94%
95%
NonFE NWFE AdaFE_CE AdaFE_RR AdaFE_SI
NonFE 0%
NWFE 92.00%
AdaFE_CE 92.30%
AdaFE_RR 93.70%
AdaFE_SI 94.60%
Gaussian (Case 2)
Figure 4.4. The accuracy of five methods with Gaussian classifier for hyperspectral image classification in case 2.
85%
87%
89%
91%
93%
95%
NonFE NWFE AdaFE_CE AdaFE_RR AdaFE_SI
NonFE 87.50%
NWFE 91.20%
AdaFE_CE 91.10%
AdaFE_RR 92.10%
AdaFE_SI 94.30%
kNN (k=3, Case 2)
Figure 4.5. The accuracy of five methods with kNN (k=3) classifier for hyperspectral image classification in Case 2.
90%
91%
92%
93%
94%
95%
96%
NonFE NWFE AdaFE_CE AdaFE_RR AdaFE_SI
NonFE 92.30%
NWFE 94.10%
AdaFE_CE 94.10%
AdaFE_RR 95.20%
AdaFE_SI 95.00%
Gaussian (Case 3)
Figure 4.6. The accuracy of five methods with Gaussian classifier for hyperspectral image classification in case 3.
92%
93%
94%
95%
96%
97%
98%
99%
NonFE NWFE AdaFE_CE AdaFE_RR AdaFE_SI
NonFE 94.20%
NWFE 95.10%
AdaFE_CE 96.00%
AdaFE_RR 95.50%
AdaFE_SI 98.10%
kNN (k=3, Case 3)
From these Table and Figures, we have the following findings.
1. In the Washington, DC Mall dataset, the highest accuracies among all methods are 93.1 % (AdaFE_SI with Gaussian classifier), 94.6 % (AdaFE_SI with Gaussian classifier), and 98.1 % (AdaFE_SI with 3NN classifier) in case 1, 2, and 3, respectively.
2. The best classification result is 98.1 % which is using AdaFE_SI with kNN (k=3) classifier.
3. According to the accuracy rate from Table 4.2, AdaFE_RR and AdaFE_SI with two different classifiers are better than conventional methods.
We choose the well-known Washington, DC Mall image as the example and only some classified images are shown for comparison. The classification mechanisms under case 1, 2, and 3 (Ni =20, 40, and 300) and five methods, NonFE, NWFE, AdaFE_CE, AdaFE_RR, and AdaFE_SI, are selected to generate the classified images.
Figures 4.9-4.13 are the classification maps from five feature extraction conditions (NonFE, NWFE, AdaFE_CE, AdaFE_RR and AdaFE_SI) with Gaussian and kNN (k=3) classifiers. It can be observed form Figures 4.9-4.13 that our novel methods with Gaussian or kNN (k=3) classifier outperform NonFE and NWFE with Gaussian or kNN (k=3) classifier.
Figure 4.8. Washington DC Mall Image.
■
Grass■
Path■
Tree■
Water■
Roof■
Road■
Shadow(a) (c)
(b) (d)
Figure 4.9. (a) NonFE with Gaussian classifier in cases 3.
■
Grass■
Path■
Tree■
Water■
Roof■
Road■
Shadow(a) (d)
(b) (e)
(c) (f)
Figures 4.10. (a)-(c) AdaFE_CE with Gaussian classifier in cases 1, 2, and 3.
Figures 4.10. (d)-(f) AdaFE_RR with Gaussian classifier in cases 1, 2, and 3.
■
Grass■
Path■
Tree■
Water■
Roof■
Road■
Shadow(a) (d)
(b) (e)
(c) (f)
■
Grass■
Path■
Tree■
Water■
Roof■
Road■
Shadow(a) (d)
(b) (e)
(c) (f)
Figures 4.12. (a)-(c) NWFE with kNN (k=3) classifier in cases 1, 2, and 3.
Figures 4.12. (d)-(f) AdaFE_CI with kNN (k=3) classifier in cases 1, 2, and 3.
■
Grass■
Path■
Tree■
Water■
Roof■
Road■
Shadow(a) (d)
(b) (e)
(c) (f)
4.2 Educational Measurement Dataset and and Experiments
4.2.1 Data Description
According to the results of Chapter 4.1.2, the proposed methods, adaptive feature extractions, have better performance than other conventional methods. For evaluating student’s learning profile and arranging suitable remedial instruction, educational tests are usually administrated. In this section, educational measurement dataset is analyzed by the proposed methods and other conventional methods.
Performances of two algorithms listed in Chapters 3.2.1-3.2.2 are compared by using adaptive testing simulation processes with Mathematics paper-based test data.
The content of the test designed for the sixth grade students is about “Sector” related concepts (see Appendix A). In Figure 4.14, the experts’ structures of the unit for this test are developed by seven elementary school teachers and three researchers. These structures are different from usual concept maps but emphasis on the ordering of nodes.
Additionally, every node can be assessed by an item. There are 21 items in this test and 828 subjects are collected in “Sector” tests.
Figure 4.14. Experts’ structure of “Sector” unit.
Finding the areas of compound sectors
Finding the areas of simple sectors
Definition of sector Finding the areas of circles
Drawing compound graphs
Drawing sectors
According to this structure in “Sector” test, it can divide subjects into six categories of remedial instructions. Table 4.3 is showed the remedial concepts and subjects of each category of remedial instruction.
Table 4.3. Six categories of remedial instructions.
Category Subjects The concepts of remedial instruction
0 80 All concepts are known, they don’t need remedial instructions.
1 50 They are careless and need to practice more.
2 36 “Finding the areas of compound sectors” and “Finding the areas of simple sectors”.
3 47 “Finding the areas of compound sectors” and “Finding the areas of simple sectors”.
4 221 “Definition of sector”, “Finding the areas of compound sectors”, and “Finding the areas of simple sectors”.
5 53
“Drawing sectors”.
“Finding the areas of simple sectors”, “Drawing compound graphs”, and “Definition of sector”.
6 30 “Finding the areas of compound sectors” and “Drawing sectors”.
7 25 “Finding the areas of compound sectors”, “Drawing sectors”, and “Finding the areas of simple sectors”.
8 286 They need to learn all concepts of remedial instruction.
Total 828
For evaluating the performance of the proposed method, twenty subjects in each category are randomly selected to form training datasets, and others are selected to form testing datasets. Table 4.4 is showed the training subjects and testing subjects in the experiment. There are ten training and testing datasets which are randomly selected for estimating system parameters and computing the mean accuracies of testing data of
Table 4.4. The number of training subjects and testing subjects of the experiment.
Category 1 2 3 4 5 6 7 8
Training
Subjects 20 20 20 20 20 20 20 20
Testing
Subjects 30 16 27 201 33 10 5 266
Total 50 36 47 221 53 30 25 748
4.2.2 Experimental Designs and Results
There is one dataset (Educational Measurement) applied to compare the performances of non feature extraction (NonFE), NWFE, AdaFE_CE, and AdaFE_RR methods in our experiments. In the AdaFE_CE, the training error from 5-fold cross validation is used to renew the weights, u is set as 5. In the AdaFE_RR, the training error from 5-fold cross validation is used to renew the weights, u is set as 5, and r is set as 0.1. We create the classifiers under each different feature space, and finally combine them to turn into a strong classifier by weighted vote method.
Mean accuracies of two algorithms listed in Chapters 3.2.1-3.2.2 and other conventional methods for educational testing experiment are shown in Table 4.5. Note that shadow part indicates the best accuracy of all combinations and the best accuracy of each applied classifier among all algorithms is written in bold type. The comparisons of mean accuracies between all algorithms using two different classifiers are displayed in Figures 4.15-4.16.
The following are some findings based on these results.
1. The best accuracies with kNN (k=3) and Gaussian are 70.2 % (AdaFE_RR) and 52.1 % (AdaFE_RR), respectively.
2. Applying kNN (k=3) and Gaussian into AdaFE_CE or AdaFE_RR can improve the classification performance effectively.
3. The best classification result is 70.2 % which is using AdaFE_RR with kNN (k=3).
4. The single classifier (Gaussian or kNN) does not work well in this dataset. It can be observed form Table 4.5 and Figures 4.15-4.16 that doing feature extraction with classifier (Gaussian or kNN) outperforms NonFE with classifier (Gaussian or kNN).
Table 4.5. The accuracy of four methods with two classifiers in educational testing experiment.
Ni = 20 Methods Classifier
Educational Measurement Data
Gaussian 16.3 %
NonFE
kNN (k=3) 35.4 %
Gaussian 48.6 % (2)
NWFE
kNN (k=3) 58.6 % (4)
Gaussian 51.7 % (2)
AdaFE_CE
kNN (k=3) 62.6 % (5)
Gaussian 52.1 % (3)
AdaFE_RR
kNN (k=3) 70.2% (4)
10%
20%
30%
40%
50%
NonFE NWFE AdaFE_CE AdaFE_RR
NonFE 16.30%
NWFE 48.60%
AdaFE_CE 51.70%
AdaFE_RR 52.10%
Gaussian
Figure 4.15. The accuracy of four methods with Gaussian classifier in educational testing experiment.
20%
30%
40%
50%
60%
70%
NonFE NWFE AdaFE_CE AdaFE_RR
NonFE 35.40%
NWFE 58.60%
AdaFE_CE 62.60%
AdaFE_RR 70.20%
kNN (k=3)
Figure 4.16. The accuracy of four methods with kNN (k=3) classifier in educational testing experiment.
4.3 UCI Datasets and Experiments
4.3.1 Data Description
In this section, we select a few well-known datasets from University of California Irvine (UCI) Machine Learning Repository (Blake & Merz, 1998) for experimental analysis. The datasets are described as following Table 4.6:
Table 4.6. The datasets of UCI Machine Learning Repository.
Datasets Number of Categories Number of Instances Number of Attributes
Glass 6 214 9
Heart 2 267 44
Yeast 4 1299 8
4.3.2 Experimental Designs and Results
There are three datasets (Glass, Heart, and Yeast) applied to compare the performances of non feature extraction (NonFE), NWFE, AdaFE_CE, and AdaFE_RR methods in our experiments. In the AdaFE_CE, the training error from 5-fold cross validation is used to renew the weights, u is set as 5. In the AdaFE_RR, the training error from 5-fold cross validation is used to renew the weights, u is set as 5, and r is set as 0.1. We create the classifiers under each different feature space, and finally combine them to turn into a strong classifier by weighted vote method.
Mean accuracies of two algorithms listed in Chapters 3.2.1-3.2.2 and other
of each applied classifier among all algorithms is written in bold type. The comparisons of mean accuracies between all algorithms using two different classifiers are displayed in Figures 4.17-4.22.
The following are some findings based on these results.
1. In Glass, Heart, and Yeast datasets, the highest accuracies among all methods are 77.6 % (AdaFE_RR with 3NN), 82.4 % (AdaFE_RR with 3NN), and 61.4
% (AdaFE_RR with 3NN), respectively.
2. Applying kNN (k=3) and Gaussian into AdaFE_CE or AdaFE_RR can improve the classification performance effectively.
Table 4.7. The accuracy of four methods with two classifiers in UCI datasets experiment.
Datasets Methods Classifier
Glass Heart Yeast
Gaussian 21.7% 74.9% 27.0%
NonFE
kNN (k=3) 75.3% 80.1% 56.2%
Gaussian 56.2% (6) 78.3% (4) 58.4% (8) NWFE
kNN (k=3) 72.0% (6) 79.4% (12) 56.5% (2) Gaussian 60.4% (7) 79.4% (2) 60.9% (4) AdaFE_CE
kNN (k=3) 74.3% (8) 82.0% (15) 60.3% (3) Gaussian 60.8% (6) 79.7% (3) 60.5% (7) AdaFE_RR
kNN (k=3) 77.6% (8) 82.4% (4) 61.4% (7)
10%
20%
30%
40%
50%
60%
NonFE NWFE AdaFE_CE AdaFE_RR
NonFE 21.70%
NWFE 56.20%
AdaFE_CE 60.40%
AdaFE_RR 60.80%
Gaussian
Figure 4.17. The accuracy of four methods with Gaussian classifier in Glass dataset experiment.
60%
65%
70%
75%
80%
NonFE NWFE AdaFE_CE AdaFE_RR
NonFE 75.30%
NWFE 72.00%
AdaFE_CE 74.30%
AdaFE_RR 77.60%
kNN (k=3)
70%
72%
74%
76%
78%
80%
NonFE NWFE AdaFE_CE AdaFE_RR
NonFE 74.90%
NWFE 78.30%
AdaFE_CE 79.40%
AdaFE_RR 79.70%
Gaussian
Figure 4.19. The accuracy of four methods with Gaussian classifier in Heart dataset experiment.
70%
72%
74%
76%
78%
80%
82%
84%
NonFE NWFE AdaFE_CE AdaFE_RR
NonFE 80.10%
NWFE 79.40%
AdaFE_CE 82.00%
AdaFE_RR 82.40%
kNN (k=3)
Figure 4.20. The accuracy of four methods with kNN (k=3) classifier in Heart dataset experiment.
20%
25%
30%
35%
40%
45%
50%
55%
60%
65%
NonFE NWFE AdaFE_CE AdaFE_RR
NonFE 27.00%
NWFE 58.40%
AdaFE_CE 60.90%
AdaFE_RR 60.50%
Gaussian
Figure 4.21. The accuracy of four methods with Gaussian classifier in Yeast dataset experiment.
50%
52%
54%
56%
58%
60%
62%
64%
NonFE NWFE AdaFE_CE AdaFE_RR
NonFE 56.20%
NWFE 56.50%
AdaFE_CE 60.30%
AdaFE_RR 61.40%
kNN (k=3)
CHAPTER 5: CONCLUSION AND FUTURE WORK
5.1 Conclusion
In Chapter 2, nonparametric weighted feature extraction (NWFE), adaptive boosting, reject region, neighborhood system, and classifiers are introduced which are the previous works for Chapters 3, 4, and 5.
In Chapter 3, a novel method named adaptive feature extraction for constructing various classifiers is proposed for mitigating the Hughes effect (small training sample problem) and improving high dimensional data classification performances.
In Chapter 4, experimental results of hyperspectral image dataset show that the proposed algorithm can improve on Gaussian and kNN (k=3) classifiers, especially in the situation of small ensemble size. The best classification accuracy can be obtained by using AdaFE_SI with Gaussian or knn (k=3) classifier. Experimental results of educational testing and UCI datasets show that the application of the proposed method is useful.
Based on the above summary, the adaptive feature extraction method is a robust classification process for high dimensional data.
In this thesis, AdaFE_CE is proposed and the traditional NWFE is a special case of AdaFE_CE when performing only a round; if the ratio r which is the factor to
decide the number of rejected samples from training samples is set as 1, then NWFE is the special cases of AdaFE_RR. Our novel methods integrate NWFE, AdaBoost, reject region, and neighborhood system’s advantages to develop better efficacy. The experimental results show that only fewer rounds by applying the algorithm we proposed can obtain the higher accuracy and achieve the best result no matter what kinds of classifiers are applied.
5.2 Suggestions for Future Work
1. Try to integrate feature selection into multiple classifier system to scale new heights in classification result in the future.
2. Adding other feature extractions and classifiers to enlarge the adaptive feature extraction methods.
3. To use other high dimensional data with huge dimensionality such as face recognition data to test the completeness and suitability of the adaptive feature extraction methods.
APPENDIX A: THE TEST OF “SECTOR” UNIT
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