Deep Error-Correcting Output Codes
Abstract
:1. Introduction
- We integrate an online learning method into the ECOC coding, which improves the efficiency of ECOC, especially for large-scale applications.
- We employ ECOC as building blocks of deep networks, which sufficiently utilizes the available label information of data and improves the effectiveness and efficiency of previous deep learning algorithms.
- We propose the DeepECOCs model, which combines the ideas of ensemble learning, online learning and deep learning.
2. Related Work
3. Deep Error-Correcting Output Codes (DeepECOCs)
3.1. The ECOC Framework
3.2. Incremental Support Vector Machines (Incremental SVMs)
3.2.1. KKT Conditions
3.2.2. Incremental Learning Procedure
- (1)
- Initialize to 0, then calculate ;
- (2)
- If , terminate (a is not a margin or error vector);
- (3)
- If , apply the largest possible increment so that one of the following conditions occurs:
- (a)
- : add a to margin set , terminate;
- (b)
- : add a to error set , terminate;
- (c)
- Elements of migrate across , and ; update membership of elements, and if changes, update accordingly.
3.3. DeepECOCs
Algorithm 1 The training procedure of DeepECOCs; L is the number of layers, I-SVM() is the incremental SVM binary classifier, is the sigmoid function, and is the softmax function. |
Require: |
The set of training samples ; |
The labels corresponding to training samples . |
Ensure: |
Parameters and . |
1: Initialize the first layer input ; |
2: for to do |
3: Initialize the weights and bias of i-th ECOC module; |
4: ; |
5: Pre-train process (ECOC coding step): |
6: (1) Learn the ECOC matrix with a coding strategy, and obtain (binary case) or (ternary case); |
7: (2) Train the incremental SVM binary classifiers according to : |
8: for to P do |
9: I-SVM; |
10: ; |
11: end for |
12: ; |
13: ; |
14: ; |
15: end for |
16: . |
17: Use the back-propagation algorithm for fine-tuning. |
18: return and , . |
3.4. Combining Convolutional Neural Networks (CNNs) with DeepECOCs
4. Experiments
4.1. Classification on 16 UCI Data Sets
4.2. Classification on the USPS Data Set
4.3. Classification on the MNIST Data Set
4.4. Classification on the CMU Mocap Data Set
4.5. Classification on the CIFAR-10 Data set
4.6. Combining CNNs with DeepECOCs
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Problem | ♯ of I | ♯ of A | ♯ of C | Problem | ♯ of I | ♯ of A | ♯ of C |
---|---|---|---|---|---|---|---|
Dermatology | 366 | 34 | 6 | Yeast | 1484 | 8 | 10 |
Iris | 150 | 4 | 3 | Satimage | 6435 | 36 | 7 |
Ecoli | 336 | 8 | 8 | Letter | 20,000 | 16 | 26 |
Wine | 178 | 13 | 3 | Pendigits | 10,992 | 16 | 10 |
Glass | 214 | 9 | 7 | Segmentation | 2310 | 19 | 7 |
Thyroid | 215 | 5 | 3 | Optdigits | 5620 | 64 | 10 |
Vowel | 990 | 10 | 11 | Shuttle | 14,500 | 9 | 7 |
Balance | 625 | 4 | 3 | Vehicle | 846 | 18 | 4 |
Problem | OneVsOne | OneVsAll | DECOC | ECOCONE | ||||
---|---|---|---|---|---|---|---|---|
LibSVM | I-SVM | LibSVM | I-SVM | LibSVM | I-SVM | LibSVM | I-SVM | |
Dermatology | 0.9671 | 0.9770 | 0.7928 | 0.9605 | 0.9671 | 0.9638 | 0.9671 | 0.9770 |
Iris | 0.9333 | 0.9333 | 0.7030 | 0.7030 | 0.9333 | 0.9333 | 0.9333 | 0.9333 |
Ecoli | 0.5944 | 0.6507 | 0.3940 | 0.4553 | 0.5281 | 0.5828 | 0.5944 | 0.6556 |
Wine | 0.9892 | 0.9892 | 0.9731 | 0.9731 | 0.9892 | 0.9731 | 0.9839 | 0.9892 |
Glass | 0.4838 | 0.4189 | 0.3216 | 0.3270 | 0.2973 | 0.3486 | 0.3027 | 0.5378 |
Thyroid | 0.5897 | 0.6239 | 0.5897 | 0.6239 | 0.5897 | 0.4017 | 0.5897 | 0.6239 |
Vowel | 0.4187 | 0.4956 | 0.3953 | 0.6591 | 0.2736 | 0.3278 | 0.4476 | 0.4956 |
Balance | 0.8927 | 0.8927 | 0.9042 | 0.9042 | 0.8927 | 0.8927 | 0.8927 | 0.8927 |
Yeast | 0.4741 | 0.5744 | 0.2383 | 0.2760 | 0.3751 | 0.5693 | 0.4147 | 0.6000 |
Satimage | 0.8361 | 0.8692 | 0.7620 | 0.8334 | 0.7411 | 0.8532 | 0.8305 | 0.8604 |
Letter | 0.7443 | 0.8216 | 0.2166 | 0.4536 | 0.7530 | 0.8375 | 0.7440 | 0.8120 |
Pendigits | 0.9688 | 0.9859 | 0.9021 | 0.9773 | 0.9065 | 0.9758 | 0.9691 | 0.9850 |
Segmentation | 0.8595 | 0.8872 | 0.6187 | 0.6759 | 0.7969 | 0.6706 | 0.8601 | 0.8872 |
OptDigits | 0.9492 | 0.9860 | 0.8866 | 0.9649 | 0.8793 | 0.9808 | 0.9492 | 0.9860 |
Shuttle | 0.9178 | 0.9475 | 0.8312 | 0.9034 | 0.8352 | 0.9407 | 0.9179 | 0.9532 |
Vehicle | 0.6324 | 0.7595 | 0.7378 | 0.4892 | 0.6054 | 0.7243 | 0.6324 | 0.7595 |
Problem | Epoch | Problem | Epoch | ||
---|---|---|---|---|---|
Dermatology | 0.1 | 2000 | Yeast | 0.01 | 4000 |
Iris | 0.1 | 400 | Satimage | 0.01 | 4000 |
Ecoli | 0.1 | 2000 | Letter | 0.01 | 8000 |
Wine | 0.1 | 2000 | Pendigits | 0.01 | 2000 |
Glass | 0.01 | 4000 | Segmentation | 0.01 | 8000 |
Thyroid | 0.1 | 800 | Optdigits | 0.01 | 2000 |
Vowel | 0.1 | 4000 | Shuttle | 0.1 | 2000 |
Balance | 0.1 | 4000 | Vehicle | 0.1 | 4000 |
Problem | Single | AE | DAE | V1 | V2 | V3 | V4 |
---|---|---|---|---|---|---|---|
Dermatology | 0.9513 | 0.9429 ± 0.0671 | 0.9674 ± 0.0312 | 0.9731 ± 0.0314 | 0.8852 ± 0.0561 | 0.9722 ± 0.0286 | 0.8834 ± 0.0349 |
Iris | 0.9600 | 0.9600 ± 0.0562 | 0.9333 ± 0.0889 | 0.8818 ± 0.0695 | 0.8137 ± 0.0768 | 0.9667 ± 0.0471 | 0.9667 ± 0.0471 |
Ecoli | 0.8147 | 0.7725 ± 0.0608 | 0.8000 ± 0.0362 | 0.8275 ± 0.0427 | 0.7868 ± 0.0633 | 0.9102 ± 0.0701 | 0.9183 ± 0.0611 |
Wine | 0.9605 | 0.9765 ± 0.0264 | 0.9563 ± 0.0422 | 0.9063 ± 0.0793 | 0.9625 ± 0.0604 | 0.9875 ± 0.0264 | 0.9625 ± 0.0437 |
Glass | 0.6762 | 0.6669 ± 0.1032 | 0.6669 ± 0.0715 | 0.7563 ± 0.0653 | 0.6875 ± 0.0877 | 0.8013 ± 0.0476 | 0.7830 ± 0.0893 |
Thyroid | 0.9210 | 0.9513 ± 0.0614 | 0.9599 ± 0.0567 | 0.8901 ± 0.1177 | 0.9703 ± 0.0540 | 0.9647 ± 0.0431 | 0.9560 ± 0.0633 |
Vowel | 0.7177 | 0.6985 ± 0.0745 | 0.7101 ± 0.0756 | 0.7020 ± 0.0529 | 0.6563 ± 0.0721 | 0.7628 ± 0.0716 | 0.6874 ± 0.0438 |
Balance | 0.8222 | 0.8036 ± 0.0320 | 0.8268 ± 0.0548 | 0.8528 ± 0.0534 | 0.8108 ± 0.0634 | 0.8879 ± 0.1331 | 0.9090 ± 0.0438 |
Yeast | 0.5217 | 0.5641 ± 0.0346 | 0.5891 ± 0.0272 | 0.5861 ± 0.0318 | 0.5368 ± 0.0582 | 0.6080 ± 0.0385 | 0.5968 ± 0.0378 |
Satimage | 0.8537 | 0.8675 ± 0.0528 | 0.8897 ± 0.0304 | 0.8763 ± 0.0576 | 0.8238 ± 0.0453 | 0.8977 ± 0.0752 | 0.9108 ± 0.0483 |
Letter | 0.9192 | 0.9234 ± 0.0547 | 0.9381 ± 0.0641 | 0.9498 ± 0.0587 | 0.9322 ± 0.0251 | 0.9553 ± 0.0327 | 0.9465 ± 0.0414 |
Pendigits | 0.9801 | 0.9831 ± 0.0123 | 0.9886 ± 0.0034 | 0.9828 ± 0.0047 | 0.9768 ± 0.0034 | 0.9917 ± 0.0021 | 0.9817 ± 0.0082 |
Segmentation | 0.9701 | 0.9584 ± 0.0317 | 0.9596 ± 0.0211 | 0.9683 ± 0.0412 | 0.9567 ± 0.0527 | 0.9757 ± 0.0296 | 0.9724 ± 0.0371 |
Optdigits | 0.9982 | 0.9785 ± 0.0101 | 0.9856 ± 0.0088 | 0.9882 ± 0.0104 | 0.9845 ± 0.0122 | 0.9934 ± 0.0027 | 0.9901 ± 0.0033 |
Shuttle | 0.9988 | 0.9953 ± 0.0012 | 0.9976 ± 0.0014 | 0.9991 ± 0.0017 | 0.9983 ± 0.0018 | 0.9996 ± 0.0012 | 0.9993 ± 0.0010 |
Vehicle | 0.7315 | 0.6987 ± 0.0521 | 0.7348 ± 0.0454 | 0.7128 ± 0.0384 | 0.6624 ± 0.0472 | 0.7466 ± 0.0481 | 0.7097 ± 0.0521 |
Mean rank | 5.2500 | 6.3125 | 4.9375 | 4.3125 | 7.0625 | 1.4375 | 3.1875 |
Problem | AE | DAE | V1 | V2 | V4 | V5 |
---|---|---|---|---|---|---|
CMU | 0.6171 | 0.6422 | 0.8030 | 0.6364 | 0.7652 | 0.6030 |
Problem | AE | DAE | V1 | V2 |
---|---|---|---|---|
CIFAR(36) | 0.3501 | 0.3678 | 0.4530 | 0.3895 |
CIFAR(256) | 0.4352 | 0.4587 | 0.4936 | 0.4521 |
Problem | V3 | V4 | V5 | V6 |
CIFAR(36) | 0.4031 | 0.5089 | 0.4517 | 0.4752 |
CIFAR(256) | 0.5236 | 0.5588 | 0.4589 | 0.5224 |
Methods | ResNet-Baseline | ResNet-DeepECOCs |
---|---|---|
Accuracy | 0.9098 | 0.9208 |
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Wang, L.-N.; Wei, H.; Zheng, Y.; Dong, J.; Zhong, G. Deep Error-Correcting Output Codes. Algorithms 2023, 16, 555. https://doi.org/10.3390/a16120555
Wang L-N, Wei H, Zheng Y, Dong J, Zhong G. Deep Error-Correcting Output Codes. Algorithms. 2023; 16(12):555. https://doi.org/10.3390/a16120555
Chicago/Turabian StyleWang, Li-Na, Hongxu Wei, Yuchen Zheng, Junyu Dong, and Guoqiang Zhong. 2023. "Deep Error-Correcting Output Codes" Algorithms 16, no. 12: 555. https://doi.org/10.3390/a16120555