Multi Similarity Metric Fusion in Graph-Based Semi-Supervised Learning
Abstract
:1. Introduction
2. An Overview on Multi-Metric Fusion
3. Proposed Method
3.1. Review of Flexible Manifold Embedding (FME)
3.2. Multi Similarity Metric Fusion
3.3. Incorporating Label Space Information
Algorithm 1. The proposed method. |
Input: Feature from one view X; |
Initial label matrix Y = [Y1, Yu]; |
Parameters μ and γ. |
Output: Predicted label matrix F, projection matrix Q, and bias vector b. |
1. Construct M different graphs from the available view. |
2. Compute the Laplacian matrices of the graphs. |
3. Initialize the soft label matrix F = Y. |
4. for t = 1: Max iteration. |
5. Generate the correlation graph based on F by Equation (11). |
6. Fuse the M + 1 Laplacian graph to obtain adopting Equation (12). |
7. Feed to FME and calculate a new soft label matrix F. |
8. Reinitialize the part of F matrix corresponding to the labeled samples. |
9. end for. |
10. To calculate the labels of unseen samples, use the projection matrix Q and the bias vector b to predict the labels of them. |
4. Experimental Results
4.1. Experimental Setup
4.2. Comparison with Individual Graphs
4.3. Comparison with Other Methods
4.4. CPU-Time and Computational Complexity
5. Discussion and Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Notation | Description |
---|---|
N | Number of samples |
M | Number of metrics |
X = [x1, x2, …, xN] | Data matrix |
C | Number of classes |
d | Sample dimension |
Y | Initial binary label matrix |
F | Prediction label matrix |
W | Similarity matrix |
L | Laplacian matrix |
Fusion Laplacian matrix | |
Q | Projection matrix |
b | Bias vector |
t | Iteration number |
Dataset | Size | # of Classes | Features | Dimension |
---|---|---|---|---|
PF01 | 1819 | 107 | VGG Face-FC7 | 4096 |
VGG Face-FC6 | 4096 | |||
LBP | 900 | |||
Extended_Yale | 1774 | 28 | VGG Face-FC7 | 4096 |
VGG Face-FC6 | 4096 | |||
LBP | 900 | |||
PIE | 1926 | 68 | VGG Face-FC7 | 4096 |
VGG Face-FC6 | 4096 | |||
LBP | 900 | |||
FERET | 1400 | 200 | VGG Face-FC7 | 4096 |
VGG Face-FC6 | 4096 | |||
LBP | 900 |
Dataset | # Labeled Samples | Feature | Accuracy (Mean ± STD ) | ||
---|---|---|---|---|---|
k-NN graph | Adaptive k-NN Graph | Proposed Method | |||
PF01 | 1 | FC7 | 89.63 ± 7.97 | 89.07 ± 8.39 | 92.42 ± 2.86 |
FC6 | 90.85 ± 7.16 | 89.54 ± 8.99 | 93.99 ± 0.85 | ||
LBP | 51.79 ± 11.64 | 49.16 ± 11.54 | 56.19 ± 8.97 | ||
2 | FC7 | 94.16 ± 1.09 | 93.94 ± 1 | 94.36 ± 1.19 | |
FC6 | 94.74 ± 1.04 | 94.22 ± 1.11 | 94.75 ± 0.98 | ||
LBP | 63.77 ± 6.82 | 61.08 ± 6.98 | 65.47 ± 5.86 | ||
Extended_Yale | 1 | FC7 | 40.33 ± 20.86 | 40.33 ± 20.94 | 43.5 ± 19.34 |
FC6 | 44.67 ± 22.76 | 44.32 ± 22.9 | 50.38 ± 19.27 | ||
LBP | 91.32 ± 5.17 | 91.69 ± 5.66 | 94.25 ± 1.52 | ||
2 | FC7 | 54.24 ± 22 | 54.13 ± 21.99 | 55.35 ± 21.68 | |
FC6 | 57.01 ± 22.99 | 56.81 ± 23.06 | 58.68 ± 21.77 | ||
LBP | 96.01 ± 2.3 | 96.17 ± 2.07 | 96.73 ± 1.93 | ||
PIE | 1 | FC7 | 77.36 ± 9.82 | 77.17 ± 9.79 | 79.04 ± 8.21 |
FC6 | 76.52 ± 11.43 | 75.73 ± 11.7 | 79.77 ± 8.81 | ||
LBP | 45 ± 7.71 | 44.56 ± 7.16 | 46.79 ± 7.36 | ||
2 | FC7 | 87.57 ± 6.41 | 87.14 ± 6.46 | 88.35 ± 5.5 | |
FC6 | 86.24 ± 7.19 | 85.6 ± 7.26 | 87.21 ± 5.9 | ||
LBP | 60.82 ± 6.15 | 59.22 ± 6.26 | 61.64 ± 5.99 | ||
FERET | 1 | FC7 | 98.65 ± 0.13 | 98.63 ± 0.13 | 98.83 ± 0.08 |
FC6 | 98.83 ± 0.14 | 98.87 ± 0.12 | 99.03 ± 0.13 | ||
LBP | 8.41 ± 6.32 | 7.8 ± 5.88 | 8.62 ± 6.24 | ||
2 | FC7 | 98.96 ± 0.27 | 98.97 ± 0.29 | 98.99 ± 0.3 | |
FC6 | 99.05 ± 0.31 | 99.1 ± 0.25 | 99.13 ± 0.26 | ||
LBP | 15.67 ± 7.26 | 14.26 ± 6.65 | 16.04 ± 6.76 |
Dataset | Method | Accuracy (Mean ± STD) | |
---|---|---|---|
FC7 | FC6 | ||
PF01 1 labeled sample | SMGI | 80.33 ± 13.01 | 78.12 ± 15.87 |
MLGC | 80.01 ± 12.84 | 77.83 ± 15.69 | |
DGFLP | 80.54 ± 13.3 | 78.14 ± 15.72 | |
MDLP | 76.29 ± 17.07 | 74.71 ± 19.12 | |
Proposed method | 92.42 ± 2.86 | 93.99 ± 0.85 | |
PF01 2 labeled samples | SMGI | 88.12 ± 2.4 | 87.31 ± 3.35 |
MLGC | 87.79 ± 2.39 | 87.07 ± 3.39 | |
DGFLP | 88.33 ± 2.72 | 87.4 ± 3.59 | |
MDLP | 85.55 ± 1.82 | 85.42 ± 2.81 | |
Proposed method | 94.36 ± 1.19 | 94.75 ± 0.98 | |
Extended_Yale 1 labeled sample | SMGI | 37.62 ± 19.08 | 39.28 ± 18.94 |
MLGC | 37.11 ± 17.93 | 39.56 ± 17.98 | |
DGFLP | 37.93 ± 19.14 | 39.8 ± 19.21 | |
MDLP | 29.21 ± 19.55 | 31.24 ± 20.2 | |
Proposed method | 43.5 ± 19.34 | 50.38 ± 19.27 | |
Extended_Yale 2 labeled samples | SMGI | 48.87 ± 18.32 | 51.48 ± 18.64 |
MLGC | 47.72 ± 17.68 | 50.87 ± 18.12 | |
DGFLP | 49.57 ± 18.61 | 51.96 ± 19.02 | |
MDLP | 42.6 ± 18.56 | 45.57 ± 19.01 | |
Proposed method | 55.35 ± 21.68 | 58.68 ± 21.77 | |
PIE 1 labeled sample | SMGI | 67.71 ± 9.07 | 63.03 ± 12.48 |
MLGC | 66.46 ± 8.72 | 62.12 ± 12.62 | |
DGFLP | 68.96 ± 9.17 | 63.59 ± 12.22 | |
MDLP | 63.01 ± 10.54 | 60.04 ± 12.83 | |
Proposed method | 79.04 ± 8.21 | 79.77 ± 8.81 | |
PIE 2 labeled samples | SMGI | 77.65 ± 6.26 | 74.57 ± 7 |
MLGC | 76.16 ± 6.24 | 73.47 ± 6.95 | |
DGFLP | 79.06 ± 6.65 | 75.54 ± 7.46 | |
MDLP | 73.39 ± 6.71 | 70.11 ± 7.95 | |
Proposed method | 88.35 ± 5.5 | 87.21 ± 5.9 | |
FERET 1 labeled sample | SMGI | 98.38 ± 0.25 | 98.56 ± 0.24 |
MLGC | 98.25 ± 0.3 | 98.52 ± 0.31 | |
DGFLP | 98.43 ± 0.13 | 98.55 ± 0.13 | |
MDLP | 96.32 ± 0.72 | 97.12 ± 0.4 | |
Proposed method | 98.83 ± 0.08 | 99.03 ± 0.13 | |
FERET 2 labeled samples | SMGI | 98.71 ± 0.29 | 98.9 ± 0.32 |
MLGC | 98.49 ± 0.39 | 98.82 ± 0.31 | |
DGFLP | 98.65 ± 0.43 | 98.8 ± 0.37 | |
MDLP | 97.01 ± 0.49 | 97.5 ± 0.86 | |
Proposed method | 98.99 ± 0.3 | 99.13 ± 0.26 |
Accuracy (Mean ± STD) | |||||
---|---|---|---|---|---|
SMGI | MLGC | DGFLP | MDLP | Proposed Method | |
PF01 | 47.66 ± 10.94 | 46.55 ± 11.37 | 47.82 ± 11.1 | 17.47 ± 11.25 | 56.19 ± 8.97 |
1 labeled sample | |||||
PF01 | 56.77 ± 7.16 | 55.83 ± 7.82 | 56.9 ± 7.23 | 13.7 ± 10.58 | 65.47 ± 5.86 |
2 labeled samples | |||||
Extended_Yale | 73.48 ± 10.52 | 58.29 ± 11 | 80.77 ± 9.98 | 12.34 ± 20.31 | 94.25 ± 1.52 |
1 labeled sample | |||||
Extended_Yale | 80.05 ± 4.79 | 65.18 ± 6.87 | 86.73 ± 5.21 | 7.01 ± 11.61 | 96.73 ± 1.93 |
2 labeled samples | |||||
PIE | 36 ± 5.9 | 34 ± 5.51 | 36.09 ± 5.58 | 16.28 ± 5.12 | 46.79 ± 7.36 |
1 labeled sample | |||||
PIE | 49.84 ± 7.85 | 48.06 ± 7.72 | 50.65 ± 7.63 | 30.4 ± 9.86 | 61.64 ± 5.99 |
2 labeled samples |
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Bahrami, S.; Bosaghzadeh, A.; Dornaika, F. Multi Similarity Metric Fusion in Graph-Based Semi-Supervised Learning. Computation 2019, 7, 15. https://doi.org/10.3390/computation7010015
Bahrami S, Bosaghzadeh A, Dornaika F. Multi Similarity Metric Fusion in Graph-Based Semi-Supervised Learning. Computation. 2019; 7(1):15. https://doi.org/10.3390/computation7010015
Chicago/Turabian StyleBahrami, Saeedeh, Alireza Bosaghzadeh, and Fadi Dornaika. 2019. "Multi Similarity Metric Fusion in Graph-Based Semi-Supervised Learning" Computation 7, no. 1: 15. https://doi.org/10.3390/computation7010015
APA StyleBahrami, S., Bosaghzadeh, A., & Dornaika, F. (2019). Multi Similarity Metric Fusion in Graph-Based Semi-Supervised Learning. Computation, 7(1), 15. https://doi.org/10.3390/computation7010015