Algorithms | LSR | SMR | LRR | SSC | StrSSC | RSSC | Ours | |
Accuracy | Mean | 93.57% | 94.35% | 92.46% | 94.04% | 94.08% | 96.60% | 97.00% |
Median | 92.85% | 94.07% | 92.13% | 93.60% | 93.70% | 96.10% | 96.90% |
Subspace clustering segments a collection of data from a union of several subspaces into clusters with each cluster corresponding to one subspace. The geometric information of the dataset reflects its intrinsic structure and can be utilized to assist the segmentation. In this paper, we propose side-information-induced reweighted sparse subspace clustering (SRSSC) for high-dimensional data clustering. In our method, the geometric information of the high-dimensional data points in a target space is utilized to induce subspace clustering as side-information. We solve the method by iterating the reweighted $ l_1 $-norm minimization to obtain the self-representation coefficients of the data and segment the data using the spectral clustering framework. We compare the performance of our proposed algorithm with some state-of-the-art algorithms using synthetic data and three famous real datasets. Our proposed SRSSC algorithm is the simplest but the most effective. In the experiments, the results of these clustering algorithms verify the effectiveness of our proposed algorithm.
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Table 1. Performance comparison of the different algorithms using the synthetic data
Algorithms | LSR | SMR | LRR | SSC | StrSSC | RSSC | Ours | |
Accuracy | Mean | 93.57% | 94.35% | 92.46% | 94.04% | 94.08% | 96.60% | 97.00% |
Median | 92.85% | 94.07% | 92.13% | 93.60% | 93.70% | 96.10% | 96.90% |
Table 2. The clustering errors (%) of some different algorithms using the Extended Yale B dataset
No. of subject | Algorithms | LSR | SMR | LRR | SSC | StrSSC | RSSC | Ours |
2 Subjects | Mean | 7.35 | 1.75 | 2.13 | 1.87 | 1.23 | 0.57 | 0.48 |
Median | 7.03 | 0.78 | 0.78 | 0 | 0 | 0 | 0 | |
3 Subjects | Mean | 9.92 | 3.03 | 3.49 | 3.29 | 2.84 | 1.08 | 0.78 |
Median | 10.41 | 2.08 | 2.08 | 0.52 | 0.52 | 0 | 0.52 | |
4 Subjects | Mean | 13.66 | 3.25 | 4.86 | 3.80 | 2.95 | 1.65 | 1.07 |
Median | 14.07 | 2.34 | 3.91 | 1.95 | 0.78 | 0.39 | 0.39 | |
5 Subjects | Mean | 17.56 | 3.91 | 5.92 | 4.33 | 3.31 | 2.21 | 1.40 |
Median | 17.81 | 2.50 | 4.99 | 2.50 | 1.25 | 0.62 | 0.62 | |
6 Subjects | Mean | 20.95 | 5.28 | 6.83 | 4.87 | 3.73 | 2.79 | 1.68 |
Median | 21.07 | 2.86 | 5.99 | 3.39 | 2.08 | 1.30 | 1.04 | |
7 Subjects | Mean | 24.31 | 6.38 | 7.75 | 5.40 | 4.01 | 3.43 | 2.03 |
Median | 24.10 | 3.13 | 7.14 | 4.46 | 2.68 | 1.79 | 1.34 | |
8 Subjects | Mean | 27.52 | 6.83 | 11.05 | 5.92 | 4.38 | 3.98 | 2.59 |
Median | 27.83 | 3.71 | 7.42 | 4.69 | 3.13 | 1.86 | 1.56 | |
9 Subjects | Mean | 31.01 | 7.14 | 10.32 | 6.46 | 4.56 | 4.55 | 2.84 |
Median | 31.42 | 4.51 | 7.81 | 4.77 | 3.65 | 2.43 | 1.65 | |
10 Subjects | Mean | 33.49 | 7.81 | 16.95 | 7.40 | 4.74 | 4.90 | 3.33 |
Median | 32.81 | 7.03 | 18.91 | 5.63 | 4.22 | 3.59 | 2.03 |
Table 3. The clustering errors (%) of some comparative algorithms using the COIL 20 dataset
No. of subject | Algorithms | LSR | SMR | LRR | SSC | StrSSC | RSSC | Ours |
2 Subjects | Mean | 15.05 | 13.75 | 14.86 | 8.13 | 0.76 | 1.35 | 0.43 |
Median | 13.91 | 10.42 | 13.07 | 0 | 0 | 0 | 0 | |
3 Subjects | Mean | 22.16 | 21.97 | 21.81 | 10.87 | 1.86 | 1.37 | 0.72 |
Median | 20.22 | 19.44 | 19.65 | 1.85 | 0 | 0 | 0 | |
20 Subjects | Mean(Mdian) | 25.49 | 24.72 | 24.67 | 20.07 | 15.73 | 16.32 | 7.78 |
Table 4. The clustering errors (%) of some comparative algorithms using the USPS dataset
No. of subject | Algorithms | LSR | SMR | LRR | SSC | StrSSC | RSSC | Ours |
2 Subjects | Mean | 15.49 | 15.25 | 14.76 | 11.80 | 11.48 | 10.90 | 10.80 |
Median | 13.91 | 13.42 | 13.07 | 9.00 | 8.50 | 9.50 | 7.00 | |
3 Subjects | Mean | 29.13 | 28.91 | 28.81 | 27.59 | 27.88 | 27.44 | 26.67 |
Median | 27.02 | 16.34 | 26.37 | 21.83 | 25.67 | 23.82 | 21.33 | |
10 Subjects | Mean(Median) | 46.25 | 45.97 | 45.53 | 44.89 | 44.25 | 44.03 | 43.95 |
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Illustration of a simple instance of subspace clustering
Angles of pairs of data in the databases
Convergence of SRSSC on the Extended YaleB dataset
Visualization of the similarity matrices that were obtained by the different methods
Some sample images from the Extended Yale B database
The average computation times of the different algorithms using the Yale B dataset
Some sample images from the COIL 20 database (top) and the images that belong to the same object (bottom)
Some sample images from the USPS database