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SCIENCE CHINA Information Sciences, Volume 61, Issue 11: 112209(2018) https://doi.org/10.1007/s11432-017-9421-3

Discriminative graph regularized broad learning system for image recognition

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  • ReceivedDec 12, 2017
  • AcceptedMar 30, 2018
  • PublishedOct 17, 2018

Abstract

Broad learning system (BLS) has been proposed as an alternative method of deep learning. The architecture of BLS is that the input is randomly mapped into series of feature spaces which form the feature nodes, and the output of the feature nodes are expanded broadly to form the enhancement nodes, and then the output weights of the network can be determined analytically. The most advantage of BLS is that it can be learned incrementally without a retraining process when there comes new input data or neural nodes. It has been proven that BLS can overcome the inadequacies caused by training a large number of parameters in gradient-based deep learning algorithms. In this paper, a novel variant graph regularized broad learning system (GBLS) is proposed. Taking account of the locally invariant property of data, which means the similar images may share similar properties, the manifold learning is incorporated into the objective function of the standard BLS. In GBLS, the output weights are constrained to learn more discriminative information, and the classification ability can be further enhanced. Several experiments are carried out to verify that our proposed GBLS model can outperform the standard BLS. What is more, the GBLS also performs better compared with other state-of-the-art image recognition methods in several image databases.


Acknowledgment

This work was supported in part by National Natural Science Foundation of China (Grant No. 61572540), Macau Science and Technology Development Fund (FDCT) (Grant Nos. 019/2015/A, 024/2015/AMJ, 079/2017/A2), and the University Macau MYR Grants.


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  • Figure 1

    The structure of BLS. First, the input features are randomly mapped into a series of features spaces. Second, the random features are transformed to the enhancement nodes. At the output layer, all the features are connected together to link the label layer.

  • Figure 2

    Sample from three face databases. Samples of three subjects in (a) the ORL databases, (b) the ExYaB database, and (c) the UMIST database.

  • Figure 3

    (Color online) Sample images from the four challenging visual database. The first row shows ten kinds of action in Standford $40$ Actions database; the second row shows various kinds of birds in CUB200-2011 database; the third row shows ten kinds of flowers in Flower 102 database; the forth row shows ten kinds of objects in Caltech 256 database.

  • Figure 4

    (Color online) Effects of parameters combinations of $(\lambda_1,\lambda_2)$ in IGBLS on UMIST. (a) ${\rm~Tn}=5$, (b) ${\rm~Tn}=10$, (c) ${\rm~Tn}=15$.

  • Figure 5

    (Color online) Effects of parameters combinations of $(\lambda_1,\lambda_2)$ in IPGBLS on UMIST. (a) ${\rm~Tn}=5$, (b) ${\rm~Tn}=10$, (c) ${\rm~Tn}=15$.

  • Figure 6

    (Color online) Effects of parameters combinations of $(k1,k2)$ in IPGBLS on UMIST. (a) ${\rm~Tn}=5$, (b) ${\rm~Tn}=10$, (c) ${\rm~Tn}=15$.

  •   

    Algorithm 1 Discriminative GBLS models

    indent 4.0em

    Random ${\boldsymbol~W}_{e_i}$, $\pmb{\beta}_{e_i}$, $i=1,2,\ldots,N_w$;

    Calculate ${\boldsymbol~Z}_i=\phi(\boldsymbol{XW}_{e_i}+\pmb{\beta}_{e_i})$, $i=1,2,\ldots,N_w$;

    Set the feature mapping group ${\boldsymbol~Z}^n=[{\boldsymbol~Z}_1,{\boldsymbol~Z}_2,\ldots,{\boldsymbol~Z}_n]$;

    Step 2:

    indent 4.0em

    Random ${\boldsymbol~W}_h$, $\pmb{\beta}_h$;

    Calculate ${\boldsymbol~H}^m=\xi({\boldsymbol~Z}^n{\boldsymbol~W}_h+\pmb{\beta}_h)$;

    Step 3:

    indent 4.0em

    Set ${\boldsymbol~A}=[{\boldsymbol~Z}^n,{\boldsymbol~H}^m]$;

    Construct the adjacent matrix ${\boldsymbol~V}$ by 7 and 12; then calculate the graph regulation term by 8 and 16;

    Calculate the output weight matrix ${\boldsymbol~W}$ by 11 and 18.

    Require:training set $\{\boldsymbol{X,Y}\}$, the feature mapping function $\phi(\cdot)$, the activation function $\xi(\cdot)$, the number of feature mapping groups $N_w$, feature nodes $N_f$, enhancement nodes $N_e$, regularization parameter $(\lambda_1,\lambda_2)$ and NNs $(k1,~k2)$;

    Output:Output weight ${\boldsymbol~W}$;

    Step 1:

  •   
    2*Number BLS IGBLS IPGBLS
    $N_w$ $N_f$ $N_e$ $N_w$ $N_f$ $N_e$ $N_w$ $N_f$ $N_e$
    3*ORL ${\rm~Tn}~=~5$ $20$ $25$ $500$ $15$ $20$ $380$ $20$ $20$ $400$
    ${\rm~Tn}~=~6$ $10$ $26$ $460$ $12$ $16$ $400$ $20$ $20$ $640$
    ${\rm~Tn}~=~7$ $20$ $20$ $400$ $20$ $20$ $240$ $22$ $20$ $500$
    3*ExYaB ${\rm~Tn}~=~10$ $30$ $60$ $3000$ $20$ $50$ $2000$ $40$ $50$ $1300$
    ${\rm~Tn}~=~20$ $30$ $60$ $4000$ $20$ $50$ $3000$ $30$ $35$ $3000$
    ${\rm~Tn}~=~30$ $30$ $60$ $5000$ $30$ $40$ $2000$ $34$ $40$ $2000$
    3*UMIST ${\rm~Tn}~=~5$ $10$ $9$ $400$ $11$ $9$ $900$ $11$ $9$ $900$
    ${\rm~Tn}~=~10$ $30$ $20$ $300$ $15$ $10$ $300$ $12$ $9$ $860$
    ${\rm~Tn}~=~15$ $10$ $9$ $575$ $10$ $9$ $300$ $11$ $11$ $400$
  •   
    2*Number BLS IGBLS IPGBLS
    Training (%) Testing (%) Time (s) Training (%) Testing (%) Time (s) Training (%) Testing (%) Time (s)
    3*ORL ${\rm~Tn}~=~5$ $100$ $95.00$ $0.44$ $100$ $96.11$ $0.32$ $100$ $\mathbf{97.50}$ $0.35$
    ${\rm~Tn}~=~6$ $100$ $97.50$ $0.37$ $100$ $98.11$ $0.31$ $100$ $\mathbf{98.13}$ $0.35$
    ${\rm~Tn}~=~7$ $100$ $98.33$ $0.41$ $100$ $\mathbf{99.17}$ $0.39$ $100$ $99.14$ $0.35$
    3*ExYaB ${\rm~Tn}~=~10$ $100$ $85.60$ $2.96$ $100$ $88.35$ $1.62$ $100$ $\mathbf{90.12}$ $2.25$
    ${\rm~Tn}~=~20$ $100$ $95.59$ $4.05$ $100$ $96.61$ $2.76$ $100$ $\mathbf{97.28}$ $2.87$
    ${\rm~Tn}~=~30$ $100$ $97.17$ $5.67$ $100$ $98.82$ $2.82$ $100$ $\mathbf{98.98}$ $2.96$
    3*UMIST ${\rm~Tn}~=~5$ $100$ $84.21$ $0.38$ $100$ $87.16$ $0.24$ $100$ $\mathbf{88.21}$ $0.26$
    ${\rm~Tn}~=~10$ $100$ $96.53$ $0.70$ $100$ $97.60$ $0.26$ $100$ $\mathbf{98.13}$ $0.27$
    ${\rm~Tn}~=~15$ $100$ $98.18$ $0.78$ $100$ $98.54$ $0.36$ $100$ $\mathbf{99.27}$ $0.31$
  •   
    2*Method ${\rm~Dim}=84$ ${\rm~Dim}=150$ ${\rm~Dim}=300$
    Accuracy (%) time (s) Accuracy (%) time (s) Accuracy (%) time (s)
    SVM $94.9$ $5.87$ $96.4$ $6.58$ $97.0$ $8.26$
    NN $85.8$ $3.89$ $90.0$ $4.09$ $91.6$ $4.76$
    SRC $95.5$ $180.90$ $96.8$ $205.02$ $97.9$ $261.38$
    LRC $94.5$ $4.28$ $95.1$ $4.72$ $95.9$ $6.49$
    CRC$\_$RLS $95.0$ $2.12$ $96.3$ $2.64$ $97.9$ $3.72$
    GELM $94.45$ $6.10$ $95.21$ $6.90$ $96.69$ $7.41$
    BLS $93.40$ $0.87$ $95.05$ $1.73$ $96.41$ $2.25$
    IGBLS $95.69$ $0.83$ $96.90$ $1.87$ $98.21$ $2.31$
    IPGBLS $\mathbf{96.11}$ $1.12$ $\mathbf{97.67}$ $1.91$ $\mathbf{98.36}$ $2.46$
  •   
    2*Method FFT Gabor LBP
    2*Average (%)
    Accuracy (%) time (s) Accuracy (%) time (s) Accuracy (%) time (s)
    SVM $5.8$ $9.62$ $42.4$ $9.74$ $18.5$ $10.96$ $22.3$
    SRC $33.6$ $2230$ $68.7$ $2236$ $61.6$ $2238$ $54.6$
    LRC $13.9$ $19.35$ $25.4$ $20.05$ $26.3$ $23.27$ $21.9$
    CRC$\_$RLS $14.0$ $9.11$ $25.4$ $9.22$ $26.3$ $9.44$ $21.9$
    LCCR $22.2$ $11.49$ $64.6$ $11.62$ $66.5$ $11.74$ $51.1$
    GELM $33.5$ $5.23$ $67.8$ $4.96$ $58.86$ $5.68$ $53.4$
    BLS $35.2$ $0.28$ $69.90$ $0.33$ $65.3$ $0.57$ $56.8$
    IGBLS $38.34$ $0.37$ $\mathbf{71.81}$ $0.35$ $66.44$ $0.53$ $58.86$
    IPGBLS $\mathbf{38.85}$ $0.37$ $71.32$ $0.41$ $\mathbf{66.76}$ $0.48$ $\mathbf{58.98}$
  •   
    2*Method Standford 40 Flower 102 CUB200-2011 Caltech 256
    Accuracy (%) Time (s) Accuracy (%) Time (s) Accuracy (%) Time (s) Accuracy (%) Time (s)
    SVM $79.0$ $26.97$ $90.9$ $30.67$ $75.4$ $51.63$ $80.1$ $228.52$
    Kernel SVM $79.8$ $296.01$ $92.2$ $377.24$ $76.6$ $691.84$ $81.3$ $3085$
    NSC $74.7$ $47.16$ $90.1$ $67.36$ $74.5$ $98.38$ $80.2$ $487.27$
    CRC$\_$RLS $78.2$ $25.78$ $93.0$ $30.74$ $76.2$ $49.36$ $81.1$ $234.27$
    SRC $78.7$ $2655$ $93.2$ $3228$ $76.0$ $5282$ $81.3$ $25535$
    CROC $79.1$ $56.32$ $93.1$ $74.71$ $76.2$ $109.76$ $81.7$ $490.53$
    ProCRC $80.9$ $26.82$ $94.8$ $32.48$ $78.3$ $52.27$ $83.3$ $234.69$
    GELM $78.7$ $54.63$ $90.3$ $55.11$ $76.7$ $57.75$ $81.8$ $69.89$
    BLS $81.4$ $14.32$ $95.3$ 20.26 $78.8$ $20.74$ $84.0$ $26.37$
    IGBLS $81.7$ $15.61$ $95.1$ $20.33$ $79.5$ $21.88$ $84.6$ $28.65$
    IPGBLS $\mathbf{82.3}$ $15.92$ $\mathbf{95.6}$ $21.47$ $\mathbf{80.4}$ $23.46$ $\mathbf{84.9}$ $30.42$
  •   
    2*Algorithms Recognition rate (%)
    Standford 40 Flower 102 CUB200-2011 Caltech 256
    IGBLS $81.7$ $95.1$ $79.5$ $84.6$
    IPGBLS $\mathbf{82.3}$ $\mathbf{95.6}$ $\mathbf{80.4}$ $84.9$
    DeepCAMP [36] $52.6$
    A-FCN [37] $79.7$
    CNN-SVM [38] $74.7$
    CNNaug-SVM [38] $86.8$ $66.7$
    FV-CNN [40] $61.8$
    VGG19 [34] $\mathbf{85.1}$
    CNN-S [39] $77.6$

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