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Trusted Multi-View Classification

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This repository contains the code of our ICLR'2021 paper Trusted Multi-View Classification [中文介绍] [中文讲解] and the code of our IEEE TPAMI'2022 paper Trusted Multi-View Classification with Dynamic Evidential Fusion. We will gradually improve and enhance the code. Here we provide a demo and detailed instructions for constructing trustworthy multi-view/multi-modal classification algorithm.

Quick Start

To convert your networks into a trusted multimodal classification model, it is better to refer to the following steps:

Step 1: The softmax layer of a conventional neural-network-based classifier is replaced with an activation function layer (e.g., RELU) to ensure that the network outputs non-negative values.
Step 2: Employ the proposed method to construct a trusted classifier for each modality. (1) Treat the output of the neural network as evidence $\mathbf{e}$. (2) Construct Dirichlet distribution with $\mathbf{e}$+1. (3) Calculate subjective uncertainty $u$ and belief masses for each modality.

Step 3: Use dempster’s combination rule rather than traditional fusion strategies to combine the uncertainty and belief masses from different modalities.

<details> <summary> Code of dempster’s combination rule (click the triangle to expand the code). </summary>

def DS_Combin(self, alpha):
    """
    :param alpha: All Dirichlet distribution parameters.
    :return: Combined Dirichlet distribution parameters.
    """
    def DS_Combin_two(alpha1, alpha2):
        """
        :param alpha1: Dirichlet distribution parameters of view 1
        :param alpha2: Dirichlet distribution parameters of view 2
        :return: Combined Dirichlet distribution parameters
        """
        alpha = dict()
        alpha[0], alpha[1] = alpha1, alpha2
        b, S, E, u = dict(), dict(), dict(), dict()
        for v in range(2):
            S[v] = torch.sum(alpha[v], dim=1, keepdim=True)
            E[v] = alpha[v]-1
            b[v] = E[v]/(S[v].expand(E[v].shape))
            u[v] = self.classes/S[v]

        # b^0 @ b^(0+1)
        bb = torch.bmm(b[0].view(-1, self.classes, 1), b[1].view(-1, 1, self.classes))
        # b^0 * u^1
        uv1_expand = u[1].expand(b[0].shape)
        bu = torch.mul(b[0], uv1_expand)
        # b^1 * u^0
        uv_expand = u[0].expand(b[0].shape)
        ub = torch.mul(b[1], uv_expand)
        # calculate C
        bb_sum = torch.sum(bb, dim=(1, 2), out=None)
        bb_diag = torch.diagonal(bb, dim1=-2, dim2=-1).sum(-1)
        # bb_diag1 = torch.diag(torch.mm(b[v], torch.transpose(b[v+1], 0, 1)))
        C = bb_sum - bb_diag

        # calculate b^a
        b_a = (torch.mul(b[0], b[1]) + bu + ub)/((1-C).view(-1, 1).expand(b[0].shape))
        # calculate u^a
        u_a = torch.mul(u[0], u[1])/((1-C).view(-1, 1).expand(u[0].shape))

        # calculate new S
        S_a = self.classes / u_a
        # calculate new e_k
        e_a = torch.mul(b_a, S_a.expand(b_a.shape))
        alpha_a = e_a + 1
        return alpha_a

    for v in range(len(alpha)-1):
        if v==0:
            alpha_a = DS_Combin_two(alpha[0], alpha[1])
        else:
            alpha_a = DS_Combin_two(alpha_a, alpha[v+1])
    return alpha_a

</details>

Step 4: Use a multi-task strategy and overall loss function in the paper to optimize the model.

<details> <summary> Code of overall loss function (click the triangle to expand the code). </summary>

def KL(alpha, c):
    beta = torch.ones((1, c)).cuda()
    S_alpha = torch.sum(alpha, dim=1, keepdim=True)
    S_beta = torch.sum(beta, dim=1, keepdim=True)
    lnB = torch.lgamma(S_alpha) - torch.sum(torch.lgamma(alpha), dim=1, keepdim=True)
    lnB_uni = torch.sum(torch.lgamma(beta), dim=1, keepdim=True) - torch.lgamma(S_beta)
    dg0 = torch.digamma(S_alpha)
    dg1 = torch.digamma(alpha)
    kl = torch.sum((alpha - beta) * (dg1 - dg0), dim=1, keepdim=True) + lnB + lnB_uni
    return kl

def ce_loss(p, alpha, c, global_step, annealing_step):
    S = torch.sum(alpha, dim=1, keepdim=True)
    E = alpha - 1
    label = F.one_hot(p, num_classes=c)
    A = torch.sum(label * (torch.digamma(S) - torch.digamma(alpha)), dim=1, keepdim=True)

    annealing_coef = min(1, global_step / annealing_step)

    alp = E * (1 - label) + 1
    B = annealing_coef * KL(alp, c)

    return (A + B)

</details>

This method is also suitable for other scenarios that require trusted integration, such as Ensemble Learning, Multi-View Learning.

Citation

If you find TMC helps your research, please cite our paper:

@inproceedings{
han2021trusted,
title={Trusted Multi-View Classification},
author={Zongbo Han and Changqing Zhang and Huazhu Fu and Joey Tianyi Zhou},
booktitle={International Conference on Learning Representations},
year={2021},
url={https://openreview.net/forum?id=OOsR8BzCnl5}
}
@article{han2022trusted,
  title={Trusted Multi-View Classification with Dynamic Evidential Fusion},
  author={Han, Zongbo and Zhang, Changqing and Fu, Huazhu and Zhou, Joey Tianyi},
  journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
  year={2022},
  publisher={IEEE}
}

Acknowledgement

We thank the authors of EDL. Other loss functions except for cross entropy to quantify classification uncertainty are also provided in EDL.

Questions?

Please report any bugs and I will get to them ASAP. For any additional questions, feel free to email zongbo AT tju DOT edu DOT cn.

Related works

There are many interesting works inspired by this paper and the following are related follow-up works: