Deep Broad Learning for Emotion Classification in Textual Conversations

After the utterance-level and speaker-level encoding are obtained in Sections 3.3 and 3.4, respectively, BL is adopted to calculate the weight of each emotion label and to obtain the emotion label prediction in each utterance.

Since BL is composed of feature node, enhancement node, and an output layer, the feature embeddings are first linearly mapped into $n$ groups of feature nodes, and then feature nodes are nonlinearly mapped into $m$ groups of enhancement nodes. Finally, the feature nodes and enhancement nodes are input into the output layer to obtain the probability distribution of emotions. During the training process of BL, the weights of feature nodes and enhancement nodes are generated randomly and fixed, and the weights of the output layer are optimized by the ridge regression method.

However, in DBL, the deep features of utterances are extracted through the CNN and Bi-LSTM, which need not be linearly transformed into features of BL. Thus, in BL, they are directly treated as the feature nodes, which are nonlinearly transformed into the enhancement nodes. Finally, the feature nodes and enhancement nodes are concatenated to input into the output layer for calculating the weight of each label.

Thus, the utterance-level features $C_u$ and speaker-level features $C_s$ in a conversation are concatenated and nonlinearly mapped into $m$ groups of enhancement nodes. The $j$ -th group of enhancement nodes $E_j$ is represented as follows:

(11) $$E_j=\xi ([C_u,C_s]W_{ej}+{\beta }_{ej})\in {𝐑}^{N\times t},j=1,2,\mathrm{\dots },m$$

where $t$ denotes the number of enhancement nodes of each group, $W_{ej}$ and ${\beta }_{ej}$ are randomly generated, which denote the weight matrix and bias matrix, respectively, and $\xi$ denotes a nonlinear activate function.

We assume that $E=[E_1,E_2,\mathrm{\dots },E_m]$ as $m$ groups of enhancement nods. Thus, the output $Y$ can be represented as follows:

(12) $$\begin{array}{c}\hfill \begin{array}{cc}\hfill Y& =[C_u,C_s,E]W_{\text{BL}}=A\times W_{\text{BL}}\hfill \end{array}\hfill \end{array}$$

where $W_{\text{BL}}$ denotes the output weight of BL, and $A$ denotes the actual input of BL.

To shorten the calculation time and to prevent over-fitting, the ridge regression is adopted as an objective function in the general BL, which is represented as follows:

(13) $$\underset{W_{\text{BL}}}{\arg \min }{\Vert A\times W_{\text{BL}}-Y\Vert }_2^2+\lambda {\Vert W_{\text{BL}}\Vert }_2^2$$

where $\lambda$ denotes the regularization parameters.

Finally, according to the regularized least square method, $W_{\text{BL}}$ can be represented as follows:

(14) $$W_{\text{BL}}={(\lambda I+A{A}^{\text{T}})}^{-1}{A}^{\text{T}}\hat{Y}$$

where I denotes an identity matrix and $\hat{Y}$ denotes the ground truth label of each utterance.

The specific process is shown in Algorithm 1.