1. Introduction

2. Background and Context: Sentiment Analysis

3. Related Works

4. Proposed Model: CNN - LSTM and Doc2vec for Document-Level Sentiment Analysis

4.3. Convolution Layer

In Canadian maritime case law sentiment analysis, the Conv1D layer is crucial in CNN+LSTM models. Renowned for extracting intricate sentiment patterns from complex legal texts by identifying local textual patterns and navigating the length and intricacy of documents. (see Figure 5). By spotlighting these linguistic nuances, conv1D filters enhance the model’s capacity to distinguish between positive and negative sentiments [29].

"LeNet" and "AlexNet," two prominent CNNs, share linear neuron model principles. CNNs, unlike traditional MLPs, incorporate weight sharing and restricted connection in convolutional layers.

However, integrating Conv1D with LSTM layers proves a powerful tool for discerning emotions in complex legal documents. Conv1D’s localized receptive model captures particular segments and global feelings, aided by max-pooling layers to preserve excessive feature loss. This approach benefits Canadian marine case law, providing a more accessible understanding of rulings and accommodating diverse perspectives.

The 1D forward propagation (1D-FP) expressions in each CNN layer are as follows:

$$x_k^l=b_k^l\sum _{i=1}^{N_{l-1}}conv1D(w_{ik}^{l-1},s_i^{l-1})$$

The input is denoted by the symbol $x_k^l$, where$b_k^l$ is the bias of the k th neuron at layer l, $s_i^{l-1}$ is the output of the i th neuron at layer l-1, and $w_{ik}^{l-1}$ is the kernel from the i th neuron at layer l-1 to the k th neuron at layer l.

$$y_k^l={f(x}_k^l)\mathrm{and}{s}_k^l=y_k^l\downarrow ss$$

With l = 1 as input and l as output, the back-propagation procedure begins at the MLP-layer. There are NL distinct types of data in the repository. In the output layer, we represent the mean-squared error (MSE) between an input vector p and its target and output vectors, t p and [$y_k^l$, yNL L]:

$$E_p=MSE\left(t^p,{\left[y_l^L,\dots ,y_{N_L}^L\right]}^{\prime }\right)=\sum _{i=1}^{N_L}(y_i^L-t_i^p{)}^2$$

$E_p$'s derivative by each network parameter may be calculated using the delta error, k l = E xk l. To be more precise, the chain rule of derivatives may be used to update not just the bias of the current neuron but also the weights of all of the neurons in the layer above.

Figure 6. CNNs back-propagation and forward propagation.

Figure 6. CNNs back-propagation and forward propagation.

CNNs with several layers use both back-propagation and forward propagation.

Through forward and reverse propagation, the last hidden CNN layer is linked to the first hidden MLP layer (see Figure 7)

1)

Initialize weights and biases (e.g., randomly, ~U(-0.1, 0.1)) of the network.

2)

For each BP iteration DO:

a.

For each PCG beat in the dataset, DO:

• FP: A layer's neuron outputs may be found by forward propagation from the input layer to the output layer.

$$sil,\forall i\in [1,Nl],and\forall l\in [1,L].$$

BP: Compute delta error at the output layer and back-propagate it to first hidden layer to compute the delta errors. $∆kl,\forall k\in [1,Nl],and\forall l\in [1,L].$

PP: Post-process to compute the weight and bias.

• Update: Update the weights and biases by the (accumulation of) sensitivities scaled with the learning factor.

5. Experimental Results

5.3. Comparison

This section compares CNN, LSTM, BiLSTM, and CNN-LSTM to the CNN-BiLSTM model.

This study examines the sentiment analysis of Canadian maritime case law using two machine learning models: deep learning (CNN+LSTM) and more traditional methods (Logistic Regression, Multinomial Naive Bayes, Linear Support Vector Machine). The study's success is credited with employing CNN and LSTM models to collect sentiment information from judicial documents.

5.3.1. CNN Model

The ability of CNN models to extract local patterns and features from text input makes them particularly well-suited to tasks that require recognizing nearby signals or characteristics. They can spot terms, phrases, or clauses in legal papers that convey emotion. CNNs provide computational efficiency during training because of their ability to learn local patterns quickly through utilizing shared weights across several input areas. The training time is drastically reduced, making it particularly suitable for big legal text datasets. In this case, CNNs are powerful feature extractors that can glean important information from texts, including patterns, structures, or even individual words. The local environment brief pieces of text are quickly captured by them, and they excel at identifying patterns within such sections. The effectiveness of a CNN model in detecting emotions in Canadian maritime case law papers was demonstrated and found by its 98% accuracy rate in the tests [34].

5.3.2. LSTM Models

Long short-term memory (LSTM) models excel in understanding the context and sequence of words in text data, making them excellent for jobs requiring such an understanding. A thorough comprehension of the complex textual environment is essential in legal sentiment analysis. LSTMs are well-suited to the level of detail needed to comprehend the nuanced sentiment patterns and intricate interconnections common in legal writings. LSTM models are more complex and have a more significant number of parameters than CNN models. However, they still achieve high accuracy rates, which reflects how well they read sentiment dynamics in Canadian maritime case law. LSTM models are more complex and have a more significant number of parameters than CNNs. However, they still achieve high accuracy rates, which reflects how well they read sentiment dynamics in Canadian maritime case law.

5.3.3. CNN-LSTM Model

The study assesses the efficacy of CNN and LSTM models over 50 training epochs using visual representations of loss and accuracy measurements. While the accuracy graph illustrates how well the model can classify data, the loss graph shows how well it can reduce inaccurate predictions. In addition, the loss graph reflects the model's skill in minimizing prediction mistakes, whereas the accuracy graph depicts its skill in accurately incorporating labels into opinions. By making it more straightforward to visualize how the model evolved during training to integrate documents from Canada's marine case law, the SE visuals add to the broader discussion on sentiment analysis in the law [35].

Each CNN+LSTM model displays loss and accuracy graphs across 50 iterations during training.

In a groundbreaking study of Canada's maritime sector, Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM) models were employed to analyze case law and identify patterns of emotion. The impressive successes in emotion categorization, as depicted in Table 3, underscore the complexity of emotion in this intricate area of law. This research also showcases the effectiveness of advanced machine learning in navigating the challenging landscape of maritime law, where understanding and addressing emotions add an additional layer of complexity for legal professionals.

An impressive 98.01% test accuracy rate was achieved by CNN and LSTM Model 1 (see Figure 10), showcasing its dominance in sentiment categorization, and understanding of the intricacies of Canadian maritime case law texts. On the other hand, Model 2 (see Figure 11), a descendant of Model 1, highlighted the robustness of the CNN+LSTM architecture with a test accuracy of 97.94%, proving its efficacy in extracting sentiment information from dense legal texts.

Similarly, Model 3 (see Figure 12) achieved a test accuracy rate of 98.05%, and the third model earned a test accuracy rate of 98.05%, demonstrating the approach's resilience in predicting sentiment dynamics within Canadian maritime case law despite the continuously high accuracy rates of CNN and LSTM models.

This research illustrates the effectiveness of CNN+LSTM models in analyzing legal sentiment analysis. It demonstrates how these models can more accurately detect sentiment patterns in Canadian maritime case law papers and successfully grasp the nuances of legal language. Legal analytics, policymaking, and the creation of AI-powered legal tools all stand to benefit significantly from this breakthrough [36].

Table 3. Results obtained for each deep learning model.

Table 3. Results obtained for each deep learning model.

Model	Test Accuracy
CNN+LSTM model 1	98.01%
CNN+LSTM model 2	97.94%
CNN+LSTM model 3	98.05%

Figure 13. Model performance comparison for all models used.

Figure 13. Model performance comparison for all models used.

Several machine learning algorithms were used to study Canadian maritime case law sentiment. With an average accuracy of 0.9805, CNN+LSTM models exhibited excellent precision in interpreting the nuances of legal documents. Logistic regression, multinomial naive Bayes, and linear support vector machine (SVM) are classic models that have significantly contributed to our knowledge of sentiment analysis by emphasizing the trade-offs between complexity, interpretability, and performance.

Multinomial Nave Bayes is practical with text data, whereas Logistic Regression sheds light on the effect of model complexity. In linear SVM, the emphasis is on parameterization and dataset dimensionality. This additional data will help us select more suitable policymaking and legal analytics models. With this new information, we can better choose appropriate models for legal analytics and policy development [37].

6. Conclusions

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