1. Introduction

2. Literature Review

3. Methodology

3.1. Proposed Solution

The basic idea underlying the proposed approach is explained below. We map the extracted features to a distributed vector (hence the encoding phase) and it is used to classify point cloud classes. In this section, after a brief overview of the notation and conventions we used, the various components of the network we tested will be described in detail. The proposed model is shown in Figure 1.

We used uppercase letters like W and U to represent matrices, lowercase letters like b and x to represent vectors and x = [x^<1>, x^<2>, . . . , x^<n>] to represent a vector of the input component. The index i represents the i-the component of this input component. We will indicate the set of parameters of our model with the capital Θ.

Input layer: Each record of feature is displayed as a vector x = [x^<1>, x^<2>, . . . , x^<n>]. Where the i-the index of this vector represents the i-the property of this input compo- nent. We normalized the input because of the varying numerical scale of the input components. The encoding layer: A single distributed vector must record the mean- ing of the input. By having an input component s containing the h attribute, the result of the encoding phase output can be expressed as enc(s) = h^<k>, where h^<k>R^j and the value of j is a hyperparameter. We used a recurrent layer to encode the input layer. In this layer, the amount activated in the hidden layer depends on the current input value and the output value in the previous step. In general, we will have:

h<k> = g(r<k>, h<k−1>, θenc)

(1)

Where g is the recurrent cell, r^<k> the current input feature, h<k−1> the output of the hidden layer at time k, and h^<k−1> is the output of the hidden layer at time k − 1 and enc are the learnable parameters in the learning phase. Accordingly, the encoding phase is as follows:

$$enc\left(S\right)=h<k>=g(r<k>,h<k-1>,{\mathsf{\theta }}_{enc})$$

(2)

enc(S ) requires recurrent layers to produce. An overview of the proposed return layers is shown in Figure 2.

In fact, the proposed method is a four-layer structure. These four layers at a glance are:

• Input layer: In this layer, each of the input features that are related to a classifi- cation are given to the GRU inputs.
• GRU layer: The inputs of the GRU layer are vectors derived from the input layer.
• LSTM layer: The inputs of the LSTM layer are vectors derived from the GRU layer.
• Output layer: The output of the LSTM network is initially flattened.

Here are the details of each of these steps:

GRU layer: After the preprocessing operation is performed on the research data set, the data is sent to the GRU layer in the form of a normalized window. In this step, the number of GRU layer blocks was equal to the number of features. Figure 4 shows how this process works. In Figure 3, the first layer is the input layer and features and

the second layer is the GRU layer. This figure shows the sending of samples to the GRU layer. The inputs of the GRU layer are vectors obtained through sliding windows

and the output is calculated through the following equations.

(3)

Where $z_t$is update gate, rt is rest gate, $h_{\dot{t}}^{\mathrm{j}}$ is candidate gate, and $h_t$ is output activation. WZ, WR, $W_h$, UZ, UR, UN are learnable matrixes, bn, $b_s$, $b_r$are learnable biases, σ is sigmoid activation function, and an element-wise multi-plication.

LSTM layer: The next step in the proposed method is to send the output of the GRU layer as input to the LSTM layer. Figure 4 shows how this process works.

Figure 4. An overview of LSTM.

Figure 4. An overview of LSTM.

The LSTM input in step T is the vector X ∈ RE. The hidden vector sequence is in LSTM, is calculated by the following equations:

(4)

Where i the input gate, o the output gate, f the forget gate, and g the update gate, [Wi, $W_f$ , $W_g$, Wo, bi, bf , $b_g$, $b_o$] is the set of parameters to be learned. q<k> is updated through the following relationship:

$$q^{<k>}=f^{<k>}ʘq^{<k-1>}+i^{<k>}ʘg^{<k>}$$

(5)

where the $ʘ$ symbol represents the element-wise product between two vectors.

Finally, the activation of the cell is accomplished through the following relationship:

$$h^{<k>}=o^{<k>}ʘtanh\left(q^{<k>}\right)$$

(6)

To determine the class of each point, it is sufficient to apply a sigmoid to the encoding phase output as follows:

$$z=sigmoid\left(W_{s}E+b_s\right)x$$

(7)

4. Result and Discussion

4.1. Baseline Models

• Gradient Boosting Classifier: This method is used to develop classification and regression models to optimize the model learning process, which is primarily non-linear and is more commonly known as decision or regression trees. Re- gression and classification trees, individually, are poor models, but when con- sidered as a set, their accuracy is greatly improved. Therefore, the sets are built gradually and incrementally so that each set corrects the error of the previous set mathematically in the form of the following equation [23]:

Figure 5. Sliding window process.

Figure 5. Sliding window process.

$${\mathrm{f}}_{\mathrm{k}}\left(x\right)={\sum }_{m=1}^k{\mathsf{\gamma }}_{\mathrm{k}}{\mathrm{h}}_{\mathrm{m}}\left(x\right)$$

(9)

2.

Support Vector Machine(SVM):The purpose of this classifier is to make a hy- pothesis or train a model that predicts the class labels of unknown data or valida- tion data samples that consist only of features. This model tries to find the largest margin between the data by creating a hyperplane. SVM kernels are generally used to map non-linear separable data into a higher-dimensional feature space sample consisting only of features[24]:

(10)

Where K is the kernel, this kernel in our training data model is RBF, which is defined as follows:

(11)

3.

XGBoost : XGBoost [25] is widely used by data scientists to achieve advanced results in many machine learning challenges. The main idea of this algorithm is to present a new algorithm with dispersion awareness for scattered data, and a quantitative scheme for approximate tree learning. XGBoost has a very high predictive power, which makes it the best option for accuracy in various events because it can be used in both linear and tree models. This algorithm is approxi- mately 10 times faster than existing gradient upgrade algorithms. This algorithm includes various objective functions, regression, classification and ranking. XG- Boost works as follows: If, for example, we have a DS dataset that has m attributes and n instances of DS = (hi, <!-- MathType@Translator@5@5@MathML2 (no namespace).tdl@MathML 2.0 (no namespace)@ --><math><mrow><msub><mrow><mtext>y</mtext></mrow><mrow><mtext>i&#x0020;</mtext></mrow></msub></mrow></math><!-- MathType@End@5@5@ -->) : i = 1, ..., n, hi ∈ Rm, y ∈ R. pred The yi predicted output is a group tree model produced by following equations[26]:

(12)

Where K represents the number of trees. ${\mathrm{f}}_{\mathrm{k}}$ represents (k-th tree). This model need to find the best set of functions by minimizing the loss and regularization objective according to following equation:

(13)

Where l the loss function and Ω is a measure of the complexity of the model and can help prevent the model from over-fitting. This criterion is obtained using the following equation:

(14)

where T represents the number of leaves and w is the weight of each leaf in the decision tree. In decision trees, to minimize the objective function, function amplification is used in the model training process, which is used by adding a new function f as a continuation of the model training. Therefore, in iteration t, a new function is added as follows:

$$\iota \left(\mathrm{t}\right)={\sum }_{i=1}^{n}l\left(y^i,y_{Pred}^{i}t-1+{\mathrm{f}}_{\mathrm{t}}\left({\mathrm{h}}_{\mathrm{i}}\right)\right)a^{n-k}+\mathrm{\Omega }\left({\mathrm{f}}_{\mathrm{t}}\right)$$

(15)

(16)

(17)

(18)

4.

Random forests(RF): RF consist of a set of decision trees(DT)[27]. Mathemat- ically, let Cˆb(x) be the class prediction of the bth tree; the class obtained from the random forest Cˆr f (x) is defined as follows:

(19)

5.

Decision tree(DT):DT are powerful and popular tools used for both classifi- cation and prediction tasks. A DT represents rules that can be understood by humans and used in knowledge systems such as databases. These classification systems are in the form of tree structures. One of the most important questions that arise in decision tree-based models is how to choose the best split. The data set used is assumed to be a sample representation of real data, in which case reducing the error on the training data set can reduce the error on the test data. For this purpose, an attribute should be selected for the split that causes the sep- aration of training samples of each class as much as possible, in other words, it causes the child nodes with less impurity. The following three different criteria can be used for this purpose[28,29]:

• Gini
• Entropy

Table 1. hyperparameters for different approaches.

Table 1. hyperparameters for different approaches.

Model	Hyper parameters
Gradient Boosting Classifier	n estimators=3000, learning rate=0.05, max depth=4, subsample=1.0, criterion=’friedman mse’, min samples split=2, min samples leaf=1
XGB Classifier	learning rate=0.1, n estimators=200, nthread=8, max depth=5, subsample=0.9, colsample bytree=0.9
SVM	C=1.0, kernel=’rbf’, degree=3, gamma=’scale’, coef0=0.0, shrinking=True, tol=0.0001
Random Forest	n estimators=100
Decision Tree	n estimators=100
LSTM	LSTM Block=100, Dropout=0.5, layers(LSTM(100),Dropout(0.5),Dense(100),Dense(8))
GRU	GRU Block=100, layers(GRU(200),Dense(100),Dense(8))
GRU+LSTM	GRU Block=100, LSTM Block=100, layers(GRU(100), LSTM(100), Dense(100) ,Dense(8))
Decision Tree		0.9489	0.9535	0.9524	0.9529

Model	Accuracy	Precision	Recall	F1-Score
Gradient Boosting Classifier	0.8775	0.8627	0.9207	0.8904
SVM	0.8823	0.9212	0.9178	0.9194
XGB Classifier	0.9183	0.9234	0.9118	0.9175
Random Forest	0.9345	0.9347	0.9336	0.9341
Decision Tree	0.9489	0.9535	0.9524	0.9529

Miss classification error

The following Table 4.1 are the hyperparameters of these models.

Table 2 shows the results of traditional machine learning approaches on the target data set. These approaches need to extract features manually. The Gradient Boosting Classifier approach in these data reached Accuracy=0.8775, Precision=0.8627, Re- call=0.9207, and F1-Score=0.8904. The SVM model obtained better results than GB. This model was able to achieve Accuracy=0.8823. The superiority of this model in other metrics could also be considered, and it achieved Precision=0.92, Recall=0.9178, and F1=0.9194. XBG Classifier obtained higher accuracy than the two examined ap- proaches, but in terms of F1 and Recall metrics, it obtained weaker results than SVM. This approach achieved Precision=0.9234, Recall=0.9118, and f1-score=0.9175. The Random Forest and Decision Tree approaches achieved the best results among them. These two approaches were able to reach a high accuracy of 0.93%. The Random Forest approach achieved Accuracy=0.9345, Precision=0.9347, Recall=0.9336, and F1=0.9341, respectively, and the Decision Tree approach also achieved Accuracy=0.9489, Precision=0.9535, Recall=0.9524, and F1-score=0.9529. acquired.

4.2. Proposed Models

Table 2 shows the results of the proposed approach on the data set. These three approaches were compared in four criteria of evaluation of Accuracy, Precision, Recall and F1. All approaches have achieved a high accuracy of 0.99%. The GRU approach achieved an accuracy of 0.9989%, which is lower than the other two approaches. The LSTM approach also achieves an accuracy of 0.9990. Which was less hybrid than the proposed approach and better than the GRU. The difference between these approaches in the f1 criterion seems much better. The proposed approach has been able to achieve f1 = 0.9452%. All of these algorithms were implemented in 10 epochs and 10 blocks, 3000 batch size, and 10 fully connected layer size were used for each approach. In fact, it was tried to consider equal conditions for each of the algorithms.

Diagrams of different approaches to different performances are given in Figure 8. According to the accuracy chart, it can be concluded that all three models do not have overfitting. On the other hand, according to the error diagram and their logarithmic shape, it can be concluded that underfitting did not occur in all three models.

The remarkable thing about deep learning models is their parameter space. This space is continuous, which requires the correct selection of values. Two critical pa- rameters in these networks are batch size and learning rate: Batch Size: Batch size determines the number of samples that a neural network uses in one session to train. The selection of categories has a balance between processing power and model learn- ing speed. Learning rate: The learning rate shows the speed of convergence of an algorithm in deep learning. Incorrect selection of this value can trap the model in local minima.

Figure 6. Accuracy, loss, precision,recall, and f1 of different approach.

Figure 6. Accuracy, loss, precision,recall, and f1 of different approach.

Figure 7. Accuracy, loss, precision,recall, and f1 of different approach.

Figure 7. Accuracy, loss, precision,recall, and f1 of different approach.

Figure 8. Accuracy, loss, precision,recall, and f1 of different approach.

Figure 8. Accuracy, loss, precision,recall, and f1 of different approach.

Figure 3 and Figure 4 show the effect of choosing different categories and dropouts. The values [8,16,32,64,128,296,512,1024] were considered for the batch size, and [0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9] for the dropout size. The best results for models with high batch sizes and the worst results in Dropout are obtained for models with low rates.

5. Conclusions

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