Using artificial intelligence tools for level of service classifications within the smart city concept

2.1 Level of service

Level of service (LoS) in transport is a criterion that can be used to quantitatively describe the extent of traffic conditions within a traffic stream. This criterion takes into account measures such as speed, travel time, maneuverability, traffic interruption, comfort, and convenience.

Since the data used in this thesis were collected in the city of Prague, we will follow the Czech standards [6], which categorize traffic flow data into six categories of LoS. The definitions of each category are described in words as follows:

• LoS 1 – The traffic flow is free.

• LoS 2 – The traffic flow is almost continuous.

• LoS 3 – The traffic situation is stable.

• LoS 4 – The traffic situation is still stable.

• LoS 5 – The lane capacity is full.

• LoS 6 – The section is congested.

As each location may differ in conditions, such as the number of lanes in a given direction, the maximum speed limit, and traffic light control, a traffic expert must categorize each location individually. We aim to develop a system that automatically categorizes locations based on their types.

2.2 Location

For testing purposes, traffic data (speed of traffic flow and traffic flow) on Legerova Street in Prague collected during the year 2020 were used. It is a three-lane street as shown in Figure 1, with the position of the traffic sensors marked.

Figure 1

Map of the Legerova Street.

In Figure 2, the data are categorized based on the Greenshield fundamental model into six categories according to the Czech standards. Based on the experts’ evaluation, the areas, shown by colored rectangles, which represent the individual LoS are determined. Individual points in Figure 2 represent real measured data.

Figure 2

The LoS categories for Legerova Street in Prague according to traffic and speed of vehicles.

2.3 Data preparation

We checked the traffic data for possible errors. The collected traffic data includes information on time, cumulative number of vehicles passed, and average speed of vehicles per 5 minutes. All values are stored separately for three vehicle categories (cars, trucks, unrecognized). We have prepared hourly aggregated data regardless of vehicle category. We excluded incomplete records in which some data were missing and visualized the data to identify any anomalous values.

3.1 Deep neural networks (DNNs)

DNNs are used today in many scientific fields as well as in a number of applications used on a daily basis, such as voice and image recognition, assistive services, or classification.

A DNN by default consists of more than three layers including an input layer, an output layer, and several hidden layers. Each layer consists of interconnected nodes. In DNNs, each layer of nodes trains on a different set of features based on the previous layer’s output. So, the more you go into the net, the more you can advance into it, and the more complex features the nodes can recognize. These nets allow to identify complex nonlinear relationships. The major advantage that DNNs hold is the ability to deal with unstructured and unlabeled data, which is most of the world’s data [8].

Numerous use cases can be found ranging from classification, making predictions, signal processing to examples of using generative artificial intelligence (AI) models. Michalíková and Pažický [9] used AI to determine the position of a tire in the processed image for traceological purposes. In the study of Vagač et al. [10], DNN was used to extract features based on which it was possible to look for similarity between pairs of images. Povinský et al. [11] deal with the use of DNN to create a chatbot compatible with TJBot. Some papers deal with explainability [12] and error detection in neural networks [13]. Another application of DNN for prediction of molecular docking score can be found in the previous studies [14,15].

Usually, it requires significant computational resources to train a DNN model, which means access to high-performance resources including GPGPUs. Another challenge is the acquisition of data with sufficient quantity and quality for DNN training process. The drawback of the DNN is the lack of interpretability, especially those DNNs with many layers used. This can make it difficult to understand how the model is making predictions and to identify any errors or biases in the model. DNN’s strength is in the automatic feature training process, which can find even nonlinear relationships in data, as well as that they can process both structured and unstructured data of different types. With sufficient data and proper optimization, DNNs can achieve very high accuracy and robustness in predictions.

3.2 Fuzzy inference systems (FISs)

Fuzzy sets were proposed in 1965 [16]. They were designed to deal with uncertainty and to create rules in human language. Therefore, their results are easy to explain. FIS derived from fuzzy sets can capture expert knowledge and represent it in the form of IF-THEN rules. Let us give an example of such a rule for our problem:

“IF Traffic Flow is Very_Low AND Speed is High, THEN Level_Of_Service is equal to 1.”

FISs use simple operations, such as max, min, weighted average, to obtain results from the IF-THEN rules. Several applications of FISs can be found, for instance in the study by Mardani et al. [17], where the outputs of more adaptive network-based fuzzy inference systems (ANFISs) were combined and used to predict and analyze the mutual relationship between the selected variables, which affect carbon dioxide emissions. Tashayo and Alimohammadi [18] used a Hierarchical FIS to model urban air pollution.

Intuitionistic fuzzy sets, which represent an extension of fuzzy sets, are also suitable for modeling various situations and problems. Poryazov et al. [19] used two approaches to the intuitionistic fuzzy estimation of the uncertainty of compositions of traffic quality services. Intuitionistic fuzzy sets are also a suitable tool for classification, as in the study by Michalíková and Dudáš [20], where the authors present the design, implementation, and experimental evaluation of parallel algorithms for classifying tire tread pattern images based on intuitionistic fuzzy set methods that incorporate similarity measure, distance function, and selected intuitionistic fuzzy negations. In the study by Michalíková et al. [21], a fuzzy interference system of the Takagi-Sugeno type is used for the identification of wood-decaying basidiomycetous macrofungi.

In general, there are two basic approaches to creating FISs: to obtain rules analyzing large amounts of data or to use the knowledge of experts who describe in human language terms certain properties of the input variables. Often a combination of these two approaches is used. A drawback of the FISs is considered to be the difficulty of parameter tuning, which has a large impact on the result. This problem arises especially in the case of small amounts of training data, where parameter optimization using known data may not be sufficiently accurate. However, with precise information from an expert, high accuracy can be achieved even without a large amount of known data. The main advantage of the FIS is generation of human-readable and implementable rules.

3.3 High-dimensional computing (HDC)

Commonly used algorithms in machine learning are often computationally intensive and thus require significant hardware performance. On the other hand, solutions that could be applied on less powerful hardware are desirable, allowing them to be executed at the edge, e.g., embedded systems or IoT devices. High-dimensional computing (HDC) is emerging as a promising solution to this situation. The basic idea behind HDC is brain-inspired information storage and processing and is based on a very simple neural architecture [22].

The principle of HDC is to project input data onto vectors in high-dimensional space. For this, a uniform static mapping to randomly generated high-dimensional vectors (HVs) containing numbers is usually used. The dimension of the HV is usually larger than 10,000, which provides sufficient space for information representations. In addition, HVs are usually initialized randomly, so they can be assumed to be orthogonal to each other. Various embeddings can be used to represent HVs, for instance, from bipolar vectors (values + 1 , − 1 ) to complex numbers, which can be distributed in a random, level, or circular way [23].

Consequently, we can do three operations with the data embedded as HVs: addition, multiplication, and permutation of elements, each of which has a specific physical meaning.

Addition – takes two HVs as operands and performs element-wise addition on the numbers at the same positions. It is usually used to aggregate the information of two HVs from the same modality and create a superposition of them.

Multiplication – takes two HVs as operands and performs element-wise multiplication on the numbers at the same positions. It is usually used to combine information from different modalities and create new information of another modality based on these two.

Permutation – takes only one HV as an operand and performs cyclic rotation of elements over the HV. It is usually used to reflect temporal or spatial pattern of information.

Two types of HDC memory are used: item memory and associative memory. Item memory stores information about input data. Associative memory is used to represent the output model. Measuring the similarity measure of two HVs, i.e., the similarity of two pieces of information, is mostly done using Hamming distance or cosine similarity metrics. The entire setup is elementary and lends itself to fast, low-power hardware realization [24].

Several applications of HDC can be found. For example, determining the belonging of a text to a particular language based on clustering [25], speach recognition [26], human activity recognition [27,28], and anomaly detection [29]. Ni et al. [30] deal with uncertainty quantification of a predictive regression model. Many works showed that HDC is an energy-efficient, low-latency, and noise-resilient alternative to conventional machine learning tools.

The major challenge of HDC is the encoding process, which is application-specific. The appropriate encoding process has to be manually designed and evaluated. In HDC, only the associative memory is trainable, but the elements inside each class HV is not individually trainable due to their holographic representation of HVs [23]. Since the information is represented in high-dimensional vectors, the process can require significant memory, particularly when handling large data sets. Like DNNs, HDCs can also be difficult to interpret. The main advantage of the HDC is its speed and better energy efficiency, smaller model size, and acceleration on heterogeneous platforms. HDC can handle incomplete or noisy data, which is beneficial when data quality is low.

4.1 DNNs

The first approach used is based on DNNs, which are now commonly used for a number of classification tasks. Our DNN implementation is based on the Python libraries Tensorflow and Keras together with the Sklearn and Numpy libraries. Before the actual training of the neural network, all the input data are proportionally split into training, testing, and validation data in the ratio of 75, 15, and 10%, respectively. Figure 2 shows that number of points belonging to each LoS category is not evenly distributed across all categories, e.g., LoS 6 contains a small number of points. Therefore, we aim to have all LoS values reasonably represented in each data set after splitting.

The network topology is set to 8 dense layers, the number of neurons in individual layers is 20, 60, 80, 120, 100, 80, 60, and 6 in the last output layer. Each layer except the last one uses the ReLu activation function, and the dropout rate is set to 0.002. The initial weights in the neural networks were set according to the standard He uniform Keras function, with default settings.

The use of He initialization in combination with the ReLU activation function can significantly reduce the problem of vanishing and/or exploding gradients at the beginning of training. The batch normalization proposed by Ioffe and Szegedy [31] can be employed to address this problem during training. It also leads to a lower sensitivity to the initialization of the DNN weights and allows the use of larger learning rates, which significantly speeds up the learning process. Adding normalization before each hidden DNN layer makes each epoch take much longer, but this is balanced by faster convergence and fewer epochs needed to achieve the same performance.

The model was trained for a fixed number of 200 epochs total using the stochastic gradient descent optimizer, and a learning rate of 0.001 and momentum of 0.9. Other parameters were kept at their default values. The general idea of methods based on gradient descent approach is to tweak parameters iteratively to minimize a cost function. It measures the local gradient of the error function with regard to the parameter vector, and it goes in the direction of descending gradient until the gradient is equal to zero. The learning rate parameter determines the size of step in each iteration. If it is too big, optimizer may jump over the minimum. If it is too small, optimization takes too much time to find minimum.

Another problem of gradient descent method is convergence to local minimum. The stochastic gradient descent picks a random instance in the training set at every step and computes the gradients based only on that single instance. Working on a single instance at a time makes the algorithm much faster because it has very little data to manipulate at every iteration. It also makes it possible to train on huge training sets, since only one instance needs to be in memory at each iteration. This approach can help to jump out of local minima, but it also cause that it never settle at the minimum due to random selection of instance in each iteration. We can observe this behavior in Figure 4. In the later stage of the optimization, the loss as well as accuracy functions fluctuate.

Figure 4

Loss function and accuracy of DNN model.

A validation set was used to mitigate the trained model’s possible overfitting and ensure the best model selection. Figure 4 depicts evolution of the loss function and accuracy during the training process.

After training, we use the trained model to assign an output LoS value to each input record (speed and traffic flow). The model outputs six probability values, one for each LoS category. To compare the results, the category with the highest probability value is used for each input pair and compared to the real output provided by the expert. We obtained 53 incorrectly determined values, which represents a 98.61% accuracy of input evaluation.

We can look at the obtained results (Figure 5). Incorrectly classified data pairs are marked in squares. The color of the circle represents the correct LoS value and the color of the square represents the incorrectly assigned LoS value. Most of the misclassified data pairs are located at the boundaries between LoS categories. This is evident especially in areas with low density of training data points. Better results can be achieved mainly by adding more training data in this areas.

Figure 5

Classification of points under consideration using DNN. Points marked in squares represent misclassified values.

4.2 FISs

To model the data we used also fuzzy approach. There are several types of FISs. We chose the Takagi-Sugeno FIS [32] because this system was designed to approximate data that can be described by linear functions on certain parts of the domain and that need to be approximated on the remaining parts of the domain to obtain a continuous function. When we plot our data into the 3D graph (Figure 6), we see that the presented FIS is perfectly suited to solving the mentioned problem. Takagi-Sugeno FIS consists of fuzzy IF-THEN rules. The inputs and outputs of these rules are specific. Input variables are represented by fuzzy set membership functions. Several types of fuzzy set membership functions have been defined [33]. In this research, we used the so-called trapezoidal and Gaussian membership functions. Output variables are described by polynomial functions (most often constant or linear functions).

Figure 6

3D graph of LoS on Legerova street in Prague.

In the first step, the rule base consists of fuzzy IF-THEN rules need to be designed. Subsequently, the data can be classified. There are two ways to design a rule base. If we have enough amount of data, we can obtain rules by analyzing them. If the solved problem is well described by expert knowledge, we can translate this knowledge directly into fuzzy IF-THEN rules. In our research, we used both approaches. We process these rules in the MATLAB software, in the Fuzzy Logic Designer toolbox.

First, we analyze data automatically using specific methods. One of them, called Grid partition method, was designed such way that it divide the domain of each input variable into the required number of equal parts. Let the required number of domain division be n . Since in our research we have two input variables (Traffic Flow and Speed), then the entire 2D input space is divided into n 2 rectangles. On each rectangle, each input variable is described using fuzzy set membership function. Consequently to each rectangle an output linear function is assigned. This function is computed as approximation of the output values (the values of LoS) on considered rectangle. When using this method, the rule base contains n 2 rules (each rectangle define one rule). Typically, to increase the quality of classification, the values of the input and output variables can be optimized.

To optimize parameters, we chose the ANFIS method [34], which is based on a combination of neural networks and fuzzy sets. Therefore, we divided the data into training, testing, and validation sets with the ratio of 70, 15 and 15%, and we used ANFIS method to achieve the highest possible classification accuracy.

We used different number of domain divisions, from 4 to 7. The reason for choosing these values was that we wanted to obtain a small number of rules. We also used different sets of training, testing, and validation data, which were randomly generated. The best results were obtain when we divided each domain into the six parts (i.e., 36 rules were created), and each variable was described by trapezoidal membership functions. From 3,825 input data pairs, 3,789 pairs were classified correctly, that represent 99.06% accuracy of classification. We were not satisfied with obtained results, and therefore, we used also another methods.

The second used fuzzy method, subtractive clustering method, also analyze data automatically. This approach is based on a specific clustering method, where the points with the largest number of neighbors are chosen as cluster centers [35]. Then the rules are created in such a way that the fuzzy membership functions of input variables are computed from the values of cluster centers. On the other hand, the output functions are computed as approximations of the output values of cluster centers and their neighbors. Depending on the parameters set by the user, the method determines the number of cluster centers. By changing the method parameters, it is possible to achieve a smaller/larger number of cluster centers and thus also the smaller/larger number of rules, which leads to possibility of optimization of the number of rules in the system. In the next step, the parameters of input and output variables need to be optimized. To optimize parameters, we used the ANFIS method.

To achieve different number of cluster centers (and also different number of rules), we change the value of parameter range of influence of the cluster center. This parameter can reach any value from the unit interval. When we set up the parameter to value 0.25, we obtained six rules, which seems appropriate given the six classes we classify into. Using this FIS only 3,746 pairs from 3,825 considered pairs were classified correctly. The best results we obtained when we set up this parameter to value 0.15. The system created 13 rules and correctly classified 3,753 pairs. These results represent the lowest obtained accuracy of classification, just 98.11%.

Because the investigated problem can be well described in human language, we decided to design the rules also in the form of expert knowledge. We used so-called trapezoidal membership functions as input functions and constant functions as output functions. The input Traffic Flow was described by six membership functions Very_Low – Low – Middle – High – Very_High – Extremely_High Flow. The input Speed was described by five membership functions Very_Low – Low – Middle – High – Very_High Speed. As an example, trapezoidal membership functions of fuzzy values for the variable Speed are displayed in Figure 7.

Figure 7

Example of membership functions of input variable Speed.

Constant functions were used as output variables. We decided to consider as a domain of output variable the interval [0, 6] and as the constant output values, we considered values one, two, …, and six. Considering the solved problem, we created 27 fuzzy IF-THEN rules. The output of Takagi-Sugeno FIS was the function that represented the approximation of the considered mutual relations (Figure 8).

Figure 8

3D graph of LoS obtained using Takagi-Sugeno FIS.

Figure 8  shows that for some input values, the approximation function reached a value equal to zero (gray parts of the function graph). Since the domain of the considered function is a rectangle, some areas are not used as input values in the description of the LoS. These data values represent anomalies, and using of these settings for the approximation function, we could detect them very quickly.

By using the function created by the proposed FIS, we can assign the output LoS value to each input pair of speed and traffic flow values. As an output of the approximation function, we mostly obtain a natural number, while at the boundaries of two levels of LoS, we usually obtain the decimal number. This is also one of the advantages of the proposed system that will be used in the future. The decimal output value indicates that the considered input pair represents the output that does not strictly belong to one type of LoS.

When we want to compare the obtained results (the obtained values of LoS) first we have to round the obtained decimal numbers to natural numbers. In our research, we have 3,825 input data pairs. After we processed them using an approximation function, we obtained only 28 incorrectly determined values of LoS. This represents a 99.27% accuracy of classification.

It is very interesting to look at the obtained results (Figure 9). Most of the incorrectly classified data pairs are located on the line, which represents the speed value equal to 30. When the values of traffic flow are between 1,750 and 3,500, then this line represent the border between LoS 2 and LoS 4. From our results, it follows that the incorrectly classified points are classified into the LoS 3. If we look at the output FIS function (Figure 8), we can see that the function is continuous in the given area and creates a junction between output value 2 and output value 4 (which, of course, gives an output value equal to 3). Similar situation is when the values of traffic flow are between 0 and 1,750. Then the line, which represents the speed value equal to 30, represents the border between LoS 2 and LoS 5. In this area, the incorrectly classified points are classified into the LoS 4 or LoS 3. It follows from the same reason as in the previous case.

Figure 9

Classification of points under consideration using FIS. Points marked in squares represent misclassified values.

Despite achieving satisfactory classification accuracy, we decided to focus on improving the classification of points in the aforementioned area. It is necessary to change the function curve around the input speed value 30 so, that the resulting curve is steeper. We change the parameters of membership functions low and middle of input variable speed (Figure 7) as close to value 30, as is possible (Figure 10).

Figure 10

Improved membership functions of input variable speed.

With this adjustment, we achieved an improvement in the number of correctly classified points. We obtain only five incorrectly determined values of LoS. These results represent the 99.87% accuracy of classification. Incorrectly classified points are displayed in Figure 11.

Figure 11

Improved classification of points under consideration using FIS. Points marked in squares represent misclassified values.

4.3 HDC

The HDC implementation is based on the Python libraries Torch and Torchhd together with the Sklearn and Numpy libraries. Similarly to the DNN, all the input data are column-wise normalized and proportionally split into training and testing data in the ratio of 80 and 20%, respectively.

Embedding to high-dimensional random vector (or HV) for input data is generated according to the intRVFL model [36] by embeddings.Density routine from the Torchhd library. Each row of input data is encoded into dense bipolar MAPTensor HV [37] with a dimension of 10,000 elements from { − 1 , 1 } . Used HVs are random with equal probabilities for + 1 and − 1 . The important property of high-dimensional spaces is that with an extremely high probability, all random HVs are dissimilar to each other (quasi-orthogonal). This encoding ensures that similarities in the input space are preserved in the hyperspace too.

Since this is a classification task, six models need to be created and trained, one for each LoS value. The new model is usually represented as an HV with the same dimension as the embeddings HVs and is initialized with 0 value. Training each of the six models involves element-wise addition of the HV encoding the input data to the corresponding model HV. It means that all HVs from one LoS category are aggregated to one model HV.

The model is then tested to determine its accuracy. Each row of test data is assigned a LoS value based on the maximum cosine similarity of input HV with the six trained model HVs. The higher similarity between input data HV and model HV is, the higher is probability it belongs to the LoS category represented by the model HV. These models achieve classification accuracy of 76.34%.

To achieve higher classification accuracy using HDC, the generated models can be iteratively re-trained in several epochs. The re-training process consists of going through all the input data again, and in the case of an incorrect assignment of a LoS value to a given input line, its HV is subtracted from the model to which it was incorrectly assigned and added to the model to which it should belong according to equation (1). This procedure leads to decrease the similarity of the input HV to the incorrect model assignment and, in turn, increase its similarity to the correct model. The model accuracy evolution within iterations is shown in Figure 12.

Figure 12

Accuracy of HDC model.

The highest HDC classification accuracy was achieved after 99 epochs, with 8 out of 3,825 values being incorrectly determined, representing 99.79% accuracy of input evaluation. Incorrectly classified points are displayed in Figure 13.

Figure 13

Classification of points under consideration using HDC. Points marked in squares represent misclassified values.

We can observe that the majority of misclassified points lie on the border between two LoS categories, especially in areas with low density of points form correct LoS category. Due to this fact evaluated input point is in hyperspace more similar to the closest point from incorrect neighboring LoS category.

Further improvement can be done on the HDC approach with respect to faster convergence of models training. We will add variable α to equation (1) to control the strength of training process, like in equation (2).

This modification speeds up the HDC training process. In Figure 14, we can see progress in accuracy during the training process with α = 10 .

Figure 14

Accuracy of HDC model after modification.

In this case, convergence to the highest models accuracy occurred after 62 epochs, with only 4 out of 3,825 values being incorrectly determined, which represents 99.95% accuracy of input evaluation. Incorrectly classified points are displayed in Figure 15.

Figure 15

Classification of points under consideration using modified HDC. Points marked in squares represent misclassified values.