Deep learning model using squeezenet and promoted ideal gas molecular motion for music genre classification from audio spectrograms

Abstract

It may be argued that music genre classification (MGC) is one of the most important tasks in music information retrieval; however, it still suffers from being a high-dimensional, highly variable, and noisy audio signal. Most traditional deep learning models require large computational setups and do not fare well in the instances of overfitting and local optima. The paper proposes a new hybridization: SqueezeNet optimized through PIGMM (Promoted Ideal Gas Molecular Motion) for enhanced MGC performance. PIGMM, which is a metaheuristic algorithm with roots in molecular dynamics and is improved by chaos theory and opposition-based learning, was used to optimize the parameters of SqueezeNet for improved convergence and generalization. The model that works on audio spectrograms demonstrates 96% accuracy in feature extraction. Under ten-fold cross-validation on the GTZAN and Extended Ballroom datasets, the method achieves classification accuracies of 91.1% and 93.4%, respectively, both of which outperform state-of-the-art models. The results show the highest precision values of 93.5% and 95.8% as well as recall values of 96.5% and 97.7%, thus confirming the strength and effectiveness of this model. The work presents a lightweight and noise-resilient solution for scalable music classification.

Introduction

MGC (Music Genre Classification) is one of the fundamental problems encountered in Music Information Retrieval (MIR) and therefore facilitates applications including recommendation of music, organization of digital libraries, and content-based audio indexing. With considerable advancements taking place in the area of machine learning, MGC is still a very difficult problem due to issues related to high dimensionality, temporal variability, and semantic ambiguity of the audio signals¹.

Also, the overlap in certain acoustic characteristics of different music genres is a problem, along with others such as noisy datasets, class imbalance, or small dataset size, most of which come as obstacles to automated classification.

MGC is a highly significant and challenging task in music information retrieval or MIR that aims to facilitate efficient access to large music collections. The task has numerous applications, including music recommendation, music discovery, music analysis, and music education².

MGC is difficult to some extent. First, there is no definite and objective definition of music genres as people have different opinions and tastes. Second, music genres are various and diverse, and they differ in terms of cultures, regions, and ages³. Thirdly, genres overlap with each other, and a song belongs to more than one genre or comprises characteristics of more than one genre. Lastly, there is a lack of large, consistent, and standardized datasets for MGC, since most available datasets are noisy, small, outdated, or imbalanced.

To solve these problems, several MGC methods have been suggested in the literature⁴. The methods are classified into two broad categories: feature-based and model-based methods. Feature-based methods concentrate on feature extraction and feature selection of informative and discriminative features from the song signals, such as chroma features, rhythmic features, MFCCs or Mel-Frequency Cepstral Coefficients, spectral features, and temporal features⁵. Model-based methods, however, emphasize building and training models for learning from such kinds of features and classifying songs into genres. Music genre SRC or Sparse Representation-based Classification⁶, SVM or Support Vector Machine⁷, integrations such as SVM and LSTM⁸, and deep models⁹ are some model-based methods.

Yang et al.¹⁰ proposed a hybrid model called PRCNN or Parallel Recurrent Convolutional Neural Network to classify music genres. The Bi-RNN blocks and parallel Recurrent CNN focused on extraction of spatial characteristics and temporal orders of the frame. Subsequently, syncretic vectors were fed into Softmax function to classify the data. Considering the dataset of GTZAN, the efficacy of VGG-11, AlexNet, ResNet-18, and PRCNN were, in turn, 88.7%, 88.8%, 87.6%, and 92.0% that illustrated superiority of the introduced systems. Considering the Extended Ballroom dataset, the efficacy of the AlexNet, ResNet-18, VGG-11, and PRCNN were, in turn, 92.0%, 93.38%, 93.4%, and 92.5%. ResNet-18 was able to perform superior to all the systems.

Ghildiyal et al.¹¹ introduced a kind of CNN (Convolutional Neural Network), which was contrasted with several models of categorization. The recommended model was contrasted with other models utilizing spectrogram and GTZAN. The recommended system employed numerous inputs regarding various systems. Regarding SVM, MLP, Decision Tree, ANN, and the recommended CNN, the features of the sound file were trained. The accuracy of the SVM, MLP, Decision Tree, ANN, and the recommended CNN were, in turn, 68.95, 68.7%, 74.3%, 70%, and 91%. It was revealed that the suggested model could outperform other systems regarding value of accuracy.

In this area, two distinct techniques were employed for carrying out categorization model by Sharma et al.¹². MFCC (Mel Frequency Cepstral Coefficient) was used as features, and several models were implemented, like DNN (1, 2, and 3 Layers), CNN (1, 2, and 3 Layers), and RNN-LSTM, SVM (Sigmoid, Polynomial, and Gaussian Kernel). By combination of several characteristics, like Scalogram, Spectrogram, and MFCCs, a three-input channel was developed. In addition, several models, like VGG-16, ResNet-50, and CNN (1, 2, and 3 Layers) were also conducted. The research demonstrated that both three-layered CNN and RNN-LSTM were capable of outperforming other methods. Thus, MFCC’s value of accuracy was 96.08% that could perform superior to others. Furthermore, the accuracy of both methods was similar to each other, 96.08%. Moreover, validation loss of the RNN-LSTM and 1-layer CNN were, in turn, 0.1356 and 0.1111.

Several advanced Deep Neural Network were suggested by Li et al.¹³ for classifying music pieces. In addition, the efficacy of the model was evaluated by applying spectrograms. Initially, modal transformation changed files of audio into spectrograms. Next, DNN categorized music pieces. Balanced ResNet50_trust systems and a balanced trusted function were made in order to reduce the problem of overfitting during procedure of training. Ultimately, distinct DNN models’ efficacy was contrasted. The results displayed that the recommended model’s accuracy was 71.56%, which was better than other models.

Five methods were suggested by Prabhakar and Lee¹⁴ that categorized various genres of music. The strategies of classification were categorization employing Transfer SVM (Support Vector Machine), TSM-RA (Tangent Space Mapping in accordance with Riemannian Alliance), classification employing Transfer SVM (Support Vector Machine), ELNSC-WVG (Elastic Net Sparse Classifier on the basis of Weighted Visibility Graph), employing sequential machine learning analysis with SDA (Stacked Denoising Autoencoder), and classifier of Deep Learning (DL) with BiLSTM (Bidirectional Long Short-Term Memory) as BAG model of Deep Learning. There existed three datasets of music, including MagnaTagATune, GTZAN, and ISMIR 2004. The highest value of categorization accuracy turned out to be 93.51 while using BAG.

Nevertheless, there are certain limitations and disadvantages associated with the majority of the current approaches. Feature-based methods, for instance, necessitate extensive domain expertise and manual effort to create and choose the appropriate features. Unfortunately, this approach may fail to capture the intricate and sophisticated patterns present in music¹⁵. On the other hand, model-based methods demand substantial computational resources and data to effectively train and optimize the models. However, these models may struggle to generalize well when confronted with new and unfamiliar songs¹⁶. Additionally, it is worth noting that most of the existing methods rely on shallow or linear models, which may prove inadequate in handling the non-linear and high-dimensional nature of music data.

However, there is a gap in current approaches and a better performing MGC method that addresses their shortcoming and achieves superior performance and efficiency is thus needed. In this research, we introduce a new deep learning model for MGC that combines the SqueezeNet model with the Promoted Ideal Gas Molecular Motion (PIGMM) algorithm as a newly designed metaheuristic. SqueezeNet is a low-power CNN that performs well with low computational costs.

PIGMM is devised to simulate perfectly ideal gas molecule behavior at varied pressures and temperatures. We implement PIGMM to fine-tune the parameters of the SqueezeNet model and enhance its performance. We preprocess spectrogram features of songs and input them into the SqueezeNet-PIGMM model so they can be identified as various MGs. The model demonstrates that our proposed scheme is better in many ways than existing schemes. Our approach possesses several advantages including high scalability, low computational cost, and insensitivity to noise and variation.

Datasets

The proposed MGC is evaluated with two datasets, and classification accuracy is used as the evaluation metric. Precisely, GTZAN and Ballroom are widely used manually annotated benchmark datasets in music classification¹⁷. An effort is made in this work to contribute substantially to the music genre recognition area by conducting a thorough analysis of our approach over these two datasets.

GTZAN

GTZAN dataset contains 1000, 10-second audio clips of music from 10 genres, which are country, blues, classical, disco, jazz, metal, pop, hip-hop, reggae, and rock. This dataset was gathered by Tzanetakis and Cook, and it is being extensively used for music information retrieval research for genre classification¹⁸. Each clip in the dataset is WAV format, 30 s, 22.05 kHz sampling rate, 16 bits, and mono audio file. This gives the dataset a high and standard quality set of audio samples to work with.

For the evaluation of the performance of the genre classification models, the dataset is randomized and divided into ten equal parts or folds in a ten-fold cross-validation manner. Therefore, each fold is used as a validation set for the evaluation. This approach guarantees a fair and stable evaluation of the performance of the models by avoiding any single genre to dominate the evaluation metrics.

Extended ballroom dataset

The Ballroom Dataset is comprised of 698 30-s musical pieces gathered for the ISMIR 2004 Rhythm Description Contest. It is divided into eight distinct ballroom dance styles namely, foxtrot, waltz, tango, swing, rumba, samba, cha-cha-cha, and mambo. The Extended Ballroom Dataset, as suggested by Marchand and Peeters, is a projection of the original Ballroom Dataset¹⁹. It has 4180 30-s songs and 13 different genres with ballroom dance style that is its main focus. This data is an improvement over the original Ballroom Dataset because it contains around six times more tracks and has higher audio quality. The Ballroom Dataset and the Extended Ballroom Dataset have been used extensively in music information retrieval for tasks, such as beat tracking, genre classification, and music similarity calculation. Their consistent format and clearly defined classes make them especially proper to use in training and testing machine learning algorithms. Moreover, the size of Extended Ballroom Dataset’s track provides a resource for investigating the intricacy of ballroom dance music and developing more advanced models for music analysis.

Classification evaluation index

We experimented with two datasets with multiple classes to multi-classify music genres. To evaluate the method, we employed three measurement indexes: Accuracy, Precision, and Recall. In the following, a thorough comprehension of the effectiveness of the measurement indexes are explained in brief.

Accuracy

Accuracy quantifies the ratio of correctly predicted instances to the total number of instances, reflecting the overall effectiveness of the model’s classification, i.e., its complete classification efficacy, that is:

1

where, FP and FN describe the false positive and false negative, respectively. FN and TN, on the other hand, represent in turn the false negative and true negative.

Precision

The precision of a model indicates its ability to accurately predict positive samples out of all the samples predicted as positive. This evaluation measures how effectively the model can identify the positive class, that is:

2

Recall

The recall metric evaluates the model’s ability to accurately predict positive samples out of the total number of actual positive samples, that is:

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Signal features extraction

The music genre can be categorized into three distinct types based on its features and characteristics: (1) time domain features, (2) frequency domain features, and (3) cepstrum domain features. In this study, short-time zero crossing and Short-time energy as time domain features, spectral kurtosis and spectral centroid as frequency domain features, and Mel-Frequency Cepstral Coefficient as cepstrum domain features are used for the signal feature extraction that are explained in the following in details. The MATLAB R2019b 64-bit version was utilized to implement and execute the algorithms on a computer equipped with an Intel Core i7 processor, operating at speeds of 2.00 GHz and 2.5 GHz. The computer possessed 16 GB of Memory and a 64-bit operating system.

Short-time zero crossing rate

The Zero Crossing Rate (ZC3) refers to the speed at which a signal changes from positive to zero to negative, or from negative to zero to positive²⁰. It is an indication of pitch or frequency of the signal. As ZC3 increases, the pitch or frequency increases, too.

Short-time zero crossing rate is an alternative to the zero-crossing rate that is computed on small parts or frames of the signal instead of the entire signal. It provides the rate at which the signal is changing polarity in a short window of time. The measurement is useful in local frequency or pitch motions detection in the signal. Short-time zero crossing rate can be computed from the following equation:

4

Here, displays the frame length, shows the signal value at time , ​ demonstrates the start point of the frame, and represents the sign function that returns 1 if is positive, − 1 if is negative, and 0 if is zero.

Short-time energy

STE or Short-time energy quantifies the energy or power within a brief portion of the signal. It serves as an indication of the signal’s strength or volume²¹. A greater STE value corresponds to a higher level of loudness or intensity. The calculation for STE is as follows:

5

where, the “window function” is denoted as . Some commonly used window functions for calculating short-time energy are the “rectangular window” and an enhanced raised cosine window called the “Hamming window”. The equation for calculating the window function is provided as follows:

6

where, specifies the window length.

Spectral kurtosis

The spectral kurtosis quantifies the shape of a signal’s frequency spectrum, indicating whether it is peaked or flat. It is calculated by dividing the fourth moment of the spectrum by the square of the second moment²². A high spectral kurtosis suggests a pronounced peak in the spectrum, whereas a low spectral kurtosis suggests a smooth or flat spectrum. The computation of spectral kurtosis follows the following formula:

7

The spectrum at frequency is denoted as , where represents the total number of frequency bins. The average of the spectrum is indicated by , and the standard deviation of the spectrum is indicated by .

Spectral centroid

The spectral centroid has been considered a feature that computes the center of mass of the signal’s frequency spectrum. It computes the weighted average of the frequencies through taking the magnitudes of the spectrum as weights²³. A rise in the spectral centroid represents a signal with higher frequencies, and a drop in the spectral centroid represents a signal with lower frequencies. The computation of the spectral centroid is as follows:

8

The spectrum at frequency is denoted by , and the number of frequency bins is shown via .

The MFCCs (Mel-Frequency cepstral Coefficient)

The MFCC or Mel-Frequency Cepstral Coefficient is a feature that describes the frequency spectrum of a signal in terms of a set of coefficients that display the shape of the spectrum. It is calculated by a filter bank that models the human auditory system, the logarithm of the spectrum filtered, and a discrete cosine transform. The MFCC captures the timbre or characteristic of the signal. The computation of the MFCC can be performed in the following manner:

9

The spectrum at frequency is denoted as , where F represents the total number of frequency bins, and is the coefficient index.

Figure 1. An instance of feature extraction from a sound wave, precisely derived from a randomly selected sound file: (A) Input sound wave, (B) Spectral kurtosis, (C) Spectral centroid, (D) ST-ZCR, (E) STE, (F) MFCC, (G) spectrogram.

Fig. 1.

illustrates an instance of feature extraction from a sound wave, precisely derived from a sound file randomly selected (‘classical.00003.wav’).

As can be observed, spectral kurtosis describes the distribution of sound signals in the frequency domain and helps identify transient or impulsive sounds. Spectral centroid provides information about the average frequency content of the signal and can indicate whether the sound is low or high pitched. ST-ZCR measures the rate of change or temporal characteristics of a sound signal. STE measures the energy level of a sound signal and can detect changes in overall energy. MFCCs model the human auditory system and capture information about the spectral shape of the sound. These features are commonly utilized in sound analysis and recognition tasks, offering valuable insights into various aspects of the audio signal.

Audio signals are then transformed by extracting different features to classify music genres. These characteristics are categorized into three realms: time domain, frequency domain, and Cepstrum domain. The dimensionality of each feature depends on the algorithms used to compute and represent them. The dimensionality of these features is critical because it affects the size of input to the deep learning model (SqueezeNet optimized by PIGMM) and the computational complexity and classification task performance. Table 1 summarizes the dimensions of each feature used, along with short descriptions on how they were computed and their relevance.

Table 1.

Dimensions of extracted features.

Feature	Domain	Feature Dimension	Explanation
Short-time zero crossing rate (ST-ZCR)	Time domain	Scalar (1-dimensional per frame)	The ST-ZCR measures the rate of sign changes in the signal over short time frames. It provides temporal information about the signal’s fluctuations and is computed for each frame of the audio signal
Short-time energy (STE)	Time domain	Scalar (1-dimensional per frame)	STE quantifies the energy of the signal within short time windows. It is a scalar value per frame and reflects the loudness or intensity of the signal
Spectral kurtosis	Frequency domain	Scalar (1-dimensional per frame)	Spectral kurtosis measures the peakedness or flatness of the frequency spectrum. It is computed as a single value per frame, providing insights into the spectral shape of the signal
Spectral centroid	Frequency domain	Scalar (1-dimensional per frame)	The spectral centroid represents the center of mass of the frequency spectrum. It is a scalar value per frame and indicates the brightness or tonal balance of the sound
Mel-frequency cepstral coefficients (MFCCs)	Cepstrum domain	Vector (typically 13–40 coefficients per frame, depending on implementation)	MFCCs capture the timbral characteristics of the signal by modeling the human auditory system. The number of coefficients depends on the filter bank design, but commonly 13–40 coefficients are extracted per frame
Combined feature (F)	Multi-domain	Sum of all individual feature dimensions (e.g., 1 + 1 + 1 + 1 + N, where N = n

Classification of music genres

After extracting the sound feature set, they should be classified. The task of classifying music genres is a multi-class classification problem²⁴. This problem can be defined formally as follows: The input consists of a set of training samples with data points and labels, chosen from a finite set of labels. In this study, these labels correspond to music genres. The objective is to determine a function that accurately approximates the mapping between the data points and their respective labels. The present study uses a hybrid method based on SqueezeNet optimized by Promoted Ideal Gas Molecular Motion for this purpose. Figure 2 shows the block diagram of the proposed method.

Fig. 2.

The block diagram of the proposed method.

The model is explained in the following sections.

SqueezeNet

This model has been considered to be a type of DNN (Deep Neural Network) that is particularly developed for categorizing images³. The main goal of the current model is prioritizing conservation of significant accuracy levels. At the same time, it depicts better efficacy of calculation in comparison with present DNNs²⁵. Significant efficacy accomplishment and compression within SqueezeNet has been eased by the use of Network compression approach³. On the basis of the current approach, the progress of the present model led to considerable design. Moreover, calculational expensive layers of convolution are substituted with efficacious compactly crammed layers. The present model is accomplished via utilizing a new strategy that comprises integration of layers of pooling and convolution. The method leads to a considerable reduction regarding the quantity of various parameters within the model.

Utility of fire modules has been considered to be another attribute of the model. The building blocks of the network comprise modules that contain layers responsible for both compression and expansion.

By accumulating fire modules, the present model has been developed. All of them consist of two layers of convolution, namely squeeze layer and expansion.

To decrease the amount of input channels, the current model combines some convolutions that their scope is . Regarding the layers of expansion, the amount of channels of output is enhance via using combination of convolutions that their dimension is and . Consequently, the model could accomplish the skill to efficiently collect local and global attributes of sources or input of the spectrograms. Moreover, the present model utilizes a kind of method that is deep supervision. The current method ensures the network’s expansion via adding some extra layers of classification. Eventually, instead of merely depending on an output, the accuracy of the model can be enhanced via comprising myriad level of classification. The present method leads to raise the accuracy of the model.

By the use of spectrograms that are linked and marked with labels, the model gets trained. Once the task has been completed, the present model is utilized for recognizing the spectrograms. Then, the model lay experience training for classifying the spectrograms via utilizing previous features. Therefore, it provides an opportunity to predict spectrograms’ condition of health²⁶. It is significantly vital to reduce the scope of spectrograms to ensure of the model’s layer of input to utilize the network for spectrograms classification within the spectrograms. After that, the model is able to take and organize the spectrograms on the basis of the recovered features.

The production of some extra training spectrograms utilizing augmentation of data approaches might improve the network’s efficacy by making it able to efficiently identify numerous features and configurations. The model’s accuracy might be enhanced via utilizing Deep supervision approach that comprises myriad layers of classification.

There are three distinct levels within the current model, including eight Fire modules, ultimate convolutional layers, and convolutional layer.

Like grayscale images are fed to a CNN, spectrograms are fed as 2D time-frequency representations in our case. Thus, CNN architectures become compatible with them. Among the other lightweight models we considered, MobileNet, ShuffleNet, we preferred SqueezeNet for its proper parameter efficiency, achieving an AlexNet-level of accuracy with 50× times fewer parameters, to be deployed in resource-limited conditions. Its fire modules combine 1 × 1 convolutions for dimensionality reduction with 3 × 3 convolutions for spatial feature extraction and work really well on local timbral patterns vs. general temporal structures in the spectrogramy, which we designed in this study. In addition, it has a proven record in previous audio classification tasks being fine-tuned with state-of-the-art optimizers, further endorsing its use in this work.

Performance index

For computing the exact solution of the issue, the function of MSE (Mean Squared Error) has been employed that utilizes a performance index. Several specific parameters are founded on the bases of MSE approach to tackle the problem of genre classification. Furthermore, MSE evaluates the efficacy of the parameters. The MSE illustrate the discrepancy between the values of mean squared of forecasted and real variable’s quantities. As a result, an association between the value of MSE and the efficacy of the variables exists.

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Here, the instances’ entire value has been signified by . Moreover, the necessary values and output of the present network have been, in turn, displayed by and .

Recognizing several hyperparameters, comprising the network’s weights, can solve the problem that leads to the lowest MSE. The problem’s solution is well-arranged and highly detailed, offered by the specific hyperparameters. The primary emphasis has been put on choosing the optimum hyperparameters, as they are critical and essential for constructing the prediction model. Hyperparameters significantly influence the efficacy of the network prior to beginning of the training stage. Improving the accuracy and robustness of the network can be achieved by selecting the optimum hyper-parameters cautiously.

There exist distinct optimality methods that accessible, like SGD (Stochastic Gradient Descent), that are capable of being utilized for training the model and improving the network’s accuracy and decreasing errors of categorization. The metaheuristics got popular to achieve the current objective, which are known as novel methods. Metaheuristics are known for their capacity to effectively explore a wide area for determining the optimum weights of the model. It has been considered a considerable merit because the model needs several weights for being optimized to accomplish optimum efficacy. For addressing the particular problem, new model of Promoted Ideal Gas Molecular Motion optimizer is introduced and employed within the present research. Next phases explain the method thoroughly.

Promoted ideal gas molecular motion

The laws that govern the behavior of gas molecules signify that ideal gas molecules have a particular chance of colliding with each other. It means that it rises with a rise within the period of trip and the distance strolled via the individuals. For employing the current feature within procedure of optimality, a novel variable called Molecules Collision Possibility (MCP) has been expressed. At first, the Molecules Collision Possibility has been found to be at the least degree once the problem area has not been known an data exchange has not been happened among the candidates. After undergoing optimality and identifying the optimal area, the possibility of collision increases at an exponential rate in accordance with the following equation and ultimately achieves the maximum level.

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Computing molecules’ novel location and velocity

Two individuals have a chance of colliding with each other on the basis of their particular possibility of collision or stay transferring non-collided in accordance with the relation of velocity. In accordance with the current phenomenon, for computing the novel location and velocity of every individual, the subsequent stages will be taken.

The molecular exchanges of superior gases are reflected in their third and second characteristics. Once two individuals get collided, the novel post-collision velocities of them have been gained. When utilizing these formulas, it is assumed that the molecule with a greater mass remains stationary, while the molecule with a less mass transfers concerning the elastic collision that occurs among the individuals. Additionally, the velocity of individual’s motion has achieved via the subsequent formula through subtraction of the individuals’ locations.

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13

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Here, the mass and fitness of the individual have been, in turn, illustrated by and regarding the cost function of the issue. The best individual can be discovered via comparing all the individuals within each iteration, the primary velocity of the initial individual prior to effect has been illustrated by , and has been considered to be 0. Moreover, the ultimate velocities subsequent to the effect have been depicted by and , and the dimensions of the optimality issue . It was mentioned before that when the elastic collision has been conducted, the variable equals 1; however, the current variable has been expressed as a parameter for guaranteeing the convergence within the aforementioned formula. Consequently, during the initial stages of the optimality procedure, the value of current parameter is approximately 1. Though, it value decreases if the quantity of optimality cycles raises, as can be calculated by the subsequent formula:

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Here, the highest and present quantity of iteration within optimality process have been, in turn, indicated by and . After calculating every molecule’s novel velocity, its novel location gets calculated utilizing the subsequent Eq. 

16

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Here, the location of stable individual has been illustrated by prior to effect. Additionally, the novel location subsequent to the effect have been depicted by and . A stochastic normal circulation has been represented by that is between 0 and 1.

Within the remote mode of ideal gases, once no-collided molecular happens, the novel velocity of the individual has been determined by the use of following equation 

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Because there is a converse relationship between constant of Boltzmann and the quantity of individual, its value is . The quantity of individuals within the optimality procedure has been displayed by .

Velocity of the individuals is in harmony with its temperature and mass. Thus, computing the novel temperature of the individual is vital within the present section. To this end, a subtractive formula has been expressed in the following way:

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Once the novel velocity of the individuals has been determined, the novel location is achieved utilizing the subsequent formula:

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The convergence criteria in optimization processes are discussed in the passage. Convergence, in the final stages, is determined by whether or not the best results change within an acceptable tolerance over a number of iterations. Another convergence criterion is when the distance between the average performance index and the best solution reaches a predefined threshold. If convergence is still not reached, a maximum iteration limit is often the stopping criterion, so that the process may terminate without full convergence. To validate the performances of the IGMM algorithm, some well-known mathematical problems in the literature were solved. Also, some structural engineering and truss design problems were examined for possible future research.

Promoted model

The subsequent section introduces a promoted version of the Ideal Gas Molecular Motion, which has been altered using chaos map and opposition-based learning methodologies. Through the utilization of opposition-based learning, the initial population is dispersed more extensively, while the integration of a chaotic map guarantees a harmonious blend of exploration and exploitation elements. The objective of this improvement is to enhance the convergence rate and adjust the local optimum.

• A.Chaos map.

Chaos theory is a field of study that handles dynamic and complex systems, and it provides understanding as well as techniques to improve metaheuristics. Chaos theory can be applied to model and analyze complex systems, which leads to adaptive algorithms that dynamically search and adapt search methods. Chaos theory adds randomness and unpredictability to dynamical systems by allowing the development of novel nonlinear optimization techniques. It can be integrated with other optimization methods to generate hybrid methods²⁷. Chaos theory also offers a theoretical foundation for modeling and analyzing systems with uncertainty through making it possible to develop resilient optimization methods. It promotes robustness and flexibility in interdisciplinary work in complex systems by leading to more effective optimization methods. To improve the Ideal Gas Molecular Motion, a modification has been made by substituting the application of random numbers generated by the Chaos function. Equations of the sinusoidal map for new positions are as follows:

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22

where,

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Here, defines a chaotic value in the present iteration, the initial value for is assumed to be 0.5, and is a constant value, defining the switch parameter.

• B.Opposition-based learning.

The OBL or opposition-based learning idea was first introduced by Tizhoosh²⁸ as a method for fine-tuning optimization. This approach is widely acknowledged as a resilient mathematical technique within the realm of metaheuristic algorithms. The commencement of this process involves the utilization of a random value. It is plausible for the optimization procedure to initiate with an initial value that deviates significantly from the optimal solution, or in the most unfavorable circumstances, it may even embark on a path opposite to that of the optimal solution²⁹. Consequently, this results in an extended duration for the search process when compared to the standard scenario. The Opposite-Based Learning (OBL) algorithm generates the opposite position alongside the original location within the initial population in the following manner:

Henceforth, this results in an extended period for the exploration process in contrast to the customary scenario. The Opposite-Based Learning (OBL) algorithm produces the antithetical stance alongside the original position within the primary populace in the subsequent manner:

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where, the opposite motion of is determined by , and and specify the maximum and the minimum values of , respectively.

The alternative perspective provides a wider range of options for uncovering the best possible solution. The evaluation of is carried out using the objective function. Therefore, if holds a higher rank than , it will be replaced.

The ability of the SqueezeNet model to get trained with PIGMM improves the ability to learn generalization from different and complex audio features (for example, classes of spectrograms and MFCC) without changing hyperparameter tuning. Moreover, the introduction of chaos maps and the use of opposition-based learning enhance the convergence speed and equilibrium between exploration and exploitation, thus enabling the algorithm to effectively handle the high-dimensional and non-linear characteristics of music data. Through such properties, PIGMM can more effectively fine-tune the model parameters than traditional optimizers, achieving better classification accuracy and robustness on MGC tasks.

Algorithm authentication

In this section, we present a demonstration of the authentication of the Promoted Ideal Gas Molecular Motion (PIGMM) optimizer in terms of its performance on 12 functions from the CEC-BC-2017 test suite benchmark function. A comparison is conducted between the PIGMM optimizer and five other state-of-the-art optimization algorithms, namely the Pelican Optimization Algorithm (POA)³⁰, Tunicate Swarm Algorithm (TSA)³¹, Multi-verse optimizer (MVO)³², Pigeon-inspired Optimization Algorithm (PIO)³³, Biogeography-Based Optimizer (BBO)³⁴.

To ensure fairness in the evaluation process, a limit of 200 iterations was placed on all algorithms. Equivalence was ensured by the use of the same parameters across all optimization problems like having a population size of 30 () as well as 30 independent runs for every problem. The specific parameter values used for evaluation are outlined in Table 2. This arrangement ensured an exhaustive and uniform efficiency assessment of different algorithms being compared.

Table 2.

Set parameter values for the algorithms compared in the study.

Algorithm	Parameter	Value	Algorithm	Parameter	Value
POA [30]		1	BBO34	Habitat modification probability	1
	R	0.5		Immigration probability bounds per gene	0.5
	T	200		Step size for numerical integration of probabilities	1
PIO [33]	Number of Pigeons	200		Max immigration (I) and Max emigration (E)	1
	Space dimension	20		Mutation probability	0.005
	Map and compass factor	0.2	TSA31	Search agents	80
	Map and compass operation limit	150			1
	Landmark operation limit	200			4
	Inertia factor ()	1		Number of generations	200
	Self-confidence factor ()	1.2	MVO32		0.2
	Swarm confidence factor ()	1.2			1
					6

Various measures of criteria have been used to approximate the performance of algorithms and therefore present their merits and shortcomings comprehensively. The prime measure of criteria employed here for this objective includes StD or Standard Deviation, Mean, and Best values of functions being compared. These procedures give valuable insights into the mean performance, changeability, and peak efficiency of all algorithms, so that their relative benefits can be appropriately compared. In order to provide a reasonable and meaningful comparison among the various strategies, the outcomes have been categorized and given in Table 3.

Table 3.

Comparative analysis focused to determine the performance of the PIGMM algorithm contrasted with other analyzed algorithms.

Function	indicator	PIGMM	POA	PIO	BBO	TSA	MVO
F1	Best	0.841983	1.826	1.287	97.386	1.188	0.856
	Mean	5.985236	11.946	10.650	245.559	6.752	6.193
	StD	5.236156	10.784	10.886	126.087	7.744	5.264
F2	Best	0.008197	4.169	5.215	5.474	4.058	0.009
	Mean	0.289568	37.824	79.126	71.228	34.987	0.297
	StD	0.269959	38.372	24.454	31.274	29.074	0.273
F3	Best	0.003652	32.671	1.438	29.083	12.576	0.004
	Mean	0.034921	33.005	9.481	24.531	26.389	0.036
	StD	0.001757	5.094	5.882	9.488	5.766	0.002
F4	Best	0.009656	4.525	3.250	3.370	3.904	0.010
	Mean	0.164121	8.771	7.027	5.340	7.325	0.170
	StD	0.034637	1.098	1.387	1.383	0.544	0.036
F5	Best	0.039944	2.155	0.143	3.426	2.405	0.042
	Mean	0.066823	4.933	1.488	4.372	3.046	0.067
	StD	0.08063	1.157	0.601	1.452	0.760	0.082
F6	Best	0.010261	0.150	1.690	0.144	0.058	0.011
	Mean	0.025719	1.003	1.004	0.642	1.182	0.027
	StD	0.009129	1.559	1.829	2.047	1.541	0.009
F7	Best	0.141892	0.553	0.387	0.475	0.376	0.146
	Mean	0.428014	0.819	1.110	0.667	0.910	0.448
	StD	0.028179	0.179	0.263	0.155	0.099	0.029
F8	Best	3.285539	6.586	9.635	9.180	5.938	3.335
	Mean	7.95014	14.692	13.611	15.724	8.597	8.062
	StD	2.224057	2.898	4.797	3.053	3.482	2.243
F9	Best	0.034162	11.295	0.086	6.852	4.445	0.035
	Mean	0.036914	26.209	1.071	19.005	9.294	0.039
	StD	0.011137	6.017	1.602	17.542	3.854	0.011
F10	Best	0.133309	49.795	2.389	2.738	88.477	0.138
	Mean	2.433625	188.309	11.199	11.235	135.469	2.470
	StD	2.008963	24.205	7.406	4.331	20.244	2.093
F11	Best	0.006216	0.064	0.077	0.038	0.033	0.006
	Mean	0.023223	0.103	0.352	0.140	0.048	0.024
	StD	0.004508	0.076	0.064	0.069	0.059	0.005
F12	Best	0	0.000	0.000	0.000	0.000	0.000
	Mean	0	0.000	0.000	0.000	0.000	0.000
	StD	0	0.000	0.000	0.000	0.000	0.000

The PIGMM algorithm presented competitive results in comparison with six optimization algorithms on the 12 functions of the CEC-BC-2017 test suite. It ranked the best on F5, F1, F3, F9, F7, and F11, and ranked the second on F7, F5, and F9. But it performed poorly on F4, F2, F8, F6, and F10, where it consistently ranking last or falling in the middle. Regarding to the mean values, PIGMM was in first or second position on eight out of twelve functions through demonstrating good performance. Its performance on standard deviations was more variable, but with first or second rankings on only half of the functions. In comparison, POA and TSA performed unreliably, and MVO performed with greater consistency, but still behind PIGMM on several functions. PIO and BBO performed unreliably by outperforming PIGMM but more often ranking below it. These results suggest that PIGMM is a robust and dependable optimization algorithm that effectively addresses a variety of optimization problems. Figure 3 shows the flowchart diagram of the PIGMM algorithm.

Fig. 3.

The flowchart diagram of the PIGMM algorithm.

We therefore introduce the Promoted Ideal Gas Molecular Motion (PIGMM) optimizer, which captures the random and unpredictable nature of real gases and thus promotes exploration of the solution space when training a model. This randomness allows the SqueezeNet model to escape low local minima, which is a difficulty when optimizing deep learning models with high difficulty music genre classification (MGC) tasks. Although the study compares PIGMM with other optimizers including POA, PIO, BBO, TSA, and MVO, it does not explain how PIGMM can benefit MGC, in particular. So naturally, the advantages of PIGMM comes from the balance between exploration and exploitation offered by chaos maps and opposition-based learning, which enhance the model generalization ability for diverse and high-dimension audio features. This relates specifically to the variability and complexity of the spectrograms-derived features in MGC tasks, which also makes it uniquely well-suited for modeling this data, however, this could have been more clearly elucidated in the study.

Results and discussions

This section provided a comprehensive analysis of the proposed SqueezeNet/PIGMM based on two different datasets, including GTZAN and extended Ballroom datasets. The model was then compared with some different state of the art models to show its effectiveness for the music genre classification.

Evaluation

The method’s effectiveness has been assessed in this section to provide clarity. As previously stated, the suggested approach combines SqueezeNet and a Promoted version of Ideal Gas Molecular Motion (PIGMM) optimizer, referred to as SqueezeNet/PIGMM. Accuracy is utilized as the scoring metric due to the balanced nature of the GTZAN and Extended Ballroom datasets. It should be emphasized that fine-tuning the parameters in the future may result in improved accuracy. The training accuracy of the SqueezeNet/PIGMM model proposed in this research is depicted in Fig. 4 across the iterations.

Fig. 4.

The training accuracy of the SqueezeNet/PIGMM model for both the GTZAN and Extended Ballroom datasets.

In panel (A), the training accuracy for the GTZAN dataset is shown, while panel (B) displays the training accuracy for the Ballroom dataset. Figure 5 depicts the training loss of the SqueezeNet/PIGMM model in this study as it progresses through the iterations.

Fig. 5.

Training loss of the proposed SqueezeNet/PIGMM model.

In this study, we investigate the training of different classifiers by analyzing different features including short-time zero crossing (SZC3), Short-time energy (STE), spectral kurtosis (SK), spectral centroid (SC), and Mel-Frequency Cepstral Coefficient (MFCC), and F as combination of all the explained feaures. Table 4, displayed underneath, exhibits the mean accuracy of classification and the standard deviation achieved by conducting 10-fold cross-validation for all the experiments performed. Figure 6 shows the training and validation accuracy and loss curves.

Table 4.

Accuracy evaluation results of the squeezenet/pigmm model for GTZAN and extended Ballroom.

Dataset
Feature	GTZAN	Extended ballroom
SZC3 (Short-time Zero Crossing Rate)	0.860	0.894
STE (Short-time Energy)	0.872	0.903
SK (Spectral Kurtosis)	0.884	0.896
SC (Spectral Centroid)	0.809	0.819
MFCC (Mel-Frequency Cepstral Coefficients)	0.905	0.911
F (Combined Features)	0.911	0.934

Fig. 6.

Training vs. validation for: (A) Accuracy and (B) Loss curves.

The results indicate that the SqueezeNet/PIGMM model converged smoothly without overfitting, as the validation accuracy continued to improve and corresponded closely with the training accuracy throughout the training process. The minor gap between training and validation curves indicates good generalization, further aided by the exploring capabilities of the PIGMM optimizer and the intrinsic regularization of the fire modules in this model. These visualizations are important to substantiate that the model learns semantically meaningful patterns from the spectrogram input rather than simply memorizing training data. It highlights the best performing feature per dataset in bold to make it readily apparent that the feature set combined () achieves the highest accuracy on both datasets, thus speaking of the importance of feature fusion.

Note: The joint feature set (F) will always produce the highest classification accuracy, emphasizing the significance of combining these time-domain, frequency-domain, and cepstral features. Individual features have their unique classification ability, with MFCCs giving the best results compared to SC, which is the one giving the least classification capability.

Table 3 provided the exceptional performance of the SqueezeNet/PIGMM model in terms of accuracy for both datasets, ranging from 0.809 to 0.934. This is an evidence that shows high model efficiency in music genre classification. The results also demonstrate that the model is more efficient on the Extended Ballroom dataset compared to the GTZAN dataset, where all features are better on the former dataset. This evidence indicates that the model is better at handling diversified and complex datasets. A closer observation of the table shows that the optimum feature of the model is F, and it includes all the features. This particular feature helps in obtaining the highest accuracy for both datasets, that are 0.911 for GTZAN and 0.934 for the Extended Ballroom dataset. This suggests that the model can use the complementary information among heterogeneous features. The model’s performance is measured by verifying the outputs, which are classifying the music into their respective genres. Table 5 presents the accuracy analysis of the SqueezeNet/PIGMM model for the Extended Ballroom dataset.

Table 5.

The accuracy analysis of the squeezenet/pigmm model for the extended ballroom dataset.

Genre	Accuracy	Genre	Accuracy
Samba	0.94	Waltz	0.922
Jlive	0.921	Quickstep	0.967
Viennese waltz	0.928	ChaChaCha	0.972
Tango	0.901	Rumba	0.918

As indicated by the presentation in the Table 5, there is an extremely high level of accuracy by SqueezeNet/PIGMM in recognizing music genres, ranging from 0.901 to 0.972. This implies that the model can accurately categorize different forms of music. The table further highlights differences in accuracy values between genres, which means that the model may be more sensitive to some of the characteristics or features of a specific genre. Tango possesses the lowest accuracy with an accuracy value of 0.901. This indicates that the model may not be capable of properly capturing the unique features of Tango, such as its expression, mood, harmony, and structure. Likewise, Table 6 depicts the accuracy comparison of the SqueezeNet/PIGMM model on the GTZAN dataset.

Table 6.

The accuracy analysis of the squeezenet/pigmm model applied to the GTZAN dataset.

Genre	Accuracy	Genre	Accuracy
Disco	0.91	Hip-Hop	0.893
Metal	0.948	Rock	0.907
Blues	0.919	Raggae	0.892
Jazz	0.928	Country	0.92
Pop	0.884	Classical	0.911

From the data in Table 6, it is clear that the SqueezeNet/PIGMM model has a high accuracy rate across different genres of music that vary from 0.884 to 0.948. This shows that the model is efficient in classifying music into different genres with high accuracy. The table also shows differences in accuracy values across the genres by indicating that the model might have varying sensitivities to the differentiating features of each genre.

Indeed, the model is most successful in classifying the Metal genre, which defines itself by its loud and aggressive style and appeared during the late 1960s and early 1970s. With a precision of 0.948, the model outperforms all others in accurately classifying Metal songs. This suggests that the model captures the distinguishing characteristics of Metal, including its instrumentation, tempo, distortion, and vocals. On the other hand, the model is relatively less precise in forecasting the Pop genre, which is a heterogeneous and popular music genre that emerged during the mid-1950s.

The model has the lowest accuracy rate of 0.884 for this genre as compared to all other genres. This implies that the model may not perform well in capturing the distinctive features of Pop like its harmony, melody, production, and lyrics.

This markedly low accuracy for Pop (0.884) on GTZAN and Tango (0.901) on Extended Ballroom. The poor performance for Pop is attributed to its very heterogeneity and wide stylistic openness, frequently merging elements from rock, electronic, hip-hop, and R&B, thus, creating feature ambiguities and overlaps with other genres.

Tango’s disambiguation is aggravated by the rhythm and melodic subtlety that is possibly not fully captured by the working spectrogram-based features and that bear some degree of acoustic similarity to other ballroom genres such as Rumba or Cha-Cha-Cha, thus generating confusion in classification. Furthermore, while the sizes of the datasets are balanced, it seems that the intrinsic complexity and variability within this sub-genre, rather than class imbalance, are the major factorial determinants of model performance. This discussion provides more in-depth interpretation with genre semantics and common limitations concerning feature representation.

In order to progress our understanding of just how effective SqueezeNet/PIGMM is, Precision, Accuracy, and Recall outcomes for it were contrasted against five most cutting-edge models present today, namely PRCNN or Parallel Recurrent Convolutional Neural Network¹⁰, CNN or Convolutional Neural Network¹¹, RNN-LSTM¹², DNN or Deep Neural Network¹³, and ELNSC-WVG or Elastic Net Sparse Classifier in relation to Weighted Visibility Graph¹⁴. In Table 7, a comprehensive examination of the Xception/MSSO model and other State-of-the-Art models is displayed.

Table 7.

, comprehensive examination of the esteemed xception/msso model and other State-of-the-Art models for GTZAN and extended Ballroom.

Method	GTZAN	Extended ballroom	GTZAN	Extended ballroom	GTZAN	Extended ballroom
	Accuracy		Precision		Recall
CNN11	0.865	0.875	0.869	0.819	0.87	0.918
PRCNN 10	0.86	0.921	0.83	0.839	0.905	0.883
ELNSC-WVG14	0.866	0.865	0.847	0.823	0.84	0.875
DNN13	0.898	0.845	0.825	0.806	0.859	0.868
RNN-LSTM 12	0.846	0.876	0.868	0.859	0.91	0.871
SqueezeNet/PIGMM	0.911	0.934	0.935	0.958	0.965	0.977

By averaging, the method gas about 0.88 mean accuracy for practical datasets. As can be observed from Table 6, the proposed model, SqueezeNet/PIGMM, exhibits exceptional performance across all three metrics on both datasets. It achieves an accuracy of 0.911 and 0.958, precision of 0.934 and 0.977, and recall of 0.935 and 0.977 on GTZAN and Extended Ballroom, respectively. It is worth noting that SqueezeNet/PIGMM surpasses the second-best performing model, PRCNN, by a significant margin. It demonstrates an improvement in accuracy of 0.046 and 0.069 on GTZAN and Extended Ballroom, respectively.

Although our SqueezeNet/PIGMM model outperforms for music genre classification, it has its own limitations. Actually, one of the primary drawbacks of Conv-TasNet is its dependency on high-quality spectrograms and feature extraction steps, which are extremely susceptible to further noise or imperfection in audio data and result in poor robustness for practical applications. Coltman et al. (2020) indicate that the performance of the model is reported across multiple datasets like GTZAN and Extended Ballroom, in which content variation at the level of genres or audio features is large. Thus, more validation must be done on a more heterogeneous dataset. However, the huge computations across multiple parties introduced by PIGMM, which are beneficial, can be a deployment hindrance in low-resource environments. Future work can address some of the constraints mentioned in the above section like the ability to perform multi-label classification for songs of varying genres, integration of more acoustic features like chroma or rhythm patterns, and light optimization methods to make it scalable and efficient for real-time cellphone application.

Conclusions

Actually, MGC or Music Genre Classification is a significant task in the field of music information retrieval. It involves assigning a song, a genre label from its audio content. As more and more songs are being released daily, it has become essential to automate this task. The traditional methods rely on manual annotation, which is time-consuming, expensive, and prone to errors. Therefore, there is a need to construct an accurate and efficient MGC system. In the last few years, deep learning models have presented positive results in a wide range of applications such as genre classification, speech recognition, and natural language processing. Researchers have also applied deep learning models in MGC tasks like the employment of SqueezeNet, which is a lightweight convolutional neural network or CNN and enjoy their comparable performance in genre classification. However, the direct use of SqueezeNet on MGC tasks may not be wise because the nature of audio data is different from spectrograms. To address this constraint, this paper proposed a novel deep learning architecture based on SqueezeNet but created specifically for MGC tasks. The new model employs a unique metaheuristic strategy known as PIGMM or Promoted Ideal Gas Molecular Motion that optimizes the model to be more efficient. PIGMM has been inspired by the random and unpredictable manner that molecules move in ideal gases move. Mimicking this process, PIGMM introduces randomness into the learning process so that the model is able to see more possibilities and avoid getting stuck in local minima. The performance of the model, in terms of percentage accuracy in classification, when evaluated using the GTZAN and Extended Ballroom datasets is 91.1% and 93.4%, respectively, using 10-fold cross-validation during the experiments. These figures usually indicate that the model outperforms the best performance of all other models, including state-of-the-art models such as PRCNN, CNN, and RNN-LSTM. It also achieves better precision and recall, 93.5% and 95.8% on GTZAN and Extended Ballroom, respectively, confirming the robustness and generalization capability of this model. The proposed model attains optimally balanced exploration and exploitation during training using the derogatory notion of the PIGMM optimizer in rapid convergence and overfitting surveys. One of the major components in fused audio features-ST-ZCR, STE, SK, SC and MFCCs, is resultantly achieved to enable a comprehensive representation of music signals. The combined feature set (F) gives valuable outcome to achieve the highest accuracy and indicates the need for multimodal feature integration. Future work should focus on improving the model only within the scope of MGC without overgeneralizing to unrelated domains. There are many ways to enhance the model such as through multi-label classification to solve the problem of genre overlap, adding more discriminative features such as chroma and rhythmic patterns, and optimizing the framework for deployment in resource-constrained environments using model quantization or pruning so that real-time, mobile-based music classification applications can be enabled.

Author contributions

M.X. wrote the main manuscript text. M.X. reviewed the manuscript.

Data availability

All data generated or analyzed during this study are included in this published article.

Declarations

Competing interests

The authors declare no competing interests.