# Music Genre Classification Based on VMD-IWOA-XGBOOST

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## Abstract

**:**

## 1. Introduction

- A hybrid model with VMD-IWOA-XGBOOST is proposed for music genre classification. MIC is used to screen out high-correlation features, VMD is chosen to extract the key information of features, an Improved Whale Optimization Algorithm (IWOA) is proposed to improve the parameter setting, and XGBOOST is utilized as the classification model.
- An IWOA is proposed for parameter optimization. By refining the search process, contracting encircling, and altering the spiral position, comparative analysis reveals the superiority of the IWOA.

## 2. Methodology

#### 2.1. Feature Extraction

- (1)
- The zero-crossing rate is the rate of change of a signal symbol, i.e., the probability of changing from a negative or opposite number to a positive number [26]. The over-zero rate is an important feature in the field of speech recognition and music information retrieval, and its defining formula is provided below:$$zcr=\frac{1}{T-1}{\displaystyle \sum _{t=1}^{T-1}sign\left\{{s}_{t}{s}_{t-1}<0\right\}}$$
- (2)
- The spectral center of mass is a critical physical parameter elucidating the timbral characteristics of a sound signal. It delineates the frequency-weighted average of energy distribution within a specified frequency band, functioning as the locus of gravity for its constituent frequencies. Consequently, it offers pivotal insights into the frequency and energy distributions inherent to the sound signal. It represents the brightness of the signal spectrum and is regarded as the cross-section of the STFT amplitude spectrum. The following is its defining formula:$$sc=\frac{{\displaystyle \sum _{k=1}^{K}kX\left(k\right)}}{{\displaystyle \sum _{k=1}^{K}X\left(k\right)}}$$
- (3)
- Spectral roll-off generally means that the frame center frequency is below the default threshold of the spectrum (typically 85%). This is another attribute used to estimate the spectral pattern. Spectral roll-off points serve as discriminative indicators within audio signals, facilitating the identification of distinct sounds, including the timbral nuances exhibited by various instruments. These features, typically integrated with other descriptors such as MFCCs, zero-crossing rate, and bandwidth measures, are employed synergistically to enhance the efficacy of audio processing tasks. The calculation formula is provided below:$$\sum _{n=1}^{{Q}_{t}}0.85\times X\left(k\right)$$
- (4)
- Spectral bandwidth refers to a fundamental parameter in signal processing and spectroscopy, representing the range of frequencies encompassed by a signal or a spectral distribution. It is calculated with the following formula:$${f}_{c}=\frac{{\displaystyle \sum _{k=1}^{K}}s\left(k\right)f\left(k\right)}{{\displaystyle \sum _{k=1}^{K}}s\left(k\right)}$$
- (5)
- Chroma frequency is used to indicate the energy of each tone level between musical signals, providing a metric characteristic in cases where there is a great similarity between musical segments.
- (6)
- RMSE is a method of characterizing the energy of a signal. It is expressed in Equation (5), while its rooted calculation is shown in Equation (6).$$\sum _{n=1}^{N}{\left|x\left(n\right)\right|}^{2}$$$$\sqrt{\frac{{\displaystyle \sum _{n=1}^{N}}{\left|x\left(n\right)\right|}^{2}}{N}}$$
- (7)
- In the case of Mel-frequency cepstral coefficients (MFCCs), the vast majority of its parameters are related to the amplitude of the frequency. The MFCC is an important feature of audio signals and it is used for rapid speech recognition [27]. Its equation is as follows:$$mel\left(f\right)=1125\times \mathrm{ln}\left(1+\frac{f}{100}\right)$$
- (8)
- The harmonic and percussive harmonic will reveal more horizontal or pitch-dependent changes. The percussive harmonic will show more vertical or time-dependent changes. These features are generally obtained using a fast Fourier transform (FFT).
- (9)
- Tempo is a fundamental aspect of music theory and analysis, denoting the rate or speed at which a musical piece progresses, typically measured in beats per minute (BPM).

#### 2.2. The Maximal Information Coefficient

- (1)
- Firstly, ${V}_{1}$ and ${V}_{2}$ are arranged in ascending order, and, subsequently, an ${x}_{t}$ × ${y}_{t}$ grid ${G}_{t}$ is defined as a sequence partition, where each sample point of ${V}_{1}$ is partitioned into ${x}_{t}$ parts, each sample point of ${V}_{2}$ is partitioned into ${y}_{t}$ parts, and some cells are allowed to be empty sets.
- (2)
- The probability distribution function $D{|}_{{G}_{t}}$ of all cells of the grid ${G}_{t}$ species is derived; at this time, the maximum mutual information value obtained is $\mathrm{max}$ $I\left(D{|}_{{G}_{t}}\right)$, and the value of its identity matrix is $M{\left(D\right)}_{x,y}$, as shown in Equation (8):$$M{\left(D\right)}_{x,y}=\frac{\mathrm{max}I\left({D|}_{{G}_{i}}\right)}{\mathrm{ln}\mathrm{min}\left(x,y\right)}=\frac{p\left({x}_{t},{y}_{t}\right)\mathrm{ln}\frac{p\left({x}_{t},{y}_{t}\right)}{p\left({x}_{t}\right)p\left({y}_{t}\right)}}{\mathrm{ln}\mathrm{min}\left({x}_{t},{y}_{t}\right)}=\frac{\mathrm{max}\left({\displaystyle \sum _{i=1}^{x}}{\displaystyle \sum _{j=1}^{y}}\mathrm{ln}\frac{{n}_{ij}}{N}-{\displaystyle \sum _{i=1}^{x}}\frac{{\displaystyle \sum _{j=1}^{y}}{n}_{ij}}{N}\mathrm{ln}\frac{{\displaystyle \sum _{j=1}^{y}}{n}_{ij}}{N}-{\displaystyle \sum _{i=1}^{y}}\frac{{\displaystyle \sum _{j=1}^{x}}{n}_{ij}}{N}\mathrm{ln}\frac{{\displaystyle \sum _{j=1}^{x}}{n}_{ij}}{N}\right)}{\mathrm{ln}\mathrm{min}\left({x}_{t},{y}_{t}\right)}$$
- (3)
- Since different grids $G$ lead to different probability distribution functions D|G, the maximum mutual information coefficients MIC of the variables ${V}_{1}$ and ${V}_{2}$ are searched for the optimal grid $G$ by the exhaustive method for the feature matrix:$$MIC\left(D\right)=\underset{xy<B\left(N\right)}{\mathrm{max}}\left\{M{\left(D\right)}_{x,y}\right\}=\mathrm{max}\frac{\mathrm{max}I\left({D|}_{G}\right)}{\mathrm{ln}\mathrm{min}\left(x,y\right)}=M\left(D\right)x,y$$

#### 2.3. Variational Mode Decomposition

- (1)
- The analytical signal of each mode is solved by the Hilbert transform, and the spectrum is constructed at the same time. Finally, the analytical signal of each decomposed mode component ${u}_{k}$ at time t is obtained:$$\left(\delta \left(t\right)+\frac{j}{\pi t}\right)\times {u}_{k}\left(t\right)$$
- (2)
- The predicted center frequency is multiplied with the resolved signal of each IMF component for frequency correction, and the spectrum of each decomposed IMF component is shifted to the corresponding frequency band:$$\left[\left(\delta \left(t\right)+\frac{j}{\pi t}\right)\times {u}_{k}\left(t\right)\right]{e}^{-j{\omega}_{k}t}$$
- (3)
- The variational problem with constraints is constructed by using the above-demodulated signal, calculating the bias, and then estimating the bandwidth from its squared paradigm, as shown below:$$\left(\right)open="\{">\begin{array}{l}\underset{\left\{{u}_{k}\hspace{1em}{\omega}_{k}\right\}}{\mathrm{min}}\left\{{\displaystyle \sum _{k=1}^{K}{\left|{\partial}_{t}\left[\left(\delta \left(t\right)+\frac{j}{\pi t}\right)\times {u}_{k}\left(t\right)\right]{e}^{-j{\omega}_{k}t}\right|}_{2}^{2}}\right\}\hfill \\ s.t.{\displaystyle \sum _{k=1}^{K}{u}_{k}\left(t\right)=f\left(t\right)}\hfill \end{array}$$
- (4)
- In order to transform the constrained variational problem into an $\alpha $ variational problem without constraints, the original problem can be converted into a problem of solving the Lagrange function maximum by introducing the Lagrange multiplier a with the quadratic penalty factor $\lambda $, which has the following expression:$$L\left(\left\{{\mu}_{k}\right\},\left\{{\omega}_{k}\right\},\alpha \right)=\alpha {\displaystyle \sum _{k=1}^{K}\left(\right)open="|">{\left({\partial}_{t}\left[\left(\delta \left(t\right)+\frac{j}{\pi t}\right)\times {u}_{k}\left(t\right)\right]{e}^{-j{\omega}_{k}t}\right|}_{2}^{2}}+\alpha \left(t\right),f\left(t\right)-{\displaystyle \sum _{k=1}^{K}{u}_{k}\left(t\right)}$$
- (5)
- The optimal solution of the constrained variational model is solved by updating ${u}_{k}$, ${w}_{k}$, and $\alpha $ in the frequency domain using the alternating direction multiplier method, and the updated equation is shown below:$${\widehat{\mu}}_{k}^{n+1}\left(\omega \right)=\frac{\widehat{f}\left(\omega \right)-{\displaystyle \sum _{i\ne k}{\widehat{\mu}}_{i}\left(\omega \right)+\frac{\widehat{\alpha}\left(\omega \right)}{2}}}{1+2\lambda {\left(\omega -{\omega}_{k}\right)}^{2}}$$$${\omega}_{k}^{n+1}=\frac{{\displaystyle {\int}_{0}^{\infty}\omega {\left(\right)open="|">\left({{\widehat{\mu}}_{k}}^{n+1}\left(\omega \right)\right|}_{}^{}22}}{d}{\displaystyle {\int}_{0}^{\infty}\left(\right)open="|">{\left({{\widehat{\mu}}_{k}}^{n+1}\left(\omega \right)\right|}_{2}^{2}d\omega}$$$${\alpha}^{n+1}\left(\omega \right)={\alpha}^{n}\left(\omega \right)+\Theta \left[\widehat{f}\left(\omega \right)-{\displaystyle \sum _{k=1}^{K}{{\widehat{\mu}}_{k}}^{n+1}\left(\omega \right)}\right]$$$$\sum _{k=1}^{K}\frac{\Vert {{\widehat{\mu}}_{k}}^{n+1}\left(\omega \right)-{{\widehat{\mu}}_{k}}^{n}\left(\omega \right){\Vert}_{2}^{2}}{\Vert {{\widehat{\mu}}_{k}}^{n+1}\left(\omega \right){\Vert}_{2}^{2}}}<\epsilon $$

#### 2.4. Improved Whale Optimization Algorithm

- (1)
- Adaptive weighting

- (2)
- Variable helix position

- (3)
- Differential variance scale factor

#### 2.5. XGBOOST

#### 2.6. The Proposed VMD-IWOA-XGBOOST Model

## 3. Experiment

#### 3.1. Data Set

#### 3.2. Evaluation Criteria

#### 3.3. Parameter Settings

#### 3.4. Experiment Results

#### 3.4.1. Feature Selection Results

#### 3.4.2. Decomposition Results

#### 3.4.3. Analysis of Classification Results

## 4. Conclusions

- A hybrid model with VMD-IWOA-XGBOOST is proposed for music genre classification. MIC is used to screen out five high-correlation features, the signal decomposition technique VMD is chosen to extract the key information of features, IWOA is proposed to improve parameter optimization, and XGBOOST is utilized as the classification model.
- An IWOA is developed by refining the search process, contracting encircling, and altering the spiral position. We propose using an IWOA for parameter optimization. Comparative analysis reveals that the IWOA outperforms the WOA algorithm in terms of four evaluation metrics.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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Model | Parameters | Values |
---|---|---|

BP | epoch, batch_size | 10,000, 512 |

LSTM | epoch, batch_size | 10,000, 512 |

AdaBoost | n_estimators, learning_rate | 100, 0.01 |

GBDT | n_estimators, learning_rate, max_depth | 100, 0.01, 5 |

XGBOOST | gamma, n_estimators, learning_rate, max_depth | 0, 100, 0.01, 5 |

RF | n_estimators, max_depth, min_samples_leaf | 100, 5, 2 |

WOA-XGBOOST | gamma, n_estimators, learning_rate, max_depth | [0~10] [50~5000] [0.01~0.5] [1~20] |

VMD-IWOA-XGBOOST | K, alpha, gamma, n_estimators, learning_rate, max_depth | [3~100] [100~25,000] [0~10] [50~5000] [0.01~0.5] [1~20] |

Data | Features | Weight |
---|---|---|

GTZAN | spectral_bandwidth_mean | 0.2556 |

rolloff_mean | 0.2473 | |

mfcc2_mean | 0.2201 | |

spectral_centroid_mean | 0.2165 | |

mfcc1_mean | 0.2150 | |

mfcc9_mean | 0.1650 | |

Mfcc7_mean | 0.1512 | |

spectral_centroid_var | 0.1403 | |

rolloff_var | 0.1318 | |

Mfcc4_mean | 0.1275 | |

Mfcc8_mean | 0.1244 | |

chroma_stft_mean | 0.1183 | |

Mfcc6_var | 0.1172 | |

Mfcc4_var | 0.1125 | |

Mfcc5_mean | 0.1123 | |

Mfcc6_mean | 0.1066 | |

Mfcc3_mean | 0.1012 | |

Mfcc12_mean | 0.1006 | |

Mfcc7_var | 0.0984 | |

Mfcc13_mean | 0.0973 | |

Mfcc11_mean | 0.0938 | |

spectral_bandwidth_var | 0.0929 | |

Mfcc8_var | 0.0876 | |

Mfcc5_var | 0.0823 | |

Mfcc19_mean | 0.0755 | |

Mfcc15_mean | 0.0754 | |

Mfcc10_var | 0.0747 | |

Mfcc9_var | 0.0714 | |

Mfcc17_mean | 0.0709 | |

Mfcc10_mean | 0.0688 | |

Mfcc14_mean | 0.0672 | |

Mfcc13_var | 0.0636 | |

Mfcc12_var | 0.0624 | |

Mfcc3_var | 0.0598 | |

Mfcc16_mean | 0.0539 | |

tempo | 0.0519 | |

Mfcc2_var | 0.0518 | |

Mfcc1_var | 0.0475 | |

Mfcc20_mean | 0.0456 | |

Rms_mean | 0.0450 | |

Mfcc20_var | 0.0401 | |

Mfcc15_var | 0.0387 | |

Mfcc11_var | 0.0377 | |

Mfcc19_var | 0.0352 | |

Mfcc16_var | 0.0313 | |

Mfcc18_var | 0.0294 | |

Mfcc14_var | 0.0290 | |

Mfcc18_mean | 0.0270 | |

length | 0.0256 | |

Mfcc17_var | 0.0241 | |

zero_crossing_rate_mean | 0.0184 | |

chroma_stft_var | 0 | |

Rms_var | 0 | |

zero_crossing_rate_var | 0 | |

harmony_mean | 0 | |

harmony_var | 0 | |

perceptr_mean | 0 | |

Bangla | spectral_1width | 0.3569 |

chroma_frequency | 0.2854 | |

spectral_rolloff | 0.2682 | |

mfcc1 | 0.2579 | |

mfcc2 | 0.2421 | |

spectral_centroid | 0.2141 | |

Mfcc7 | 0.2038 | |

Mfcc5 | 0.1764 | |

Mfcc9 | 0.1603 | |

Mfcc0 | 0.1586 | |

Mfcc4 | 0.1456 | |

Mfcc11 | 0.1437 | |

Mfcc13 | 0.1204 | |

Mfcc10 | 0.1099 | |

Mfcc3 | 0.0965 | |

zero_crossing | 0.0923 | |

Mfcc12 | 0.0771 | |

Mfcc17 | 0.0710 | |

Mfcc19 | 0.0697 | |

Mfcc15 | 0.0664 | |

Mfcc14 | 0.0564 | |

Mfcc6 | 0.0555 | |

Mfcc8 | 0.0528 | |

Mfcc16 | 0.0483 | |

tempo | 0.0434 | |

melspectogram | 0.0415 | |

Mfcc18 | 0.0396 | |

rmse | 0.0370 | |

delta | 0 | |

perceptr_var | 0 |

**Table 3.**Comparison between the results using the proposed method and the results using other methods.

Data | Model | Accuracy | MCC | Macro-Precision | Macro-Recall | Macro-F1-Score |
---|---|---|---|---|---|---|

GTZAN | AdaBoost | 0.335 | 0.265 | 0.276 | 0.319 | 0.271 |

BP | 0.625 | 0.588 | 0.648 | 0.639 | 0.641 | |

LSTM | 0.645 | 0.660 | 0.661 | 0.653 | 0.647 | |

GBDT | 0.640 | 0.601 | 0.649 | 0.661 | 0.642 | |

RF | 0.655 | 0.620 | 0.687 | 0.673 | 0.659 | |

XGBOOST | 0.665 | 0.630 | 0.678 | 0.686 | 0.665 | |

WOA-XGBOOST | 0.785 | 0.760 | 0.787 | 0.796 | 0.790 | |

VMD-IWOA-XGBOOST | 0.855 | 0.844 | 0.854 | 0.866 | 0.855 | |

Bangla | AdaBoost | 0.438 | 0.339 | 0.427 | 0.447 | 0.405 |

BP | 0.647 | 0.583 | 0.637 | 0.638 | 0.636 | |

LSTM | 0.679 | 0.643 | 0.645 | 0.669 | 0.667 | |

GBDT | 0.679 | 0.616 | 0.677 | 0.676 | 0.673 | |

RF | 0.653 | 0.585 | 0.652 | 0.652 | 0.648 | |

XGBOOST | 0.689 | 0.618 | 0.674 | 0.675 | 0.672 | |

WOA-XGBOOST | 0.767 | 0.720 | 0.759 | 0.759 | 0.759 | |

VMD-IWOA-XGBOOST | 0.785 | 0.742 | 0.782 | 0.782 | 0.780 |

Data | Model | Running Time (s) | p-Values |
---|---|---|---|

GTZAN | AdaBoost | 6.675 | 0.000 |

BP | 329.710 | 0.027 | |

LSTM | 1422.501 | 0.010 | |

GBDT | 90.445 | 0.003 | |

RF | 4.588 | 0.003 | |

XGBOOST | 4.742 | 0.011 | |

WOA-XGBOOST | 2382.100 | 0.350 | |

VMD-IWOA-XGBOOST | 1017.203 | / | |

Bangla | AdaBoost | 6.125 | 0.000 |

BP | 448.431 | 0.556 | |

LSTM | 2104.9 | 0.041 | |

GBDT | 55.12 | 0.044 | |

RF | 4.322 | 0.001 | |

XGBOOST | 5.235 | 0.037 | |

WOA-XGBOOST | 2879 | 0.376 | |

VMD-IWOA-XGBOOST | 1854.5 | / |

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**MDPI and ACS Style**

Gan, R.; Huang, T.; Shao, J.; Wang, F.
Music Genre Classification Based on VMD-IWOA-XGBOOST. *Mathematics* **2024**, *12*, 1549.
https://doi.org/10.3390/math12101549

**AMA Style**

Gan R, Huang T, Shao J, Wang F.
Music Genre Classification Based on VMD-IWOA-XGBOOST. *Mathematics*. 2024; 12(10):1549.
https://doi.org/10.3390/math12101549

**Chicago/Turabian Style**

Gan, Rumeijiang, Tichen Huang, Jin Shao, and Fuyu Wang.
2024. "Music Genre Classification Based on VMD-IWOA-XGBOOST" *Mathematics* 12, no. 10: 1549.
https://doi.org/10.3390/math12101549