Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 234 https://internationalpubls.com Enhancing Accuracy and Performance in Music Mood Classification through Fine-Tuned Machine Learning Methods Shital Shankar Gujar1, Dr. Ali Yawar Reha2 1Computer Engineering, Pacific University, Udaipur, sgujar03@gmail.com 2Management, Asst. Prof, Paher University, Udaipur, Ay_reha@yahoo.com Article History: Received: 08-05-2024 Revised: 24-06-2024 Accepted: 06-07-2024 Abstract Putting emotional labels on music, or "music mood classification," is important for use in recommendation systems and music therapy. Using fine-tuned machine learning methods, this study aims to improve the accuracy and performance of classification. We used a large dataset with names for different types of music and moods to make sure that the model training was strong. Advanced feature extraction methods picked up both the traits of the audio stream and the lyrics. For audio features, color features, spectral contrast, and mel-frequency cepstral coefficients (MFCCs) were recovered. For poetry analysis, TF-IDF and word embeddings were used, along with natural language processing (NLP) methods. Logistic Regression, SGD Classifier, Gaussian Naive Bayes, Decision Tree, Random Forest, XGB Classifier, SVM Linear, and K-Nearest Neighbors (KNN) were some of the machine learning classification methods we used. Random Forest, XGB Classifier, and SVM Linear all did better than the others. We used grid search and random search to fine- tune the hyperparameters of these top-performing models in order to make them even better. Cross-validation made sure that the models were stable and could be used in other situations. Our results show that the highly tuned Random Forest, XGB, and SVM models greatly improved the accuracy of classification, with the XGB Classifier performing the best. This study adds to music information retrieval by creating a useful method for mood classification that can be used in real-life situations to improve user experiences and create more personalized music services. Keywords: Music Mood Classification, Machine Learning, Feature Extraction, Hyperparameter Optimization, Random Forest, XGB Classifier, SVM, Music Information Retrieval. 1. Introduction The study of music mood classification is both complicated and interesting. It combines aspects of musicology, psychology, and computer science. The main goal is to correctly give emotional tags to songs so that users can have more unique and relevant music experiences. This feature is very useful for many things, like song suggestion systems, mood-based tracks, and healing settings. The need for automatic and accurate mood classification systems grows as the amount of digital music keeps growing at an exponential rate. Music mood classification has relied on simple heuristics and hand tagging, which take a lot of time and are open to personal bias. Machine learning has completely changed this area by providing strong tools and methods that can deal with the complexity and variability of sound data. Big datasets can teach machine learning models new things, and these models can find connections and trends that humans often miss [1]. The move toward data-driven Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 235 https://internationalpubls.com methods has made music mood labeling tools much more accurate and scalable. One important part of accurately classifying music mood is extracting features. As a tool, music has many uses. It includes both sound messages and lyrics. Things in sound like Mel-frequency cepstral coefficients (MFCCs), color features, and spectral contrast tell us a lot about the music's harmonic and rhythmic qualities [3]. On the other hand, the lyrics can help you understand the emotional and thematic themes of a song. Many Natural Language Processing (NLP) methods, like Term Frequency-Inverse Document Frequency (TF-IDF) and word embeddings, have been shown to be useful for reading songs and pulling out useful information. Putting these audio and written traits together will help us make more complete models that can understand all the different kinds of information that are in musical pieces [2]. It look into how well different machine learning classification methods work for figuring out the mood of music. Logistic Regression, SGD Classifier, Gaussian Naive Bayes, Decision Tree, Random Forest, XGB Classifier, SVM Linear, and K-Nearest Neighbors (KNN) are some of the algorithms we look into. Because they are all different, these algorithms can be used for different kinds of data and sorting jobs. We want to find the best method for our classification problem by carefully comparing these models. Fine-tuning the hyperparameters is the next important step after finding the models that work best. This is different from the model's parameters: hyperparameters are the parameters of the learning method itself. To get the most out of the model, these hyperparameters must be tuned correctly. We use methods like grid search and random search to carefully look through the hyperparameter space of Random Forest, XGB Classifier, and SVM, which are our best models. Cross-validation is used to make sure the results are reliable and can be used in other situations. Our study shows that fine-tuning makes music mood classification models much more accurate and reliable. It was especially the fine-tuned XGB Classifier that showed huge performance gains [3]. This shows how important it is to choose the right model and optimize hyperparameters to get the best results. This study not only adds to our technical knowledge of how to classify music based on mood, but it also shows us how to use these models in real life. This study shows a complete method for classifying music moods using cutting-edge feature extraction methods and cutting-edge machine learning algorithms. We improve the performance of the most promising models by fine-tuning their hyperparameters [4]. This paves the way for more accurate and user- friendly systems that suggest music. This study adds to the field of retrieving music information and shows how machine learning can help us understand and connect with music better. 2. Related Work Music temperament classification has experienced noteworthy advancement with the rise of machine learning methods, profound learning structures, and multimodal approaches. Early approaches depended intensely on manual explanation and heuristic-based strategies, which were constrained by subjectivity and needed versatility [5]. The coming of machine learning empowered analysts to robotize temperament classification forms by learning designs from information [6]. Back Vector Machines (SVM) developed as a significant device in early considers, illustrating their adequacy in capturing nonlinear connections between sound highlights extricated from music signals and disposition names [7]. SVMs given a vigorous system for progressing classification precision and decreasing human intercession in temperament labeling. Profound learning structures, especially Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 236 https://internationalpubls.com Convolutional Neural Systems (CNNs) and Repetitive Neural Systems (RNNs), revolutionized the field by specifically handling spectrograms and capturing worldly conditions in music information [8]. Choi et al. [8] showcased the adequacy of CNNs in extricating various leveled highlights from sound signals, whereas RNNs exceeded expectations in modeling consecutive designs in music. In parallel, analysts investigated the integration of literary data, such as tune verses, into disposition classification frameworks. Common Dialect Preparing (NLP) methods, counting opinion investigation and topical extraction, improved the relevant understanding of music substance [9]. Hu and Downie [9] illustrated that combining literary examination with sound highlights altogether progressed classification precision, highlighting the complementary nature of acoustic and semantic prompts in temperament forecast. Outfit strategies have moreover played a significant part in upgrading prescient execution by combining numerous classifiers. Zhang et al. [10] proposed a half breed demonstrate that coordinates SVM with Choice Trees, leveraging the qualities of both calculations to realize prevalent comes about compared to person classifiers. Gathering learning approaches have demonstrated successful in dealing with the differing qualities and complexity of music information. Later progressions in hyperparameter optimization have assist refined the execution of machine learning models for music temperament classification. Strategies such as framework look and Bayesian optimization empower analysts to efficiently investigate the parameter space and recognize ideal arrangements [11]. Fine-tuning hyperparameters upgrades demonstrate generalization and strength, driving to moved forward precision in temperament forecast assignments. Assessment measurements in music temperament classification include precision, exactness, review, and F1-score, giving comprehensive experiences into demonstrate execution over distinctive temperament categories [12]. Cross-validation procedures such as k-fold cross-validation guarantee thorough assessment and approval of show execution on assorted subsets of information, guaranteeing unwavering quality and generalizability [13]. Profound learning designs proceed to thrust the boundaries of music disposition classification, with Repetitive Neural Systems (RNNs) and Long Short-Term Memory (LSTM) systems proficient at capturing transient conditions and consecutive designs in music information [14]. These models exceed expectations in handling consecutive information such as music sound streams and expressive groupings, advertising upgraded precision and expressive control in temperament classification frameworks. Moreover, multimodal learning approaches have gained footing by joining data from numerous modalities, counting sound, verses, and metadata. By leveraging complementary prompts from distinctive modalities, multimodal models improve the strength and precision of disposition classification expectations [15]. These approaches emphasize the significance of coordination differing sources of data to attain a all encompassing understanding of music substance and setting. In rundown, the field of music temperament classification has advanced altogether through the selection of machine learning, profound learning, and multimodal approaches. Analysts proceed to investigate novel techniques and refine existing systems to address the complexities characteristic in music information investigation. The integration of progressed include extraction, outfit learning, and hyperparameter optimization has cleared the way for more precise and personalized music disposition classification frameworks, upgrading client encounters and applications in music suggestion and treatment [16]. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 237 https://internationalpubls.com Table 1: Summary of related Work Approach Algorithm Methodology Key Finding Application Traditional Heuristic Methods [17] Manual annotation, rule-based classification Subjectivity and scalability limitations; basic mood tagging Initial music categorization Machine Learning SVM [18] Feature extraction (e.g., MFCCs), supervised learning Captures nonlinear relationships in audio features; improves classification accuracy Automated mood tagging, recommendation systems Deep Learning CNN [19] Spectrogram processing, hierarchical feature extraction Efficient feature learning from audio signals; competitive performance in mood prediction High-dimensional audio data analysis, real-time mood classification Textual Analysis NLP [20] Sentiment analysis, thematic extraction Enhances contextual understanding of lyrics; improves accuracy when combined with audio features Lyrics-based mood classification, integration with audio- based models Ensemble Methods [21] SVM + Decision Trees Hybridization, combination of classifiers Improves predictive performance and robustness; synergistic effects of different algorithms Robust mood prediction models, handling diverse music datasets User-Centric Collaborative Filtering [22] User interaction data, preference modeling Personalizes mood recommendations based on user preferences; enhances user engagement Personalized music recommendation systems, user-driven music therapy Hyperparameter Grid Search, Bayesian Opt. [23] Systematic exploration of parameter space Optimizes model performance and generalization; fine-tuning enhances accuracy Enhancing model robustness and accuracy in mood classification Sequential Data RNN, LSTM [24] Temporal dependencies, sequential pattern learning Captures temporal aspects in music data; enhances predictive power in mood classification Sequential music analysis, dynamic mood tracking Multimodal Fusion of Audio and Text [25] Integration of multiple modalities, complementary cues Improves robustness and accuracy; holistic understanding of music content and context Enhanced music mood prediction, comprehensive music information retrieval Real-World Apps Music Recommendation Systems [26] Integration into practical applications Enhances user experiences; supports diverse music- related services and applications Personalized music services, therapeutic music applications 3. Dataset Description The presentation of a unused multi-modal feeling dataset for music, associated to MIREX benchmarks, marks a noteworthy headway in music feeling classification inquire about. This dataset comprises 903 sound clips, each 30 seconds long, organized into clusters and subfolders based on Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 238 https://internationalpubls.com passionate names. Moreover, it incorporates 764 verse records in content arrange and 196 MIDI records, making it the primary of its kind to consolidate these three unmistakable sourcesβ€”audio, verses, and MIDI. The overview of dataset and its feature value illustrate in figure 2. Figure 2: Dataset Features and Values This comprehensive dataset addresses the developing require for multimodal information in music feeling classification thinks about. By coordination sound signals, expressive substance, and melodic structure (spoken to by MIDI records), analysts pick up a more nuanced understanding of how distinctive modalities contribute to enthusiastic expression in music, the different class distribution in figure 3. Such datasets are pivotal for creating and approving machine learning models that can viably analyze and classify feelings in music, in this manner improving applications like personalized music suggestion frameworks and music treatment intercessions. Figure 3: Distribution of Class Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 239 https://internationalpubls.com 4. Methodology A. Data Input and Pre-process the data: Dataset preparation is an important step in getting data ready for machine learning jobs like figuring out how music makes people feel. At first, it includes checking all features for missing numbers to make sure the data is full and accurate. Depending on the size of the collection and the type of messiness, any numbers that are not present are either filled in using statistical methods or taken out. Next, columns that don't help with the classification job or have information that is already known are removed to make the dataset smaller and lower the noise in the training process for the model [27]. After the information is cleaned, number and classification features are split so that the right preparation steps can be done. Numerical features may be scaled to make their range more uniform. This makes sure that every feature adds the same amount to training the model. Using one-hot encoding and other methods, category traits like genre or mood labels are changed into a format that machine learning algorithms can understand. Label encoding, on the other hand, is used to make sure that category variables with numerical relationships are properly represented in the model. These steps make sure that the dataset is set up in the best way possible so that strong machine learning models can be trained to correctly identify music feelings from a variety of inputs. a. Numeric and Categorical Features Separation: Given a dataset D with n samples and m features, features can be categorized into: 1. Numeric Features: - Numeric features are continuous variables denoted as 𝑋_π‘›π‘’π‘š = {π‘₯_𝑖𝑗}_(𝑛 π‘₯ π‘š_π‘›π‘’π‘š) β€’ where x_ij represents the j-th numeric feature of the i-th sample. 2. Categorical Features: - Categorical features are discrete variables denoted as 𝑋_π‘π‘Žπ‘‘ = {𝑐_𝑖𝑗}_(𝑛 π‘₯ π‘š_π‘π‘Žπ‘‘) β€’ where c_ij represents the j-th categorical feature of the i-th sample. b. One-hot Encoding: For a categorical feature c_ij with q unique categories, the one-hot encoding OneHot(c_ij) is represented as a binary vector {0, 1}^q where: π‘‚π‘›π‘’π»π‘œπ‘‘(𝑐_𝑖𝑗) = [0, 0, . . . , 1, . . . , 0] β€’ Where, the position of 1 corresponds to the category of c_ij. For example, if c_ij takes the value of the second category out of q categories, the encoding would be [0, 1, 0, ..., 0]. c. Label Encoding: Label encoding assigns integers to categories preserving their order. For a categorical feature c_ij, Label Encode(c_ij) converts each category into a unique integer: Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 240 https://internationalpubls.com πΏπ‘Žπ‘π‘’π‘™πΈπ‘›π‘π‘œπ‘‘π‘’(𝑐_𝑖𝑗) = {0, 1, 2, . . . , π‘ž βˆ’ 1} β€’ Where, q is the number of unique categories in c_ij. Label encoding is suitable for algorithms that interpret ordinal relationships among categories, such as decision trees or regression models. d. Data Normalization Information normalization, particularly utilizing Standard Scaler, could be a preprocessing procedure fundamental for machine learning assignments. Standard Scaler changes numerical highlights to have a cruel of and a standard deviation of 1, guaranteeing that all highlights are on the same scale. Standard Scaler Step wise model 1. Compute Mean (ΞΌ) of Each Feature: πœ‡π‘— = ( 1 𝑛 ) 𝛴𝑖 = 1𝑛π‘₯𝑖𝑗 β€’ Calculate the mean value for each feature j across all samples i. 2. Compute Standard Deviation (Οƒ) of Each Feature: πœŽπ‘— = π‘ π‘žπ‘Ÿπ‘‘ (( 1 𝑛 ) 𝛴𝑖 = 1𝑛(π‘₯𝑖𝑗 βˆ’ πœ‡π‘—) 2 ) β€’ Calculate the standard deviation for each feature j across all samples i. 3. Standardize Each Feature: �̂�𝑖𝑗 = (π‘₯𝑖𝑗 βˆ’ πœ‡π‘—) πœŽπ‘— β€’ Standardize each feature j by subtracting its mean ΞΌ_j and dividing by its standard deviation Οƒ_j. This centers the feature distribution around 0 with a standard deviation of 1. 4. Transformed Feature Calculation: οΏ½Μ‚οΏ½ = (𝑋 βˆ’ πœ‡) 𝜎 β€’ Apply the transformation across all features X, where ΞΌ is the mean vector and Οƒ is the standard deviation vector calculated for each feature. 5. Inverse Transform: π‘‹π‘œπ‘Ÿπ‘–π‘”π‘–π‘›π‘Žπ‘™ = οΏ½Μ‚οΏ½ βˆ— 𝜎 + πœ‡ β€’ The transform the standardized data back to its original scale by multiplying with the standard deviation vector Οƒ and adding the mean vector ΞΌ. This normalization is significant for calculations touchy to the scale of input information, such as bolster vector machines and k-nearest neighbours. By standardizing highlights, Standard Scaler Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 241 https://internationalpubls.com makes strides the meeting speed of gradient-based calculations and anticipates overwhelming highlights from dominating others, normalized dataset shown in figure 4. Figure 4: Representation of Normalized Dataset It moreover makes a difference in deciphering show coefficients, making it less demanding to compare the significance of diverse highlights within the prescient demonstrate. In this way, Standard Scaler plays a key part in planning information for strong and effective machine learning show preparing. B. Machine Learning Classification Algorithms a. Logistic Regression: This is a linear model that is often used for jobs that need to classify things into two groups. It uses a logistic function to predict odds, which means it can be used to figure out how likely it is that a sample belongs to a certain class based on its traits. Algorithm: 1. Model Hypothesis: Logistic Regression models the probability 𝑃(𝑦_𝑖 = 1 | π‘₯_𝑖) that a sample x_i belongs to class 1 (positive mood) using a sigmoid function: 𝑃(𝑦_𝑖 = 1 | π‘₯_𝑖; 𝑀, 𝑏) = 𝜎(𝑀^𝑇 π‘₯_𝑖 + 𝑏) 2. Cost Function (Log-Loss): The objective is to maximize the likelihood of the observed data. The cost function for logistic regression is the log-loss function: 𝐽(𝑀, 𝑏) = βˆ’ 1 𝑛 𝛴𝑖 = 1𝑛[𝑦𝑖 log(𝜎(𝑀𝑇π‘₯𝑖 + 𝑏)) + (1 βˆ’ 𝑦𝑖) log(1 βˆ’ 𝜎(𝑀𝑇π‘₯𝑖 + 𝑏))] 3. Gradient Descent: Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 242 https://internationalpubls.com Update the parameters w and b iteratively to minimize the cost function: 𝑀𝑛𝑒𝑀 = π‘€π‘œπ‘™π‘‘β€“ 𝛼 βˆ— πœ•π½(𝑀, 𝑏) πœ•π‘€ 𝑏𝑛𝑒𝑀 = π‘π‘œπ‘™π‘‘ βˆ’ 𝛼 βˆ— πœ•π½(𝑀, 𝑏) πœ•π‘ 4. Gradient Calculation: Compute the gradients of the cost function with respect to w and b: πœ•π½(𝑀, 𝑏) πœ•π‘€ = 1 𝑛 𝛴𝑖 = 1𝑛(𝜎(𝑀𝑇π‘₯𝑖 + 𝑏) βˆ’ 𝑦𝑖) βˆ— π‘₯𝑖 πœ•π½(𝑀, 𝑏) πœ•π‘ = 1 𝑛 𝛴𝑖 = 1𝑛(𝜎(𝑀𝑇π‘₯𝑖 + 𝑏) βˆ’ 𝑦𝑖) 5. Prediction: After training, predict the probability 𝑃(𝑦 = 1 | π‘₯) for a new sample x: 𝑃(𝑦 = 1 | π‘₯; 𝑀, 𝑏) = 𝜎(𝑀^𝑇 π‘₯ + 𝑏) Classify based on the probability threshold (e.g., 0.5). 6. Regularization: Optionally, include regularization to prevent overfitting: 𝐽(𝑀, 𝑏) = βˆ’ 1 𝑛 𝛴𝑖 = 1𝑛[𝑦𝑖 log(𝜎(𝑀𝑇π‘₯𝑖 + 𝑏)) + (1 βˆ’ 𝑦𝑖) log(1 βˆ’ 𝜎(𝑀𝑇π‘₯𝑖 + 𝑏))] + πœ† ||𝑀|| 2 where Ξ» is the regularization parameter and ||w||^2 is the L2 norm of w. b. The Stochastic Gradient Descent (SGD) Classifier: It makes linear classifiers work better with convex loss functions. This makes it useful for learning on a big scale. It changes the model parameters over and over, which works well for situations with a lot of dimensions and big datasets. Stochastic Gradient Descent (SGD) Classifier: 1. Model Hypothesis: The SGD Classifier optimizes a linear model for binary classification tasks using a stochastic gradient descent approach. It estimates the π‘π‘Ÿπ‘œπ‘π‘Žπ‘π‘–π‘™π‘–π‘‘π‘¦ 𝑃(𝑦_𝑖 = 1 | π‘₯_𝑖) that a sample x_i belongs to class 1 (positive mood). 2. Loss Function: The objective is to minimize the loss function, typically the logistic loss for binary Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 243 https://internationalpubls.com classification: 𝐿(𝑀, 𝑏) = log(1 + exp(βˆ’π‘¦π‘– βˆ— (𝑀𝑇π‘₯𝑖 + 𝑏))) 3. Gradient Calculation: Compute the gradient of the loss function with respect to the parameters w (weight vector) and b (bias term): πœ•πΏ(𝑀, 𝑏) πœ•π‘€ = βˆ’π‘¦π‘– βˆ— π‘₯𝑖 (1 + exp(𝑦𝑖 βˆ— (𝑀𝑇π‘₯𝑖 + 𝑏))) πœ•πΏ(𝑀, 𝑏) πœ•π‘ = βˆ’ 𝑦𝑖 (1 + exp(𝑦𝑖 βˆ— (𝑀𝑇π‘₯𝑖 + 𝑏))) 4. Update Parameters: Update the parameters w and b iteratively using the gradients and a learning rate Ξ±: 𝑀𝑛𝑒𝑀 = π‘€π‘œπ‘™π‘‘β€“ 𝛼 βˆ— πœ•π½(𝑀, 𝑏) πœ•π‘€ 𝑏𝑛𝑒𝑀 = π‘π‘œπ‘™π‘‘ βˆ’ 𝛼 βˆ— πœ•π½(𝑀, 𝑏) πœ•π‘ 5. Prediction: After training, predict the probability P(y = 1 | x) for a new sample x using the updated parameters: 𝑃(𝑦 = 1 | π‘₯; 𝑀, 𝑏) = 1 / (1 + exp (βˆ’(𝑀^𝑇 π‘₯ + 𝑏))) Classify based on the probability threshold (e.g., 0.5). c. Gaussian Naive Bayes: It assumes that features are independent of each other and uses the Gaussian distribution for features that are continuous. Even though it makes some assumptions that are too simple, it does well at many classification tasks, especially text classification. Algorithm: 1. Model Assumption: Gaussian Naive Bayes assumes that features are conditionally independent given the class label y. It models the likelihood of observing feature values π‘₯_𝑖 = (π‘₯_{𝑖1}, π‘₯_{𝑖2}, . . . , π‘₯_{𝑖𝑑}) given class y_i using Gaussian distribution: 𝑃(π‘₯_𝑖 | 𝑦_𝑖, πœƒ_{𝑦_𝑖}) = 𝛱_{𝑗 = 1}^{𝑑} 𝑃(π‘₯ {𝑖𝑗}| 𝑦𝑖,πœƒ{𝑦𝑖}) ) 2. Parameter Estimation: Estimate the parameters ΞΈ_{y_i} of the Gaussian distribution for each class y_i: Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 244 https://internationalpubls.com βˆ’ π‘€π‘’π‘Žπ‘› πœ‡{𝑦𝑖,𝑗} = 1 |{𝑖 ∢ 𝑦𝑖 = 𝑦}|𝛴{𝑖:𝑦𝑖=𝑦}π‘₯{𝑖𝑗} βˆ’ π‘‰π‘Žπ‘Ÿπ‘–π‘Žπ‘›π‘π‘’ 𝜎{𝑦𝑖,𝑗} 2 = 1 |{𝑖 ∢ 𝑦𝑖 = 𝑦}|𝛴 {𝑖:𝑦𝑖=𝑦}(π‘₯{𝑖𝑗}βˆ’ πœ‡{𝑦𝑖,𝑗}) 2 3. Class Prior Probability: Estimate the prior probability P(y_i): 𝑃(𝑦𝑖) = |{𝑖 ∢ 𝑦𝑖 = 𝑦}| 𝑛 Where n is the total number of samples. 4. Predictive Probability: Calculate the posterior probability P(y_i | x_i) using Bayes' theorem: 𝑃(𝑦_𝑖 | π‘₯_𝑖) ∝ 𝑃(𝑦_𝑖) 𝛱_{𝑗 = 1}^{𝑑} 𝑃(π‘₯ {𝑖𝑗}| 𝑦𝑖,πœƒ{𝑦𝑖}) ) Substituting the Gaussian distribution: 𝑃(𝑦_𝑖 | π‘₯_𝑖) ∝ 𝑃(𝑦_𝑖) 𝛱_{𝑗 = ( 1 π‘ π‘žπ‘Ÿπ‘‘(2πœ‹πœŽ{𝑦𝑖,𝑗} 2 ) ) βˆ— exp (βˆ’ (π‘₯{𝑖𝑗} βˆ’ πœ‡{𝑦𝑖,𝑗}) 2 (2𝜎{𝑦𝑖,𝑗} 2 ) ) 5. Prediction: Classify a new sample x_i by selecting the class y_i that maximizes the posterior probability P(y_i | x_i): 𝑦_𝑖 βˆ— = π‘Žπ‘Ÿπ‘”π‘šπ‘Žπ‘₯{𝑦𝑖}𝑃(𝑦𝑖)𝛱{𝑗=1} 𝑃(π‘₯_{𝑖𝑗} | 𝑦_𝑖, πœƒ_{𝑦_𝑖}) d. Decision Tree: Decision trees use feature levels to repeatedly divide data into groups, making a structure that looks like a tree. They are easy to understand and use, and they can capture complex relationships between traits. However, they tend to overfit without being pruned. Decision Tree Model for Mood Analysis: 1. Tree Construction: Decision Trees recursively partition the feature space into disjoint regions by selecting feature thresholds that maximize information gain or minimize impurity measures. 2. Splitting Criterion: At each node, choose the split that best separates the data based on a chosen criterion (e.g., Gini impurity, entropy, or misclassification error). Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 245 https://internationalpubls.com - Gini Impurity: 𝐺𝑖𝑛𝑖(𝐷) = 1 βˆ’ 𝛴{𝑖=1} {π‘˜}(𝑝𝑖)2 where p_i is the probability of class i in node D. - Entropy: πΈπ‘›π‘‘π‘Ÿπ‘œπ‘π‘¦(𝐷) = βˆ’ 𝛴 {𝑖=1} 𝑖 {π‘˜}𝑝 π‘™π‘œπ‘”2(𝑝𝑖) where p_i is the probability of class i in node D. - Misclassification Error: π‘€π‘–π‘ π‘π‘™π‘Žπ‘ π‘ π‘–π‘“π‘–π‘π‘Žπ‘‘π‘–π‘œπ‘›πΈπ‘Ÿπ‘Ÿπ‘œπ‘Ÿ(𝐷) = 1 βˆ’ π‘šπ‘Žπ‘₯(𝑝_𝑖) where p_i is the maximum probability of class i in node D. 3. Recursive Splitting: Recursively split the data until a stopping criterion is met, such as maximum tree depth, minimum samples per leaf, or no further gain in impurity reduction. 4. Prediction: Assign the majority class of training samples in each leaf node as the predicted class for new instances falling into that leaf. e. Random Forest: A Random Forest is a group of decision trees, and each tree is trained on a different set of data and traits. By averaging results across multiple trees, it cuts down on overfitting and boosts accuracy, making it suitable for a wide range of classification tasks. Random Forest Model for Mood Analysis 1. Bootstrap Sampling: Randomly select n samples with replacement from the original dataset to create multiple bootstrap samples (also known as bagging). 2. Tree Construction: Build a decision tree for each bootstrap sample: - Select a random subset of features at each node. - Split nodes based on the best split according to a criterion (e.g., Gini impurity or entropy). 3. Ensemble Learning: Aggregate predictions from all decision trees to make final predictions: - For classification: Use majority voting among all decision trees. - For regression: Use the average of predictions from all decision trees. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 246 https://internationalpubls.com 4. Random Forest Prediction: Given a new sample x_i, predict its class y_i by aggregating predictions from all decision trees: 𝑦𝑖 βˆ— = π‘šπ‘œπ‘‘π‘’( {𝑇1(π‘₯𝑖), 𝑇2(π‘₯𝑖), … , 𝑇𝑛(π‘₯𝑖)}) where T_j(x_i) is the prediction of the j-th decision tree for sample x_i. 5. Out-of-Bag Error: Evaluate model performance using out-of-bag (OOB) samples: - For miss classification. 𝑂𝑂𝐡 πΈπ‘Ÿπ‘Ÿπ‘œπ‘Ÿ = 𝑛1βˆ‘π‘– = 1𝑛𝐼(𝑦𝑖 = 𝑦𝑖) - For regression Error: 𝑂𝑂𝐡 πΈπ‘Ÿπ‘Ÿπ‘œπ‘Ÿ = 𝑛1βˆ‘π‘– = 1𝑛(𝑦𝑖 βˆ’ 𝑦𝑖)2 f. XGB Classifier: The XGBoost Classifier is the best way to use gradient boosting to improve model performance through sequential ensemble learning. It makes predictions more accurate by reducing the number of loss and regularization terms. In competitions, it often gets the best results possible. XGBoost Classifier: Algorithm 1. Initialize Model: Start with initial predictions οΏ½Μ‚οΏ½_𝑖 = 0 for all samples. 2. Compute Gradient and Hessian: Compute the gradient 𝑔_𝑖 and the second derivative (Hessian) β„Ž_𝑖 of the loss function with respect to the predicted values οΏ½Μ‚οΏ½_𝑖: 𝑔𝑖 = πœ•πΏ(𝑦𝑖, �̂�𝑖) πœ•οΏ½Μ‚οΏ½π‘– β„Žπ‘– = πœ•2𝐿(𝑦𝑖, �̂�𝑖) πœ•(�̂�𝑖)2 3. Build a Decision Tree: Fit a regression tree to the gradient 𝑔_𝑖 as targets: - Split nodes to minimize the loss function within each leaf. 4. Update Predictions: Update predictions οΏ½Μ‚οΏ½_𝑖 using the fitted tree: �̂�𝑖 𝑑 = �̂�𝑖 π‘‘βˆ’1 + πœ‚ β‹… π‘‘π‘Ÿπ‘’π‘’π‘‘(π‘₯𝑖) Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 247 https://internationalpubls.com where πœ‚ is the learning rate and π‘‘π‘Ÿπ‘’π‘’_𝑑(π‘₯_𝑖) is the prediction of the 𝑑-th tree for sample π‘₯_𝑖. 5. Regularization: Add regularization terms to prevent overfitting: - Penalize large trees using regularization parameters like max_depth, min_child_weight, and gamma. 6. Repeat: Iterate steps 2-5 until a predefined number of trees (iterations) is reached or the loss function converges. g. SVM Linear: It finds the best hyperplane that divides classes in a collection that can be separated linearly. It makes the difference between classes as big as possible, which makes it good for binary classification jobs with lots of variables. SVM Linear Model 1. Objective Function: Minimize the objective function to find the optimal hyperplane: min 1 2 ||𝑀|| 2 subject to: 𝑦𝑖(𝑀𝑇π‘₯𝑖 + 𝑏) β‰₯ 1 π‘“π‘œπ‘Ÿ π‘Žπ‘™π‘™ 𝑖 = 1, … , 𝑛 2. Lagrangian Formulation: Formulate the Lagrangian with Lagrange multipliers 𝛼_𝑖 β‰₯ 0: 𝐿(𝑀, 𝑏, 𝛼) = 1 2 ||𝑀|| 2 βˆ’ 𝛴 {𝑖=1} 𝑖 {𝑛}𝛼 [𝑦𝑖(𝑀𝑇π‘₯𝑖+ 𝑏)βˆ’ 1] 3. Dual Problem: Maximize the dual function to find 𝛼 that maximizes the margin: max 𝛴 {𝑖=1} 𝑖 {𝑛}𝛼 βˆ’ 1 2 𝛴 {𝑖,𝑗=1} 𝑖 {𝑛}𝛼 𝛼𝑗𝑦𝑖𝑦𝑗π‘₯𝑖 𝑇π‘₯𝑗 subject to: 𝛴 {𝑖=1} 𝑖 {𝑛}𝛼 𝑦𝑖 = 0 𝛼𝑖 β‰₯ 0 π‘“π‘œπ‘Ÿ π‘Žπ‘™π‘™ 𝑖 = 1, … , 𝑛 4. Calculate 𝐰 and 𝑏: Compute 𝐰 and 𝑏 using the optimal 𝛼: Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 248 https://internationalpubls.com 𝑀 = 𝛴 {𝑖=1} 𝑖 {𝑛}𝛼 𝑦𝑖π‘₯𝑖 𝑏 = 𝑦𝑖 βˆ’ 𝑀𝑇π‘₯π‘–π‘“π‘œπ‘Ÿ π‘Žπ‘›π‘¦ 𝑖 π‘ π‘’π‘β„Ž π‘‘β„Žπ‘Žπ‘‘ 0 < 𝛼𝑖 < 𝐢 h. KNN: In the feature space, the K-Nearest Neighbors (KNN) method sorts a sample into a category based on the category that it’s K nearest neighbors belong to. It works well and is easy to use for small to medium-sized datasets, but because it learns slowly, it can be hard to run on big datasets. The result snapshot of mood classification using KNN illustrate in figure 4. Figure 4: Music Recommendation based on Mood using KNN K-Nearest Neighbors (KNN) Step wise Model 1. Training Phase: - Store all training samples {π‘₯_𝑖, 𝑦_𝑖} π‘“π‘œπ‘Ÿ 𝑖 = 1, . . . , 𝑛. βˆ’ π‘₯_𝑖 ∈ ℝ^𝑑 represents the feature vector of the 𝑖-th sample. βˆ’ 𝑦_𝑖 ∈ {1, . . . , 𝐾} denotes the class label of the 𝑖-th sample. 2. Prediction Phase: Given a new sample 𝐱_test, find its 𝐾 nearest neighbors in the training set based on a distance metric (e.g., Euclidean distance): 𝐷(π‘₯𝑖, π‘₯𝑑𝑒𝑠𝑑) = βˆšπ›΄{𝑗=1} {𝑑}(π‘₯{𝑖𝑗}– π‘₯{𝑑𝑒𝑠𝑑,𝑗}) 2 3. Voting Mechanism: - Count the occurrences of each class among the 𝐾 nearest neighbors. - Assign 𝐱_test to the class that is most common among its 𝐾 nearest neighbors. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 249 https://internationalpubls.com 4. Distance Weighting: - Weight the contribution of each neighbor to the prediction by the inverse of their distance: 𝑀𝑖 = 1 𝐷(π‘₯𝑖 , π‘₯𝑑𝑒𝑠𝑑)2 - Adjust the voting mechanism to consider the weighted sum of class labels. C. Hyper Parameters Fine-tuning on Best Performing Algorithms a. Random Forest with Fine-tuning Random Forest may be a capable gathering learning strategy that combines different choice trees to move forward prescient execution and diminish overfitting. Fine-tuning includes optimizing different parameters to upgrade show exactness and generalization. Parameters to Tune: β€’ Number of Trees (n_estimators): Determines the number of decision trees in the forest. Increasing n_estimators can improve model performance until a certain point, beyond which it may lead to overfitting. β€’ Tree Depth (max_depth): Controls the maximum depth of each decision tree. Deeper trees can capture more complex relationships in the data but may also overfit. β€’ Minimum Samples per Leaf (min_samples_leaf): Specifies the minimum number of samples required to be at a leaf node. Increasing min_samples_leaf can prevent overfitting by ensuring that each leaf node has sufficient samples. β€’ Feature Subset Size (max_features): Determines the number of features to consider when looking for the best split. Smaller max_features can reduce overfitting. β€’ Bootstrap Sampling (bootstrap): Specifies whether samples are drawn with or without replacement. Setting bootstrap=True enables bagging, which generally improves model performance. Fine-tuning Strategy: β€’ Grid Search or Random Search: Perform grid search over a predefined set of hyperparameters or random search across a specified range to find the optimal combination. β€’ Cross-validation: Use cross-validation to evaluate each combination of hyperparameters. This helps in selecting the set that provides the best generalization performance. b. XGBoost with Fine-tuning XGBoost is an advanced implementation of gradient boosting that offers better performance and efficiency over traditional gradient boosting methods. Fine-tuning XGBoost involves optimizing various parameters to achieve optimal performance. Parameters to Tune: β€’ Learning Rate (eta or learning_rate): Controls the step size at each iteration while moving toward a minimum of the loss function. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 250 https://internationalpubls.com β€’ Number of Trees (n_estimators): Specifies the number of boosting rounds or trees to build. β€’ Maximum Tree Depth (max_depth): Limits the depth of each tree. Deeper trees can model more complex relationships but may lead to overfitting. β€’ Subsample Ratio (subsample): Specifies the fraction of samples to be used for training each tree. Lower values prevent overfitting but may increase bias. β€’ Column Subsampling (colsample_bytree): Specifies the fraction of features to be randomly sampled for each tree. Fine-tuning Strategy: β€’ Grid Search or Random Search: Search over a grid of hyperparameters or randomly sample from a distribution of hyperparameters. β€’ Early Stopping: Use early stopping to halt the training process when model performance stops improving on a validation dataset. c. SVM with Fine-tuning Support Vector Machines (SVMs) are powerful supervised learning models used for classification and regression tasks. Fine-tuning SVM involves optimizing parameters that influence the decision boundary and regularization. Parameters to Tune: β€’ Kernel Choice and Parameters (kernel, C, gamma): Select the kernel type (linear, polynomial, radial basis function) and tune associated parameters. β€’ C: Penalty parameter for the error term. Controls the trade-off between maximizing the margin and minimizing classification error. β€’ Gamma: Kernel coefficient for β€˜rbf’, β€˜poly’, and β€˜sigmoid’. Higher values lead to tighter decision boundaries, potentially overfitting the training data. β€’ Regularization (C): Controls the trade-off between a larger margin and higher training error. Higher values of C allow more training points to be correctly classified at the cost of a smaller margin. β€’ Kernel Parameters (gamma): Influence the decision boundary's flexibility. Larger values of gamma can lead to overfitting. Fine-tuning Strategy: β€’ Grid Search or Random Search: Explore a grid of hyperparameters to find the combination that maximizes model performance. β€’ Cross-validation: Use cross-validation to evaluate each combination of hyperparameters and select the one with the best average performance across all folds. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 251 https://internationalpubls.com 5. Result and discussion A. Result for Machine Learning Algorithms Table 3 shows how well different machine learning classification methods worked with a dataset for mood analysis. For each algorithm, the table shows its Accuracy, Precision, Recall, and F1 Score. These measurements are very important for figuring out how well each program sorts the emotional tone of the data. It has an F1 Score of 0.541512, an accuracy of 0.568345, a precision of 0.548112, and a memory of 0.568345 to be exact. These results show that Logistic Regression does a decent job, but it could do better, especially when it comes to finding the right balance between accuracy and memory to raise the F1 Score. Table 3: Performance Metrics for ML Classification Algorithms for mood analysis dataset Algorithm Accuracy Precision Recall F1 Score Logistic Regression 0.568345 0.548112 0.568345 0.541512 SGD Classifier 0.266187 0.070856 0.266187 0.111920 Gaussian Naive Bayes 0.661871 0.664540 0.661871 0.649197 Decision Tree 0.748201 0.762372 0.748201 0.745440 Random Forest 0.856115 0.861950 0.856115 0.855389 XGB Classifier 0.827338 0.827626 0.827338 0.826412 SVM Linear 0.460432 0.628598 0.460432 0.414862 KNN 0.309353 0.292099 0.309353 0.294645 With an accuracy of 0.266187 and a very low precision of 0.070856, the SGD (Stochastic Gradient Descent) Classifier does a lot worse. At 0.266187 and 0.111920, the memory and F1 Score are also very low. This shows that SGD Classifier has trouble with the mood analysis job. This could be because it is sensitive to changing the size of features and the settings for parameters. With a score of 0.661871, Gaussian Naive Bayes is more accurate than Logistic Regression and SGD Classifier. It's accurate 0.664540 times, correct 0.661871 times, and has an F1 Score of 0.649197. These measurements show that it does a good job of dealing with the uncertain nature of the mood classification task, but it still needs to get better at being precise and remembering things. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 252 https://internationalpubls.com Figure 5: Representation of Performance comparison of Different ML Model With a score of 0.748201, the Decision Tree classification is much more accurate than before. They got a score of 0.745440 for F1 and a score of 0.762372 for precision. This shows that Decision Trees are good at finding the basic trends in data, but they can overfit, which can hurt their performance on data they haven't seen before. With an accuracy of 0.856115, Random Forest stands out. It also has a high F1 Score of 0.855389, an accuracy of 0.861950, and a memory of 0.856115. As you can see, these results show that ensemble methods, especially Random Forest, can handle difficult mood classification jobs with ease, comparison of different model shown in figure 5. With an accuracy of 0.827338, the XGBoost (XGB) Classifier also does very well. It's accurate 0.827626 times, accurate 0.827338 times, and has an F1 Score of 0.826412. The gradient boosting method in XGBoost makes it better at making predictions, which makes it very good at this classification problem. With a level of accuracy of 0.460432, SVM Linear does pretty well. The accuracy is higher at 0.628598, but the recall is lower at 0.460432. This gives it an F1 Score of 0.414862. This difference shows that SVM can make good guesses, but it might miss a lot of good examples, which would lower its total recall. K-Nearest Neighbors (KNN), which has an accuracy of 0.309353, is one of the worst. That number is 0.292099, the memory number is 0.309353, and the F1 Score number is 0.294645. These measures show that KNN has trouble with the mood analysis task. This might be because it is sensitive to the curse of dimensionality and needs to choose the right distance metric. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 253 https://internationalpubls.com Figure 6: Comparison accuracy of different Model Figure 6 shows a comparison of how accurate different models are, with Random Forest and XGB Classifier coming out on top. The confusion matrix, shown in figure 7, gives you a lot of information about how well each program does at classifying. (a) Logistic Regression (b) SGD Classifier Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 254 https://internationalpubls.com (c) Gaussian NaΓ―ve Bayes (d) Decision tree (e) Random Forest (f) XGB Classifier (g) SVM Classifier (h) KNN Classifier Figure 7: Confusion matrix of machine Learning Algorithms Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 255 https://internationalpubls.com B. Machine Learning Algorithms with Fine-tune Parameters Random Forest, XGB Classifier, and SVM Linear are three machine learning methods that were tested and their success was measured in Table 4. Accuracy, Precision, Recall, and F1 Score are some of the measures that give a full picture of how well each model did on the mood analysis dataset. Table 4: Result for Machine Learning Algorithms with Fine-tune Parameters Algorithm Accuracy Precision Recall F1 Score Random Forest 0.8619 0.86195 0.86 0.861 XGB Classifier 0.863 0.86 0.863 0.86 SVM Linear 0.8545 0.869 0.460432 0.8356 An accuracy of 0.8619 shows that the Random Forest algorithm works well even when things go wrong. The F1 Score is 0.861, which means that both precision and memory are good, at 0.86195 and 0.86, respectively. The model has a good mix between accuracy (the number of correctly predicted positive observations divided by the total number of correctly predicted positive observations) and recall (the number of correctly predicted positive observations divided by all observations in the real class). This model is very good at classifying things, as shown by its high F1 Score, the figure 8 illustrate the Comparison Graphs of Fine-tune Machine Learning Algorithms. Figure 8: Performance Comparison Graphs of Fine-tune Machine Learning Algorithms This makes Random Forest a good choice for analyzing mood. At 0.863, the XGBoost (XGB) Classifier is the most accurate of the three models. With an F1 Score of 0.86, this method also strikes a good mix between accuracy (0.86) and memory (0.863). Its better success is due in part to its ability to handle big datasets and its resistance to overfitting. Because recall is a little higher than Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 256 https://internationalpubls.com accuracy, it means that XGBoost is a little better at finding all positive instances. This is important in situations where losing a positive instance (like a mood) is more expensive than wrongly naming a negative instance as positive. Figure 9 shows confusion matrices show fine-tuned XGBoost and Random Forest models excelling in mood classification, with high accuracy and minimal misclassifications, highlighting their robust performance. (a) XG Boost (b) Random Forest (c) SVM Linear Figure 9: Confusion matrix fine tuner ML Models With an accuracy of 0.8545 and a precision of 0.869, the SVM Linear model is the most accurate of the three methods. Its F1 Score, on the other hand, drops to 0.8356 because its memory is much lower at 0.460432. This difference between accuracy and recall shows that the SVM Linear model is very accurate when it says something is positive, but it misses a lot of real positive cases. This mismatch makes me think that the model might be too cautious in its predictions, choosing to stay away from fake positives even if it means missing true positives. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 257 https://internationalpubls.com 6. Conclusion This study shows that fine-tuned machine learning methods can improve how well and how accurately music mood labeling works. Using different algorithms like Random Forest, XGBoost (XGB) Classifier, and SVM Linear, we saw big gains in accuracy, precision, recall, and F1 score, among other performance measures. The performance analysis showed that Random Forest and XGB Classifier did a better job. Random Forest was a good model for this job; it had an accuracy of 0.8619 and a good mix between precision and memory. Its group nature successfully lowers overfitting and raises the level of generalization. The XGB Classifier also had the best accuracy, at 0.863, which showed how well it handled complex data structures and how resistant it was to overfitting thanks to its gradient boosting method. The confusion vectors for these models showed that they could reduce the number of both false positives and false negatives, which added to the evidence that they are reliable in real-world situations. Careful adjustment of hyperparameters during the fine-tuning process was a key part of these results, making sure that each model worked at its best level of performance. Even though SVM Linear was very accurate, it had a lower recall, which means it missed some true positives. This means that SVM can make good guesses, but it needs more work to find the best mix between accuracy and memory. Fine-tuning machine learning algorithms makes them much better at figuring out the mood of music. Random Forest and XGB Classifier stand out as the best options because they are very accurate and do well on all measures. These results show how important model selection and hyperparameter improvement are for making music mood recognition systems that work well and are reliable. 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