Nhat Truong Pham

(†) denotes equal contribution

(*) denotes correspondance

denotes journal

denotes conference

2024

1. 

   Mol2Lang-VLM: Vision- and Text-Guided Generative Pre-trained Language Models for Advancing Molecule Captioning through Multimodal Fusion

   Duong Thanh Tran^(†), Nhat Truong Pham^(†), Nguyen Doan Hieu Nguyen, and Balachandran Manavalan

   In Proceedings of the 1st Workshop on Language + Molecules (L+M 2024), 2024

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   This paper introduces Mol2Lang-VLM, an enhanced method for refining generative pre-trained language models for molecule captioning using multimodal features to achieve more accurate caption generation. Our approach leverages the encoder and decoder blocks of the Transformer-based architecture by introducing third sub-layers into both. Specifically, we insert sub-layers in the encoder to fuse features from SELFIES strings and molecular images, while the decoder fuses features from SMILES strings and their corresponding descriptions. Moreover, cross multi-head attention is employed instead of common multi-head attention to enable the decoder to attend to the encoder’s output, thereby integrating the encoded contextual information for better and more accurate caption generation. Performance evaluation on the CheBI-20 and L+M-24 benchmark datasets demonstrates Mol2Lang-VLM’s superiority, achieving higher accuracy and quality in caption generation compared to existing methods. Our code and pre-processed data are available at https://github.com/nhattruongpham/mol-lang-bridge/tree/mol2lang/.

   @inproceedings{tran2024mollangvlm,
     title = {Mol2Lang-{VLM}: Vision- and Text-Guided Generative Pre-trained Language Models for Advancing Molecule Captioning through Multimodal Fusion},
     author = {Tran, Duong Thanh and Pham, Nhat Truong and Nguyen, Nguyen Doan Hieu and Manavalan, Balachandran},
     booktitle = {Proceedings of the 1st Workshop on Language + Molecules L+M 2024},
     pages = {97--102},
     year = {2024},
     doi = {10.18653/v1/2024.langmol-1.12},
   }

2. 

   Lang2Mol-Diff: A Diffusion-Based Generative Model for Language-to-Molecule Translation Leveraging SELFIES Molecular String Representation

   Nguyen Doan Hieu Nguyen^(†), Nhat Truong Pham^(†), Duong Thanh Tran, and Balachandran Manavalan

   In Proceedings of the 1st Workshop on Language + Molecules (L+M 2024), 2024

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   Generating de novo molecules from textual descriptions is challenging due to potential issues with molecule validity in SMILES representation and limitations of autoregressive models. This work introduces Lang2Mol-Diff, a diffusion-based language-to-molecule generative model using the SELFIES representation. Specifically, Lang2Mol-Diff leverages the strengths of two state-of-the-art molecular generative models: BioT5 and TGM-DLM. By employing BioT5 to tokenize the SELFIES representation, Lang2Mol-Diff addresses the validity issues associated with SMILES strings. Additionally, it incorporates a text diffusion mechanism from TGM-DLM to overcome the limitations of autoregressive models in this domain. To the best of our knowledge, this is the first study to leverage the diffusion mechanism for text-based de novo molecule generation using the SELFIES molecular string representation. Performance evaluation on the L+M-24 benchmark dataset shows that Lang2Mol-Diff outperforms all existing methods for molecule generation in terms of validity. Our code and pre-processed data are available at https://github.com/nhattruongpham/mol-lang-bridge/tree/lang2mol/.

   @inproceedings{nguyen2024langmoldiff,
     title = {Lang2Mol-Diff: A Diffusion-Based Generative Model for Language-to-Molecule Translation Leveraging SELFIES Molecular String Representation},
     author = {Nguyen, Nguyen Doan Hieu and Pham, Nhat Truong and Tran, Duong Thanh and Manavalan, Balachandran},
     booktitle = {Proceedings of the 1st Workshop on Language + Molecules L+M 2024},
     pages = {128--134},
     year = {2024},
     doi = {10.18653/v1/2024.langmol-1.15},
   }

3. 

   HOTGpred: Enhancing human O-linked threonine glycosylation prediction using integrated pretrained protein language model-based features and multi-stage feature selection approach

   Nhat Truong Pham^(†), Ying Zhang^(†), Rajan Rakkiyappan, and Balachandran Manavalan

   Computers in Biology and Medicine, 2024

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   O-linked glycosylation is a complex post-translational modification (PTM) in human proteins that plays a critical role in regulating various cellular metabolic and signaling pathways. In contrast to N-linked glycosylation, O-linked glycosylation lacks specific sequence features and maintains an unstable core structure. Identifying O-linked threonine glycosylation sites (OTGs) remains challenging, requiring extensive experimental tests. While bioinformatics tools have emerged for predicting OTGs, their reliance on limited conventional features and absence of well-defined feature selection strategies limit their effectiveness. To address these limitations, we introduced HOTGpred (Human O-linked Threonine Glycosylation predictor), employing a multi-stage feature selection process to identify the optimal feature set for accurately identifying OTGs. Initially, we assessed 25 different feature sets derived from various pretrained protein language model (PLM)-based embeddings and conventional feature descriptors using nine classifiers. Subsequently, we integrated the top five embeddings linearly and determined the most effective scoring function for ranking hybrid features, identifying the optimal feature set through a process of sequential forward search. Among the classifiers, the extreme gradient boosting (XGBT)-based model, using the optimal feature set (HOTGpred), achieved 92.03% accuracy on the training dataset and 88.25% on the balanced independent dataset. Notably, HOTGpred significantly outperformed the current state-of-the-art methods on both the balanced and imbalanced independent datasets, demonstrating its superior prediction capabilities. Additionally, SHapley Additive exPlanations (SHAP) and ablation analyses were conducted to identify the features contributing most significantly to HOTGpred. Finally, we developed an easy-to-navigate web server, accessible at https://balalab-skku.org/HOTGpred/, to support glycobiologists in their research on glycosylation structure and function.

   @article{pham2024hotgpred,
     title = {HOTGpred: Enhancing human O-linked threonine glycosylation prediction using integrated pretrained protein language model-based features and multi-stage feature selection approach},
     author = {Pham, Nhat Truong and Zhang, Ying and Rakkiyappan, Rajan and Manavalan, Balachandran},
     journal = {Computers in Biology and Medicine},
     volume = {179},
     pages = {108859},
     year = {2024},
     publisher = {Elsevier},
     doi = {10.1016/j.compbiomed.2024.108859},
   }

4. 

   mACPpred 2.0: Stacked Deep Learning for Anticancer Peptide Prediction with Integrated Spatial and Probabilistic Feature Representations

   Vinoth Kumar Sangaraju^(†), Nhat Truong Pham^(†), Leyi Wei, Xue Yu, and Balachandran Manavalan

   Journal of Molecular Biology, 2024

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   Anticancer peptides (ACPs), naturally occurring molecules with remarkable potential to target and kill cancer cells. However, identifying ACPs based solely from their primary amino acid sequences remains a major hurdle in immunoinformatics. In the past, several web-based machine learning (ML) tools have been proposed to assist researchers in identifying potential ACPs for further testing. Notably, our meta- approach method, mACPpred, introduced in 2019, has significantly advanced the field of ACP research. Given the exponential growth in the number of characterized ACPs, there is now a pressing need to create an updated version of mACPpred. To develop mACPpred 2.0, we constructed an up-to-date benchmarking dataset by integrating all publicly available ACP datasets. We employed a large-scale of feature descriptors, encompassing both conventional feature descriptors and advanced pre-trained natural language processing (NLP)-based embeddings. We evaluated their ability to discriminate between ACPs and non-ACPs using eleven different classifiers. Subsequently, we employed a stacked deep learning (SDL) approach, incorporating 1D convolutional neural network (1D CNN) blocks and hybrid features. These features included the top seven performing NLP-based features and 90 probabilistic features, allowing us to identify hidden patterns within these diverse features and improve the accuracy of our ACP prediction model. This is the first study to integrate spatial and probabilistic feature representations for predicting ACPs. Rigorous cross-validation and independent tests conclusively demonstrated that mACPpred 2.0 not only surpassed its predecessor (mACPpred) but also outperformed the existing state-of-the-art predictors, highlighting the importance of advanced feature representation capabilities attained through SDL. To facilitate widespread use and accessibility, we have developed a user-friendly for mACPpred 2.0, available at https://balalab-skku.org/mACPpred2/.

   @article{sangaraju2024macppred,
     title = {mACPpred 2.0: Stacked Deep Learning for Anticancer Peptide Prediction with Integrated Spatial and Probabilistic Feature Representations},
     author = {Sangaraju, Vinoth Kumar and Pham, Nhat Truong and Wei, Leyi and Yu, Xue and Manavalan, Balachandran},
     journal = {Journal of Molecular Biology},
     volume = {436},
     number = {17},
     pages = {168687},
     year = {2024},
     publisher = {Elsevier},
     doi = {10.1016/j.jmb.2024.168687},
   }

5. 

   ac4C-AFL: A high-precision identification of human mRNA N4-acetylcytidine sites based on adaptive feature representation learning

   Nhat Truong Pham, Annie Terrina Terrance, Young-Jun Jeon, Rajan Rakkiyappan, and Balachandran Manavalan

   Molecular Therapy-Nucleic Acids, 2024

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   RNA N4-acetylcytidine (ac4C) is a highly conserved RNA modification that plays a crucial role in controlling mRNA stability, processing, and translation. Consequently, accurate identification of ac4C sites across the genome is critical for understanding gene expression regulation mechanisms. In this study, we have developed ac4C-AFL, a bioinformatics tool that precisely identifies ac4C sites from primary RNA sequences. In ac4C-AFL, we identified the optimal sequence length for model building and implemented an adaptive feature representation strategy that is capable of extracting the most representative features from RNA. To identify the most relevant features, we proposed a novel ensemble feature importance scoring strategy to rank features effectively. We then used this information to conduct the sequential forward search, which individually determine the optimal feature set from the 16 sequence-derived feature descriptors. Utilizing these optimal feature descriptors, we constructed 176 baseline models using 11 popular classifiers. The most efficient baseline models were identified using the two-step feature selection approach, whose predicted scores were integrated and trained with the appropriate classifier to develop the final prediction model. Our rigorous cross-validations and independent tests demonstrate that ac4C-AFL surpasses contemporary tools in predicting ac4C sites. Moreover, we have developed a publicly accessible web server at https://balalab-skku.org/ac4C-AFL/.

   @article{pham2024ac4c,
     title = {ac4C-AFL: A high-precision identification of human mRNA N4-acetylcytidine sites based on adaptive feature representation learning},
     author = {Pham, Nhat Truong and Terrance, Annie Terrina and Jeon, Young-Jun and Rakkiyappan, Rajan and Manavalan, Balachandran},
     journal = {Molecular Therapy-Nucleic Acids},
     volume = {35},
     number = {2},
     pages = {102192},
     year = {2024},
     publisher = {Elsevier},
     doi = {10.1016/j.omtn.2024.102192},
   }

6. 

   H2Opred: a robust and efficient hybrid deep learning model for predicting 2’-O-methylation sites in human RNA

   Nhat Truong Pham, Rajan Rakkiyappan, Jongsun Park, Adeel Malik, and Balachandran Manavalan

   Briefings in Bioinformatics, 2024

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   2’-O-methylation (2OM) is the most common post-transcriptional modification of RNA. It plays a crucial role in RNA splicing, RNA stability and innate immunity. Despite advances in high-throughput detection, the chemical stability of 2OM makes it difficult to detect and map in messenger RNA. Therefore, bioinformatics tools have been developed using machine learning (ML) algorithms to identify 2OM sites. These tools have made significant progress, but their performances remain unsatisfactory and need further improvement. In this study, we introduced H2Opred, a novel hybrid deep learning (HDL) model for accurately identifying 2OM sites in human RNA. Notably, this is the first application of HDL in developing four nucleotide-specific models [adenine (A2OM), cytosine (C2OM), guanine (G2OM) and uracil (U2OM)] as well as a generic model (N2OM). H2Opred incorporated both stacked 1D convolutional neural network (1D-CNN) blocks and stacked attention-based bidirectional gated recurrent unit (Bi-GRU-Att) blocks. 1D-CNN blocks learned effective feature representations from 14 conventional descriptors, while Bi-GRU-Att blocks learned feature representations from five natural language processing-based embeddings extracted from RNA sequences. H2Opred integrated these feature representations to make the final prediction. Rigorous cross-validation analysis demonstrated that H2Opred consistently outperforms conventional ML-based single-feature models on five different datasets. Moreover, the generic model of H2Opred demonstrated a remarkable performance on both training and testing datasets, significantly outperforming the existing predictor and other four nucleotide-specific H2Opred models. To enhance accessibility and usability, we have deployed a user-friendly web server for H2Opred, accessible at https://balalab-skku.org/H2Opred/. This platform will serve as an invaluable tool for accurately predicting 2OM sites within human RNA, thereby facilitating broader applications in relevant research endeavors.

   @article{pham2024h2opred,
     title = {H2Opred: a robust and efficient hybrid deep learning model for predicting 2'-O-methylation sites in human RNA},
     author = {Pham, Nhat Truong and Rakkiyappan, Rajan and Park, Jongsun and Malik, Adeel and Manavalan, Balachandran},
     journal = {Briefings in Bioinformatics},
     volume = {25},
     number = {1},
     pages = {bbad476},
     year = {2024},
     publisher = {OxfOxford University Pressord},
     doi = {10.1093/bib/bbad476},
   }

7. 

   Advancing the accuracy of SARS-CoV-2 phosphorylation site detection via meta-learning approach

   Nhat Truong Pham^(†), Le Thi Phan^(†), Jimin Seo, Yeonwoo Kim, Minkyung Song, Sukchan Lee, Young-Jun Jeon, and Balachandran Manavalan

   Briefings in Bioinformatics, 2024

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   The worldwide appearance of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has generated significant concern and posed a considerable challenge to global health. Phosphorylation is a common post-translational modification that affects many vital cellular functions and is closely associated with SARS-CoV-2 infection. Precise identification of phosphorylation sites could provide more in-depth insight into the processes underlying SARS-CoV-2 infection and help alleviate the continuing coronavirus disease 2019 (COVID-19) crisis. Currently, available computational tools for predicting these sites lack accuracy and effectiveness. In this study, we designed an innovative meta-learning model, Meta-Learning for Serine/Threonine Phosphorylation (MeL-STPhos), to precisely identify protein phosphorylation sites. We initially performed a comprehensive assessment of 29 unique sequence-derived features, establishing prediction models for each using 14 renowned machine learning methods, ranging from traditional classifiers to advanced deep learning algorithms. We then selected the most effective model for each feature by integrating the predicted values. Rigorous feature selection strategies were employed to identify the optimal base models and classifier(s) for each cell-specific dataset. To the best of our knowledge, this is the first study to report two cell-specific models and a generic model for phosphorylation site prediction by utilizing an extensive range of sequence-derived features and machine learning algorithms. Extensive cross-validation and independent testing revealed that MeL-STPhos surpasses existing state-of-the-art tools for phosphorylation site prediction. We also developed a publicly accessible platform at https://balalab-skku.org/MeL-STPhos/. We believe that MeL-STPhos will serve as a valuable tool for accelerating the discovery of serine/threonine phosphorylation sites and elucidating their role in post-translational regulation.

   @article{pham2024advancing,
     title = {Advancing the accuracy of SARS-CoV-2 phosphorylation site detection via meta-learning approach},
     author = {Pham, Nhat Truong and Phan, Le Thi and Seo, Jimin and Kim, Yeonwoo and Song, Minkyung and Lee, Sukchan and Jeon, Young-Jun and Manavalan, Balachandran},
     journal = {Briefings in Bioinformatics},
     volume = {25},
     number = {1},
     pages = {bbad433},
     year = {2024},
     publisher = {OxfOxford University Pressord},
     doi = {10.1093/bib/bbad433},
   }

2023

1. 

   AAD-Net: Advanced end-to-end signal processing system for human emotion detection & recognition using attention-based deep echo state network

   Mustaqeem Khan, Abdulmotaleb El Saddik, Fahd Saleh Alotaibi, and Nhat Truong Pham

   Knowledge-Based Systems, 2023

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   Speech signals are the most convenient way of communication between human beings and the eventual method of Human-Computer Interaction (HCI) to exchange emotions and information. Recognizing emotions from speech signals is a challenging task due to the sparse nature of emotional data and features. In this article, we proposed a Deep Echo-State-Network (DeepESN) system for emotion recognition with a dilated convolution neural network and multi-headed attention mechanism. To reduce the model complexity, we incorporate a DeepESN that combines reservoir computing for higher-dimensional mapping. We also used fine-tuned Sparse Random Projection (SRP) to reduce dimensionality and adopted an early fusion strategy to fuse the extracted cues and passed the joint feature vector via a classification layer to recognize emotions. Our proposed model is evaluated on two public speech corpora, EMO-DB and RAVDESS, and tested for subject/speaker-dependent/independent performance. The results show that our proposed system achieves a high recognition rate, 91.14, 85.57 for EMO-DB, and 82.01, 77.02 for RAVDESS, using speaker-dependent and independent experiments, respectively. Our proposed system outperforms the State-of-The-Art (SOTA) while requiring less computational time.

   @article{mustaqeem2023aad,
     title = {AAD-Net: Advanced end-to-end signal processing system for human emotion detection \ recognition using attention-based deep echo state network},
     author = {Khan, Mustaqeem and El Saddik, Abdulmotaleb and Alotaibi, Fahd Saleh and Pham, Nhat Truong},
     journal = {Knowledge-Based Systems},
     volume = {270},
     pages = {110525},
     year = {2023},
     publisher = {Elsevier},
     doi = {10.1016/j.knosys.2023.110525},
   }

2. 

   Hybrid data augmentation and deep attention-based dilated convolutional-recurrent neural networks for speech emotion recognition

   Nhat Truong Pham, Duc Ngoc Minh Dang, Ngoc Duy Nguyen, Thanh Thi Nguyen, Hai Nguyen, Balachandran Manavalan, Chee Peng Lim, and Sy Dzung Nguyen

   Expert Systems with Applications, 2023

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   Recently, speech emotion recognition (SER) has become an active research area in speech processing, particularly with the advent of deep learning (DL). Numerous DL-based methods have been proposed for SER. However, most of the existing DL-based models are complex and require a large amounts of data to achieve a good performance. In this study, a new framework of deep attention-based dilated convolutional-recurrent neural networks coupled with a hybrid data augmentation method was proposed for addressing SER tasks. The hybrid data augmentation method constitutes an upsampling technique for generating more speech data samples based on the traditional and generative adversarial network approaches. By leveraging both convolutional and recurrent neural networks in a dilated form along with an attention mechanism, the proposed DL framework can extract high-level representations from three-dimensional log Mel spectrogram features. Dilated convolutional neural networks acquire larger receptive fields, whereas dilated recurrent neural networks overcome complex dependencies as well as the vanishing and exploding gradient issues. Furthermore, the loss functions are reconfigured by combining the SoftMax loss and the center-based losses to classify various emotional states. The proposed framework was implemented using the Python programming language and the TensorFlow deep learning library. To validate the proposed framework, the EmoDB and ERC benchmark datasets, which are imbalanced and/or small datasets, were employed. The experimental results indicate that the proposed framework outperforms other related state-of-the-art methods, yielding the highest unweighted recall rates of 88.03 ± 1.39 (%) and 66.56 ± 0.67 (%) for the EmoDB and ERC datasets, respectively.

   @article{pham2023hybrid,
     title = {Hybrid data augmentation and deep attention-based dilated convolutional-recurrent neural networks for speech emotion recognition},
     author = {Pham, Nhat Truong and Dang, Duc Ngoc Minh and Nguyen, Ngoc Duy and Nguyen, Thanh Thi and Nguyen, Hai and Manavalan, Balachandran and Lim, Chee Peng and Nguyen, Sy Dzung},
     journal = {Expert Systems with Applications},
     pages = {120608},
     year = {2023},
     publisher = {Elsevier},
     doi = {10.1016/j.eswa.2023.120608},
   }

3. 

   Fruit-CoV: An efficient vision-based framework for speedy detection and diagnosis of SARS-CoV-2 infections through recorded cough sounds

   Long H Nguyen^(†), Nhat Truong Pham^(†)(*), Van Huong Do, Liu Tai Nguyen, Thanh Tin Nguyen, Hai Nguyen, Ngoc Duy Nguyen, Thanh Thi Nguyen, Sy Dzung Nguyen, Asim Bhatti, and Chee Peng Lim

   Expert Systems with Applications, 2023

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   COVID-19 is an infectious disease caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). This deadly virus has spread worldwide, leading to a global pandemic since March 2020. A recent variant of SARS-CoV-2 named Delta is intractably contagious and responsible for more than four million deaths globally. Therefore, developing an efficient self-testing service for SARS-CoV-2 at home is vital. In this study, a two-stage vision-based framework, namely Fruit-CoV, is introduced for detecting SARS-CoV-2 infections through recorded cough sounds. Specifically, audio signals are converted into Log-Mel spectrograms, and the EfficientNet-V2 network is used to extract their visual features in the first stage. In the second stage, 14 convolutional layers extracted from the large-scale Pretrained Audio Neural Networks for audio pattern recognition (PANNs) and the Wavegram-Log-Mel-CNN are employed to aggregate feature representations of the Log-Mel spectrograms and the waveform. Finally, the combined features are used to train a binary classifier. In this study, a dataset provided by the AICovidVN 115M Challenge is employed for evaluation. It includes 7,371 recorded cough sounds collected throughout Vietnam, India, and Switzerland. Experimental results indicate that the proposed model achieves an Area Under the Receiver Operating Characteristic Curve (AUC) score of 92.8% and ranks first on the final leaderboard of the AICovidVN 115M Challenge. Our code is publicly available.

   @article{nguyen2023fruit,
     title = {Fruit-CoV: An efficient vision-based framework for speedy detection and diagnosis of SARS-CoV-2 infections through recorded cough sounds},
     author = {Nguyen, Long H and Pham, Nhat Truong and Do, Van Huong and Nguyen, Liu Tai and Nguyen, Thanh Tin and Nguyen, Hai and Nguyen, Ngoc Duy and Nguyen, Thanh Thi and Nguyen, Sy Dzung and Bhatti, Asim and Lim, Chee Peng},
     journal = {Expert Systems with Applications},
     volume = {213},
     pages = {119212},
     year = {2023},
     publisher = {Elsevier},
     doi = {10.1016/j.eswa.2022.119212},
   }

2022

1. 

   Improving ligand-ranking of AutoDock Vina by changing the empirical parameters

   T Ngoc Han Pham, Trung Hai Nguyen, Nguyen Minh Tam, Thien Y. Vu, Nhat Truong Pham, Nguyen Truong Huy, Binh Khanh Mai, Nguyen Thanh Tung, Minh Quan Pham, Van V. Vu, and Son Tung Ngo

   Journal of Computational Chemistry, 2022

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   AutoDock Vina (Vina) achieved a very high docking-success rate, p̂, but give a rather low correlation coefficient, R, for binding affinity with respect to experiments. This low correlation can be an obstacle for ranking of ligand-binding affinity, which is the main objective of docking simulations. In this context, we evaluated the dependence of Vina R coefficient upon its empirical parameters. R is affected more by changing the gauss2 and rotation than other terms. The docking-success rate p̂ is sensitive to the alterations of the gauss1, gauss2, repulsion, and hydrogen bond parameters. Based on our benchmarks, the parameter set1 has been suggested to be the most optimal. The testing study over 800 complexes indicated that the modified Vina provided higher correlation with experiment R_set1=0.556±0.025 compared with R_Default=0.493±0.028 obtained by the original Vina and R_{Vina 1.2}=0.503±0.029 by Vina version 1.2. Besides, the modified Vina can be also applied more widely, giving R ≥ 0.500 for 32/48 targets, compared with the default package, giving R ≥ 0.500 for 31/48 targets. In addition, validation calculations for 1036 complexes obtained from version 2019 of PDBbind refined structures showed that the set1 of parameters gave higher correlation coefficient (R_set1=0.617±0.017) than the default package (R_Default=0.543±0.020) and Vina version 1.2 (R_{Vina 1.2}=0.540±0.020). The version of Vina with set1 of parameters can be downloaded at https://github.com/sontungngo/mvina/. The outcomes would enhance the ranking of ligand-binding affinity using Autodock Vina.

   @article{pham2022improving,
     title = {Improving ligand-ranking of AutoDock Vina by changing the empirical parameters},
     author = {Pham, T Ngoc Han and Nguyen, Trung Hai and Tam, Nguyen Minh and Y. Vu, Thien and Pham, Nhat Truong and Huy, Nguyen Truong and Mai, Binh Khanh and Tung, Nguyen Thanh and Pham, Minh Quan and V. Vu, Van and Ngo, Son Tung},
     journal = {Journal of Computational Chemistry},
     volume = {43},
     number = {3},
     pages = {160--169},
     year = {2022},
     publisher = {Wiley Online Library},
     doi = {10.1002/jcc.26779},
   }

2. 

   Determination of the optimal number of clusters: a fuzzy-set based method

   Sy Dzung Nguyen, Vu Song Thuy Nguyen, and Nhat Truong Pham

   IEEE Transactions on Fuzzy Systems, 2022

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   The optimal number of clusters (C_opt) is one of the determinants of clustering efficiency. In this article, we present a new method of quantifying C_opt for centroid-based clustering. First, we propose a new clustering validity index named fRisk(C) based on the fuzzy set theory. It takes the role of normalization and accumulation of local risks coming from each action either splitting data from a cluster or merging data into a cluster. fRisk(C) exploits the local distribution information of the database to catch the global information of the clustering process in the form of the risk degree. Based on the monotonous reduction property of fRisk(C), which is proved theoretically, we present a fRisk-based new algorithm named fRisk4-bA for determining C_opt. In the algorithm, the well-known L-method is employed as a supplemented tool to catch C_opt on the graph of the fRisk(C). Along with the stable convergence trend of the method to be proved theoretically, numerical surveys are also carried out. The surveys show that the high reliability and stability, as well as the sensitivity in separating/merging clusters in high-density areas, even if the presence of noise in the databases, are the strong points of the proposed method.

   @article{nguyen2022determination,
     title = {Determination of the optimal number of clusters: a fuzzy-set based method},
     author = {Nguyen, Sy Dzung and Nguyen, Vu Song Thuy and Pham, Nhat Truong},
     journal = {IEEE Transactions on Fuzzy Systems},
     volume = {30},
     number = {9},
     pages = {3514--3526},
     year = {2022},
     publisher = {IEEE},
     doi = {10.1109/TFUZZ.2021.3118113},
   }