Variational autoencoders (VAEs) with symmetric mixture priors have shown exceptional performance in clustering applications. However, these methods often struggle with asymmetrical distributions and extreme values. Many fields, such as medical imaging, bioinformatics, finance, and atmospheric science, frequently deal with right‐skewed data. To address this, we propose a novel VAE clustering approach that utilizes a gamma mixture prior, effectively accommodating right‐skewed distributions. Our findings highlight the significance of selecting an appropriate distribution for the data. The proposed method demonstrates the ability to achieve a more parsimonious model with fewer parameters compared to other deep learning clustering techniques, which is essential for clustering high‐dimensional data with small sample sizes. We evaluate our approach on both synthetic and real right‐skewed datasets, demonstrating superior clustering performance compared to existing deep generative clustering methods and traditional statistical models.

Background and ObjectivesAccurate measurement of the QT interval from electrocardiogram (ECG) signals is essential for assessing ventricular repolarization and arrhythmia risk; however, it remains a challenging task due to inter-observer variability in manual annotation and the limited robustness of conventional automated methods, particularly in detecting the T-wave offset. Many existing automated approaches estimate the QT interval as a single regression value, which restricts clinical interpretability because waveform boundaries cannot be explicitly verified. This study proposes QTANet, a boundary-aware framework that provides clinically interpretable QT interval estimation by explicitly detecting QRS onset and T-wave offset.MethodsQTANet performs frame-level ECG waveform classification and derives QT intervals based on detected physiological landmarks. The framework integrates a ResNet-based convolutional encoder for morphological feature extraction, discrete wavelet transform for noise-robust frequency analysis, bidirectional LSTM for temporal context modeling, and self-attention mechanisms that emphasize boundary transitions. A dynamically weighted focal loss was employed to address class imbalance. The model was trained and validated on the Lobachevsky University Database (LUDB) using five-fold cross-validation, and externally evaluated on the QT Database (QTDB; n=105) and an independent clinical dataset from Chonnam National University Hospital (CNUH; n=23).ResultsOn LUDB, QTANet achieved a frame-level classification accuracy of 94.5% (F1: 92.8%) and a QT interval estimation MAE of 12.08 ± 17.65 ms (Pearson’s r = 0.84). On external datasets, the model maintained consistent performance (QTDB: MAE 28.63 ± 36.11 ms, r = 0.63; CNUH: MAE 17.47 ± 23.17 ms, r = 0.78), outperforming both the ResNet+LSTM regression baseline and the rule-based NeuroKit2 approach across all metrics.ConclusionsBoundary-aware QT interval estimation through explicit waveform landmark detection provides a clinically interpretable and robust alternative to black-box regression methods. The proposed framework enables visual verification of detected boundaries and demonstrates consistent performance across heterogeneous recording conditions, suggesting its potential utility as a decision-support tool in cardiac monitoring and pharmacovigilance.

Clustering in high-dimensional data becomes particularly challenging when noise deviates from symmetric, zero-mean distributions such as the Gaussian or Laplace distribution. In these cases, asymmetric non-Gaussian distributions provide a more accurate representation of the data's structure, especially when learning low-dimensional subspaces. However, selecting an appropriate family of asymmetric distributions is difficult when variables within each group exhibit varying degrees of skewness-some being right-skewed and others left-skewed. In this study, we propose a novel deep generative clustering model, ManlyMM-VAE, based on the variational autoencoder (VAE) framework. The model incorporates the Manly transformation, a parametric technique that flexibly adjusts the skewness of each variable, effectively handling both right- and left-skewed data. A Manly transformation mixture model serves as the prior in the latent space. The evidence lower bound (ELBO) is derived using the stochastic gradient variational Bayes (SGVB) estimator to optimize model parameters. We also introduce a cross-validation procedure for model selection. Experimental results on both synthetic and real-world datasets show that ManlyMM-VAE effectively clusters data with varying skewness, achieving significantly higher accuracy than competing methods. Furthermore, its robustness is confirmed through clustering experiments on image data corrupted to various degrees.

Accurate QT-interval measurement requires reliable identification of QRS onset and T-wave offset. We present QTANet, a single-lead framework that classifies ECG samples as baseline, QRS or T wave and derives QT from the detected landmarks. We used 179 recordings from the Lobachevsky University Electrocardiography Database, with a fixed test set and patient-wise cross-validation, and external evaluation without fine-tuning on the QT Database (QTDB) and 33 clinical recordings. On the expert-annotated QTDB interval subset of 101 recordings, QTANet achieved a mean absolute error of 34.94 ms and measurement coverage of 95.2%, compared with 40.55 ms and 88.2% for the control without attention and 52.41 ms and 68.7% for NeuroKit2. In a separate expert-annotated subset permitting frame-level evaluation, attention increased per-recording T-wave F1 by 0.061, with improvement in 30 of 41 recordings. Attention most consistently reduced T waves misread as QRS complexes. QTANet outperformed an identically trained published U-Net externally at frame level but had higher internal QT error; a larger modern U-Net outperformed QTANet at frame level and in QTDB QT error. Internal interval-level gains were small and clinical results varied across training seeds. These findings support boundary-derived QT measurement with jointly reported error and coverage; clinical utility requires further validation.