ManlyMM-VAE: Deep Clustering With Manly Transformation Mixture Latent Embeddings for High-Dimensional Skewed Data

Area of Science:

• Machine Learning
• Data Science
• Statistical Modeling

Background:

• Clustering high-dimensional data is challenging with non-symmetric noise.
• Asymmetric distributions are crucial for accurate data representation and subspace learning.
• Existing methods struggle with mixed left- and right-skewed data within groups.

Purpose of the Study:

• To propose a novel deep generative clustering model, ManlyMM-VAE.
• To address the challenge of clustering data with asymmetric, non-Gaussian distributions.
• To effectively handle variables with varying degrees of skewness.

Main Methods:

• Developed ManlyMM-VAE, a variational autoencoder (VAE) based model.
• Incorporated the Manly transformation to flexibly adjust variable skewness.
• Utilized a Manly transformation mixture model as the latent space prior.
• Employed stochastic gradient variational Bayes (SGVB) for parameter optimization.
• Introduced a cross-validation procedure for model selection.

Main Results:

• ManlyMM-VAE demonstrated effective clustering of data with varying skewness.
• The model achieved significantly higher accuracy compared to competing methods on synthetic and real-world datasets.
• Robustness was confirmed through clustering experiments on corrupted image data.

Conclusions:

• ManlyMM-VAE provides a robust and accurate solution for clustering asymmetric, non-Gaussian data.
• The Manly transformation effectively handles mixed left- and right-skewed variables.
• The proposed model advances deep generative clustering for complex data structures.