Vectorial Dimension Reduction for Tensors Based on Bayesian Inference.

Area of Science:

• Data Science
• Machine Learning
• Applied Mathematics

Background:

• High-order tensor dimension reduction is complex.
• Conventional methods like Tucker decomposition are computationally intensive.
• Existing methods struggle with exponential parameter growth in higher-order tensors.

Purpose of the Study:

• Introduce a novel probabilistic vectorial dimension reduction model for tensorial data.
• Develop a method for direct tensor-to-vector reduction.
• Improve efficiency and accuracy in dimensionality reduction for tensors.

Main Methods:

• Representing tensors as linear combinations of basis tensors.
• Utilizing tensor CandeComp/PARAFAC (CP) decomposition for projection bases.
• Employing Bayesian inference via variational Expectation Maximization (EM) approach.
• Establishing an empirical criterion for parameter selection (CP factor number, feature count).

Main Results:

• The proposed model exhibits linear growth in parameters with tensor modes, unlike exponential growth in conventional methods.
• Demonstrated superior performance over principal component analysis (PCA)-based methods and CP decomposition.
• Achieved higher classification and clustering accuracy on publicly available datasets.

Conclusions:

• The probabilistic vectorial dimension reduction model offers an efficient and accurate approach for tensorial data.
• The model effectively addresses the challenges of high-order tensor dimensionality reduction.
• This method provides a significant advancement for applications involving complex tensor data.