Probabilistic Linear Discriminant Analysis With Vectorial Representation for Tensor Data.

Area of Science:

• Pattern Recognition
• Data Analysis
• Machine Learning

Background:

• Traditional Linear Discriminant Analysis (LDA) struggles with high-order tensor data due to vectorization or high-dimensional tensor outputs.
• Existing tensor LDA methods often preserve the high-order structure, leading to complexity.

Purpose of the Study:

• To propose a new probabilistic LDA (PLDA) model, termed tensor PLDA, specifically designed for high-order tensorial data.
• To address the limitations of traditional LDA and existing tensor LDA methods in handling complex data structures.

Main Methods:

• Decomposition of tensorial data into shared subspace, individual subspace, and noise components.
• Modeling subspace components using linear combinations of latent tensor bases.
• Assuming a multivariate Gaussian distribution for the noise component.
• Employing Bayesian inference for model learning.
• Utilizing tensor CandeComp/PARAFAC (CP) decomposition for tensor bases to reduce parameters.

Main Results:

• The proposed tensor PLDA model demonstrates effective performance in both data reconstruction and classification tasks.
• Experimental results show the model is superior or comparable to existing LDA-based methods.
• The model successfully handles the inherent structure of high-order tensor data.

Conclusions:

• Tensor PLDA offers a robust and effective approach for feature extraction and dimension reduction in high-order tensorial data.
• The probabilistic framework and tensor decomposition techniques provide advantages over traditional methods.
• This model advances pattern recognition capabilities for complex, multi-dimensional datasets.