Mode Coresets for Efficient, Interpretable Tensor Decompositions: An Application to Feature Selection in fMRI...

Area of Science:

• Multidimensional data analysis
• Machine learning
• Numerical linear algebra

Background:

• Tensor decompositions generalize matrix decompositions for analyzing multidimensional data.
• Modern datasets' large size presents challenges in balancing computational complexity and approximation accuracy.
• Subset-based methods offer efficiency, but deterministic approaches can improve approximations and enable feature selection.

Purpose of the Study:

• To introduce an efficient subset-based Tucker decomposition using coresets.
• To enable a novel feature selection scheme for tensor data.
• To balance computational efficiency with high-fidelity tensor approximation.

Main Methods:

• Selecting coresets from tensor modes to approximate the full tensor.
• Developing random and deterministic coreset selection methods.
• Minimizing error using a discrepancy measure between the coreset and the full tensor.

Main Results:

• The proposed method allows for efficient Tucker decomposition via coresets.
• Demonstrated a novel feature selection capability for tensor data.
• Achieved better tensor approximation with comparable computational complexity compared to existing methods.

Conclusions:

• Subset-based tensor decomposition with coresets is an efficient approach for large datasets.
• The method offers a unique feature selection capability.
• This technique provides a favorable balance between computational cost and approximation accuracy.