Feature Extraction for Incomplete Data Via Low-Rank Tensor Decomposition With Feature Regularization.

Area of Science:

• Machine Learning
• Computer Vision
• Data Science

Background:

• Incomplete multidimensional data (tensors) present challenges for feature extraction in fields like machine learning and computer vision.
• Existing tensor completion methods primarily focus on data recovery, not effective feature extraction from incomplete tensors.

Purpose of the Study:

• To address the underexplored problem of unsupervised feature extraction from incomplete tensors.
• To develop a unified framework combining low-rank tensor decomposition with feature variance maximization.

Main Methods:

• Proposed two Tensor Decomposition with Feature Variance Maximization (TDVM) methods: TDVM-Tucker and TDVM-CP, based on orthogonal Tucker and CP decompositions.
• Incorporated feature regularization into a general low-rank tensor approximation model.
• Developed a joint optimization scheme using alternating direction method of multipliers and block coordinate descent.

Main Results:

• TDVM methods extract informative features directly from observed entries by maximizing feature variance and approximating missing data via low-rank tensor decomposition.
• Evaluated on six real-world image and video datasets under a novel multiblock missing setting.
• Demonstrated superior performance compared to state-of-the-art approaches in face recognition, object/action classification, and clustering tasks.

Conclusions:

• The proposed TDVM methods offer an effective solution for unsupervised feature extraction from incomplete tensors.
• The framework provides a robust approach for handling missing data while simultaneously learning discriminative features.
• The methods show significant potential for applications in pattern recognition and computer vision with incomplete data.