Learning Compact Discriminant Representation via Low-Rank Bilinear Pooling.

Area of Science:

• Computer Science
• Machine Learning
• Computer Vision

Background:

• Bilinear pooling generates discriminative features but suffers from high dimensionality and variance, leading to overfitting.
• Principal Component Analysis (PCA) is a dimensionality reduction technique that can be applied to bilinear features.
• Existing factorization bilinear pooling methods may not optimally preserve feature discriminability.

Purpose of the Study:

• To address overfitting in bilinear pooling by reducing feature dimensionality and variance.
• To develop a mathematically grounded method for dimension reduction in bilinear features.
• To propose a novel bilinear pooling method that is computationally efficient and effective.

Main Methods:

• Constructed a bi-level optimization problem combining classification loss and PCA.
• Proved PCA on bilinear features is equivalent to spectral clustering, establishing a lower bound for dimension reduction.
• Proposed rank-k general bilinear projection (RK-GBP) to decompose the PCA projection matrix.
• Developed rank-k orthogonal factorization bilinear pooling (RK-OFBP) by relaxing PCA to dictionary learning for efficiency.

Main Results:

• Mathematically proved that the first log2(C) principal components capture discriminant information for C classes.
• Demonstrated that RK-OFBP simultaneously reduces dimensionality and variance of bilinear features.
• Achieved comparable classification performance to existing methods (e.g., B-CNN) using significantly lower dimensional features (e.g., 32-dimensional vectors).

Conclusions:

• The proposed RK-OFBP method effectively mitigates overfitting in bilinear pooling through principled dimension reduction.
• RK-OFBP offers a general and efficient approach to factorization bilinear pooling, outperforming prior methods on fine-grained and large-scale datasets.
• This work provides the first theoretical lower bound for dimension reduction in bilinear pooling and a practical, high-performing implementation.