Wrapped Cauchy Distributed Angular Softmax for Long-Tailed Visual Recognition
This work addresses the problem of imbalanced data in visual recognition for computer vision applications, offering an incremental improvement over existing softmax-based methods.
The paper tackles long-tailed visual recognition by proposing the Wrapped Cauchy Distributed Angular Softmax (WCDAS), a novel softmax function that incorporates Gaussian-based kernels to mitigate noise and sparse sampling, achieving state-of-the-art performance on multiple benchmark datasets.
Addressing imbalanced or long-tailed data is a major challenge in visual recognition tasks due to disparities between training and testing distributions and issues with data noise. We propose the Wrapped Cauchy Distributed Angular Softmax (WCDAS), a novel softmax function that incorporates data-wise Gaussian-based kernels into the angular correlation between feature representations and classifier weights, effectively mitigating noise and sparse sampling concerns. The class-wise distribution of angular representation becomes a sum of these kernels. Our theoretical analysis reveals that the wrapped Cauchy distribution excels the Gaussian distribution in approximating mixed distributions. Additionally, WCDAS uses trainable concentration parameters to dynamically adjust the compactness and margin of each class. Empirical results confirm label-aware behavior in these parameters and demonstrate WCDAS's superiority over other state-of-the-art softmax-based methods in handling long-tailed visual recognition across multiple benchmark datasets. The code is public available.