[Paper Review] Multimodal Retrieval With Asymmetrically Weighted Truncated-SVD Canonical Correlation Analysis.

Youssef Mroueh, Etienne Marcheret+1 more|arXiv (Cornell University)|Nov 19, 2015

Domain Adaptation and Few-Shot Learning3 citations

TL;DR

This paper proposes an asymmetrically weighted truncated-SVD canonical correlation analysis (T-SVD CCA) for multimodal retrieval, enabling efficient bidirectional image and sentence retrieval. By introducing task-specific asymmetric weighting and an efficient regularization path computation, the method improves numerical stability and generalization, with T-SVD CCA showing faster computation than Tikhonov regularization.

ABSTRACT

Joint modeling of language and vision has been drawing increasing interest. A multimodal data representation allowing for bidirectional retrieval of images by sentences and vice versa is a key aspect of this modeling. In this paper we show that canonical correlation analysis (CCA) can be adapted to bidirectional retrieval by a simple task dependent asymmetric weighting, which solves optimally the retrieval problem in a least squares sense. While regularizing CCA is known to improve numerical stability as well as generalization performance, less attention has been brought to the efficient computation of the regularization path of CCA, which is key to model selection. In this paper we develop efficient algorithms to compute the full regularization path of CCA within the classical Tikhonov and the truncated SVD (T-SVD CCA) regularization frameworks. T-SVD CCA is new to the best of our knowledge, and its regularization path can be computed more efficiently than its Tikhonov counterpart.

Motivation & Objective

• Address the challenge of bidirectional multimodal retrieval between images and text using canonical correlation analysis (CCA).
• Improve numerical stability and generalization in CCA through effective regularization.
• Develop efficient algorithms for computing the full regularization path under both Tikhonov and truncated SVD (T-SVD) regularization frameworks.
• Introduce T-SVD CCA as a novel, more computationally efficient alternative to standard Tikhonov-regularized CCA.
• Enable task-dependent asymmetric weighting to optimize retrieval performance in a least squares sense.

Proposed method

• Adapt CCA with asymmetric weighting to optimize bidirectional retrieval performance in a least squares framework.
• Introduce truncated SVD (T-SVD) regularization to CCA, enabling a new regularization path computation method.
• Develop efficient algorithms to compute the full regularization path under both Tikhonov and T-SVD CCA frameworks.
• Use task-specific asymmetric weights to prioritize retrieval direction (e.g., text-to-image or image-to-text) during optimization.
• Leverage the structure of truncated SVD to reduce computational cost while maintaining model performance.
• Formulate the optimization problem to minimize reconstruction error in a least squares sense, with regularization ensuring stability.

Experimental results

Research questions

• RQ1 Can asymmetric weighting in CCA improve bidirectional retrieval performance in a least squares optimization framework?
• RQ2 How does T-SVD CCA compare to Tikhonov-regularized CCA in terms of computational efficiency and model stability?
• RQ3 What is the most efficient way to compute the full regularization path for CCA in multimodal learning?
• RQ4 Can T-SVD CCA be effectively applied to joint language-vision representation learning with improved generalization?
• RQ5 Does the proposed method maintain or improve retrieval accuracy while reducing computational cost?

Key findings

• The proposed asymmetrically weighted T-SVD CCA achieves better numerical stability and generalization performance than standard CCA.
• T-SVD CCA enables more efficient computation of the regularization path compared to the Tikhonov-regularized counterpart.
• The regularization path for T-SVD CCA can be computed more efficiently than for Tikhonov-regularized CCA, reducing computational overhead.
• The method supports effective bidirectional retrieval by optimizing for retrieval tasks with asymmetric weighting.
• The proposed framework provides a scalable and stable solution for joint language-vision representation learning.
• The use of truncated SVD in CCA regularization leads to improved computational efficiency without sacrificing model performance.