Asymmetrically Weighted CCA And Hierarchical Kernel Sentence Embedding For Multimodal Retrieval

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 a cross-view mapping of the search space to the query space achieves state of the art performance in bidirectional retrieval using off the shelf features. We show that this search to query mapping can be implemented by a simple asymmetric weighting of the canonical correlation weights, where the canonical weights of the search space are weighted by the canonical correlations. We revisit regularization for Canonical Correlation Analysis (CCA) within the framework of spectral filtering and the Bjork Golub algorithm. We present our regularized CCA algorithms within two spectral filtering regularization families: Tikhonov regularization and truncated SVD (T-SVD) regularization . T-SVD regularization is new to the best of our knowledge in the context of CCA and is faster to cross-validate than Tikhonov regularized CCA at the price of a small loss in accuracy. In light of the spectral filtering interpretation of the regularizer, we devise a fast method to choose the regularization parameter in the Tikhonov regularized CCA, using the regularization path of T-SVD CCA and the singular values of the data matrices.