In this paper, we propose to learn shared semantic space with correlation alignment ( @math ) for multimodal data representations, which aligns nonlinear correlations of multimodal data distributions in deep neural networks designed for heterogeneous data. In the context of cross-modal (event) retrieval, we design a neural network with convolutional layers and fully-connected layers to extract features for images, including images on Flickr-like social media. Simultaneously, we exploit a fully-connected neural network to extract semantic features for texts, including news articles from news media. In particular, nonlinear correlations of layer activations in the two neural networks are aligned with correlation alignment during the joint training of the networks. Furthermore, we project the multimodal data into a shared semantic space for cross-modal (event) retrieval, where the distances between heterogeneous data samples can be measured directly. In addition, we contribute a Wiki-Flickr Event dataset, where the multimodal data samples are not describing each other in pairs like the existing paired datasets, but all of them are describing semantic events. Extensive experiments conducted on both paired and unpaired datasets manifest the effectiveness of @math , outperforming the state-of-the-art methods.
Statistical correlation models are designed to learn a subspace where cross-modal data are aligned from the perspective of statistics. Canonical correlation analysis (CCA) @cite_6 is a representative work, which projects two sets of data to a common subspace where their correlations are maximized. Similar to CCA, cross-modal factor analysis (CFA) @cite_2 minimized the Frobenius norm between the transformed cross-modal data. Kernel-CCA @cite_6 introduced kernel functions for nonlinear correlations, which is the kernel extension of CCA. @cite_26 learned a semantic space using CCA representation and semantic category information for cross-modal retrieval tasks. @cite_1 proposed a generalized multi-view analysis (GMA) as a supervised extension of CCA. Multi-view CCA @cite_14 extended CCA by incorporating the high-level image semantic keywords as the third view. Multi-label CCA @cite_15 took the multi-label annotations to establish correspondences, without relying on the pairwise modalities like CCA. As pointed out by @cite_20 , using CCA directly may lead to coarse subspace, and the relationships between real data are too complicated to be captured by linear projections alone.
@cite_14 @cite_26 @cite_1 @cite_6 @cite_2 @cite_15 @cite_20
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In this work, we address the problem of cross-modal retrieval in presence of multi-label annotations. In particular, we introduce multi-label Canonical Correlation Analysis (ml-CCA), an extension of CCA, for learning shared subspaces taking into account high level semantic information in the form of multi-label annotations. Unlike CCA, ml-CCA does not rely on explicit pairing between modalities, instead it uses the multi-label information to establish correspondences. This results in a discriminative subspace which is better suited for cross-modal retrieval tasks. We also present Fast ml-CCA, a computationally efficient version of ml-CCA, which is able to handle large scale datasets. We show the efficacy of our approach by conducting extensive cross-modal retrieval experiments on three standard benchmark datasets. The results show that the proposed approach achieves state of the art retrieval performance on the three datasets. A new algorithm via Canonical Correlation Analysis (CCA) is developed in this paper to support more effective cross-modal image clustering for large-scale annotated image collections. It can be treated as a bi-media multimodal mapping problem and modeled as a correlation distribution over multimodal feature representations. It integrates the multimodal feature generation with the Locality Linear Coding (LLC) and co-occurrence association network, multimodal feature fusion with CCA, and accelerated hierarchical k-means clustering, which aims to characterize the correlations between the inter-related visual features in images and semantic features in captions, and measure their association degree more precisely. Very positive results were obtained in our experiments using a large quantity of public data. Canonical correlation analysis (CCA) has proven an effective tool for two-view dimension reduction due to its profound theoretical foundation and success in practical applications. In respect of multi-view learning, however, it is limited by its capability of only handling data represented by two-view features, while in many real-world applications, the number of views is frequently many more. Although the ad hoc way of simultaneously exploring all possible pairs of features can numerically deal with multi-view data, it ignores the high order statistics (correlation information) which can only be discovered by simultaneously exploring all features. Therefore, in this work, we develop tensor CCA (TCCA) which straightforwardly yet naturally generalizes CCA to handle the data of an arbitrary number of views by analyzing the covariance tensor of the different views. TCCA aims to directly maximize the canonical correlation of multiple (more than two) views. Crucially, we prove that the main problem of multi-view canonical correlation maximization is equivalent to finding the best rank- @math approximation of the data covariance tensor, which can be solved efficiently using the well-known alternating least squares (ALS) algorithm. As a consequence, the high order correlation information contained in the different views is explored and thus a more reliable common subspace shared by all features can be obtained. In addition, a non-linear extension of TCCA is presented. Experiments on various challenge tasks, including large scale biometric structure prediction, internet advertisement classification, and web image annotation, demonstrate the effectiveness of the proposed method Canonical Correlation Analysis (CCA) is a well-known technique for finding the correlations between two sets of multidimensional variables. It projects both sets of variables onto a lower-dimensional space in which they are maximally correlated. CCA is commonly applied for supervised dimensionality reduction in which the two sets of variables are derived from the data and the class labels, respectively. It is well-known that CCA can be formulated as a least-squares problem in the binary class case. However, the extension to the more general setting remains unclear. In this paper, we show that under a mild condition which tends to hold for high-dimensional data, CCA in the multilabel case can be formulated as a least-squares problem. Based on this equivalence relationship, efficient algorithms for solving least-squares problems can be applied to scale CCA to very large data sets. In addition, we propose several CCA extensions, including the sparse CCA formulation based on the 1-norm regularization. We further extend the least-squares formulation to partial least squares. In addition, we show that the CCA projection for one set of variables is independent of the regularization on the other set of multidimensional variables, providing new insights on the effect of regularization on CCA. We have conducted experiments using benchmark data sets. Experiments on multilabel data sets confirm the established equivalence relationships. Results also demonstrate the effectiveness and efficiency of the proposed CCA extensions.