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 multiview 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 multi-view canonical correlation maximization problem is equivalent to finding the best rank-1 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.

There is growing interest in multilabel image classification due to its critical role in web-based image analytics-based applications, such as large-scale image retrieval and browsing. Matrix completion (MC) has recently been introduced as a method for transductive (semisupervised) multilabel classification, and has several distinct advantages, including robustness to missing data and background noise in both feature and label space. However, it is limited by only considering data represented by a single-view feature, which cannot precisely characterize images containing several semantic concepts. To utilize multiple features taken from different views, we have to concatenate the different features as a long vector. However, this concatenation is prone to over-fitting and often leads to very high time complexity in MC-based image classification. Therefore, we propose to weightedly combine the MC outputs of different views, and present the multiview MC (MVMC) framework for transductive multilabel image classification. To learn the view combination weights effectively, we apply a cross-validation strategy on the labeled set. In particular, MVMC splits the labeled set into two parts, and predicts the labels of one part using the known labels of the other part. The predicted labels are then used to learn the view combination coefficients. In the learning process, we adopt the average precision (AP) loss, which is particular suitable for multilabel image classification, since the ranking-based criteria are critical for evaluating a multilabel classification system. A least squares loss formulation is also presented for the sake of efficiency, and the robustness of the algorithm based on the AP loss compared with the other losses is investigated. Experimental evaluation on two real-world data sets (PASCAL VOC' 07 and MIR Flickr) demonstrate the effectiveness of MVMC for transductive (semisupervised) multilabel image classification, and show that MVMC can exploit complementary properties of different features and output-consistent labels for improved multilabel image classification.

It is a significant challenge to classify images with multiple labels by using only a small number of labeled samples. One option is to learn a binary classifier for each label and use manifold regularization to improve the classification performance by exploring the underlying geometric structure of the data distribution. However, such an approach does not perform well in practice when images from multiple concepts are represented by high-dimensional visual features. Thus, manifold regularization is insufficient to control the model complexity. In this paper, we propose a manifold regularized multitask learning (MRMTL) algorithm. MRMTL learns a discriminative subspace shared by multiple classification tasks by exploiting the common structure of these tasks. It effectively controls the model complexity because different tasks limit one another's search volume, and the manifold regularization ensures that the functions in the shared hypothesis space are smooth along the data manifold. We conduct extensive experiments, on the PASCAL VOC'07 dataset with 20 classes and the MIR dataset with 38 classes, by comparing MRMTL with popular image classification algorithms. The results suggest that MRMTL is effective for image classification.

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 multiview 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 multi-view canonical correlation maximization problem is equivalent to finding the best rank-1 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.