This paper presents a robust matrix elastic net based canonical correlation analysis (RMEN-CCA) for multiple view unsupervised learning problems, which emphasizes the combination of CCA and the robust matrix elastic net (RMEN) used as coupled feature selection. The RMEN-CCA leverages the strength of the RMEN to distill naturally meaningful features without any prior assumption and to measure effectively correlations between different 'views'. We can further employ directly the kernel trick to extend the RMEN-CCA to the kernel scenario with theoretical guarantees, which takes advantage of the kernel trick for highly complicated nonlinear feature learning. Rather than simply incorporating existing regularization minimization terms into CCA, this paper provides a new learning paradigm for CCA and is the first to derive a coupled feature selection based CCA algorithm that guarantees convergence. More significantly, for CCA, the newly-derived RMEN-CCA bridges the gap between measurement of relevance and coupled feature selection. Moreover, it is nontrivial to tackle directly the RMEN-CCA by previous optimization approaches derived from its sophisticated model architecture. Therefore, this paper further offers a bridge between a new optimization problem and an existing efficient iterative approach. As a consequence, the RMEN-CCA can overcome the limitation of CCA and address large-scale and streaming data problems. Experimental results on four popular competing datasets illustrate that the RMEN-CCA performs more effectively and efficiently than do state-of-the-art approaches.
@cite_19: Multi-target regression has recently regained great popularity due to its capability of simultaneously learning multiple relevant regression tasks and its wide applications in data mining, computer vision and medical image analysis, while great challenges arise from jointly handling inter-target correlations and input-output relationships. In this paper, we propose Multi-layer Multi-target Regression (MMR) which enables simultaneously modeling intrinsic inter-target correlations and nonlinear input-output relationships in a general framework via robust low-rank learning. Specifically, the MMR can explicitly encode inter-target correlations in a structure matrix by matrix elastic nets (MEN); the MMR can work in conjunction with the kernel trick to effectively disentangle highly complex nonlinear input-output relationships; the MMR can be efficiently solved by a new alternating optimization algorithm with guaranteed convergence. The MMR leverages the strength of kernel methods for nonlinear feature learning and the structural advantage of multi-layer learning architectures for inter-target correlation modeling. More importantly, it offers a new multi-layer learning paradigm for multi-target regression which is endowed with high generality, flexibility and expressive ability. Extensive experimental evaluation on 18 diverse real-world datasets demonstrates that our MMR can achieve consistently high performance and outperforms representative state-of-the-art algorithms, which shows its great effectiveness and generality for multivariate prediction.
@cite_13: 
@cite_39: We observe (Xi,Yi)i=1n where the Yi's are real valued outputs and the Xi's are m × T matrices. We observe a new entry X and we want to predict the output Y associated with it. We focus on the high-dimensional setting, where mT ≫ n. This includes the matrix completion problem with noise, as well as other problems. We consider linear prediction procedures based on different penalizations, involving a mixture of several norms: the nuclear norm, the Frobenius norm and the l1-norm. For these procedures, we prove sharp oracle inequalities, using a statistical learning theory point of view. A surprising fact in our results is that the rates of convergence do not depend on m and T directly. The analysis is conducted without the usually considered incoherency condition on the unknown matrix or restricted isometry condition on the sampling operator. Moreover, our results are the first to give for this problem an analysis of penalization (such as nuclear norm penalization) as a regularization algorithm: our oracle inequalities prove that these procedures have a prediction accuracy close to the deterministic oracle one, given that the reguralization parameters are well-chosen.
In recent years, the feature selection technique plays an important role in machine learning community. This technique is desired to extract numerous useful features and to eliminate redundancies, in order to construct a simple model architecture. To overcome the limitations of conventional feature selection approaches such as Lasso and Ridge, etc., a combined feature selection approach, termed matrix elastic net (MEN), has been successfully used for different learning algorithms @cite_39 @cite_13 @cite_19 .