Subspace Learning Based On Latent Space

The ubiquitous digit devices,sensors and social networks bring tremendous highdimensional data.The high-dimensionality leads to high time complexity,large storage burden,and degradation of the generalization ability.Subspace learning is one of the most effective ways to eliminate the curse of dimensionality by projecting the data to a low-dimensional feature subspace.For Multi-view data,the traditional single-view subspace can only learning with one view of the data.To exploit the complementary information from multiple views,numbers of multi-view learning methods have been developed and achieve superior performances in comparison with single-view learning.In this work we consider both the single-view high-dimensionality data and the multiview high-dimensionality for subspace learning.In many practical applications,the high expense of labelling data and the data explosion make most data unlabelled.Without label information,unsupervised subspace learning is more challenging due to the lack of label information.In this paper,we proposed the Analysis-Synthesis Dictionary Learning(ASDL)and the Multi-view Predictive Latent Space Learning(MVP),both of the methods are based on unsupervised subspace learning.For the ASDL,we project a sample to a low-dimensional space by learning an analysis dictionary and the feature dimension is the number of atoms in the dictionary.The coding coefficient vector is used as the low-dimensional representation of data because it reflects the distribution on the synthesis dictionary atoms.Manifold regularization is imposed on the low-dimensional representation of data to keep the locality of the original feature space.Experiments on four datasets show that the proposed unsupervised dimension reduction model outperforms the state-of-the art methods.For multi-view case,we propose a novel multi-view predictive latent space learning(MVP)model and apply it to multi-view clustering and unsupervised dimension reduction.The latent space is forced to be predictive by maximizing the correlation between the latent space and feature space of each view.By learning a multi-view graph with adaptive view-weight learning,MVP effectively combines the complementary information from multi-view data.Experimental results on benchmark datasets show that MVP outperforms the state-of-the-art unsupervised dimension reduction and multi-view clustering algorithms.Unsupervised subspace learning based on latent space is the focus of this paper.We consider sufficiently the characteristics of single-view and multi-view high-dimensional data.ASDL and MVP subspace learning algorithm are proposed in this paper,and the result of experiment embodied the proposed methods are indeed a good solution.