In the era of big data, it is becoming common to have data with multiple modalities or coming from multiple sources, known as "multi-view data". Multi-view data are usually unlabeled and come from high-dimensional spaces (such as language vocabularies), unsupervised multi-view feature selection is crucial to many applications. However, it is nontrivial due to the following challenges. First, there are too many instances or the feature dimensionality is too large. Thus, the data may not fit in memory. How to select useful features with limited memory space? Second, how to select features from streaming data and handles the concept drift? Third, how to leverage the consistent and complementary information from different views to improve the feature selection in the situation when the data are too big or come in as streams? To the best of our knowledge, none of the previous works can solve all the challenges simultaneously. In this paper, we propose an Online unsupervised Multi-View Feature Selection, OMVFS, which deals with large-scale streaming multi-view data in an online fashion. OMVFS embeds unsupervised feature selection into a clustering algorithm via NMF with sparse learning. It further incorporates the graph regularization to preserve the local structure information and help select discriminative features. Instead of storing all the historical data, OMVFS processes the multi-view data chunk by chunk and aggregates all the necessary information into several small matrices. By using the buffering technique, the proposed OMVFS can reduce the computational and storage cost while taking advantage of the structure information. Furthermore, OMVFS can capture the concept drifts in the data streams. Extensive experiments on four real-world datasets show the effectiveness and efficiency of the proposed OMVFS method. More importantly, OMVFS is about 100 times faster than the off-line methods.
Nonnegative matrix factorization @cite_8 , especially online NMF, is the third area that is related to our work. NMF has been successfully used in unsupervised learning @cite_31 @cite_23 . However, traditional NMF cannot deal with large-scale data. Different variations were proposed in the last few years. For example, @cite_0 proposed an online NMF algorithm for document clustering. @cite_22 proposed an efficient online NMF algorithm (OR-NMF) that takes one sample or a chunk of samples per step and updates the bases via robust hastic approximation. All the online NMF methods either focus on clustering or dimension reduction. None of them are designed for feature selection. Furthermore, none of them can handle multi-view data. However, our proposed OMVFS directly embeds feature selection into the online joint NMF framework with graph regularization, which handles large streaming multi-view data.
@cite_22 @cite_8 @cite_0 @cite_23 @cite_31
2121281940 2135029798 2043545458 2108119513
Nonnegative matrix factorization (NMF) has become a popular dimension-reduction method and has been widely applied to image processing and pattern recognition problems. However, conventional NMF learning methods require the entire dataset to reside in the memory and thus cannot be applied to large-scale or streaming datasets. In this paper, we propose an efficient online RSA-NMF algorithm (OR-NMF) that learns NMF in an incremental fashion and thus solves this problem. In particular, OR-NMF receives one sample or a chunk of samples per step and updates the bases via robust stochastic approximation. Benefitting from the smartly chosen learning rate and averaging technique, OR-NMF converges at the rate of in each update of the bases. Furthermore, we prove that OR-NMF almost surely converges to a local optimal solution by using the quasi-martingale. By using a buffering strategy, we keep both the time and space complexities of one step of the OR-NMF constant and make OR-NMF suitable for large-scale or streaming datasets. Preliminary experimental results on real-world datasets show that OR-NMF outperforms the existing online NMF (ONMF) algorithms in terms of efficiency. Experimental results of face recognition and image annotation on public datasets confirm the effectiveness of OR-NMF compared with the existing ONMF algorithms. Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown to minimize the conventional least squares error while the other minimizes the generalized Kullback-Leibler divergence. The monotonic convergence of both algorithms can be proven using an auxiliary function analogous to that used for proving convergence of the Expectation-Maximization algorithm. The algorithms can also be interpreted as diagonally rescaled gradient descent, where the rescaling factor is optimally chosen to ensure convergence. Currently, most research on nonnegative matrix factorization (NMF)focus on 2-factor @math factorization. We provide a systematicanalysis of 3-factor @math NMF. While it unconstrained 3-factor NMF is equivalent to it unconstrained 2-factor NMF, itconstrained 3-factor NMF brings new features to it constrained 2-factor NMF. We study the orthogonality constraint because it leadsto rigorous clustering interpretation. We provide new rules for updating @math and prove the convergenceof these algorithms. Experiments on 5 datasets and a real world casestudy are performed to show the capability of bi-orthogonal 3-factorNMF on simultaneously clustering rows and columns of the input datamatrix. We provide a new approach of evaluating the quality ofclustering on words using class aggregate distribution andmulti-peak distribution. We also provide an overview of various NMF extensions andexamine their relationships. Matrix factorization techniques have been frequently applied in information retrieval, computer vision, and pattern recognition. Among them, Nonnegative Matrix Factorization (NMF) has received considerable attention due to its psychological and physiological interpretation of naturally occurring data whose representation may be parts based in the human brain. On the other hand, from the geometric perspective, the data is usually sampled from a low-dimensional manifold embedded in a high-dimensional ambient space. One then hopes to find a compact representation,which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure. In this paper, we propose a novel algorithm, called Graph Regularized Nonnegative Matrix Factorization (GNMF), for this purpose. In GNMF, an affinity graph is constructed to encode the geometrical information and we seek a matrix factorization, which respects the graph structure. Our empirical study shows encouraging results of the proposed algorithm in comparison to the state-of-the-art algorithms on real-world problems.