In this paper, we propose a speed-up approach for subclass discriminant analysis and formulate a novel efficient multi-view solution to it. The speed-up approach is developed based on graph embedding and spectral regression approaches that involve eigendecomposition of the corresponding Laplacian matrix and regression to its eigenvectors. We show that by exploiting the structure of the between-class Laplacian matrix, the eigendecomposition step can be substituted with a much faster process. Furthermore, we formulate a novel criterion for multi-view subclass discriminant analysis and show that an efficient solution for it can be obtained in a similar to the single-view manner. We evaluate the proposed methods on nine single-view and nine multi-view datasets and compare them with related existing approaches. Experimental results show that the proposed solutions achieve competitive performance, often outperforming the existing methods. At the same time, they significantly decrease the training time.
In multi-view learning, the data @math is described from @math views and we seek to find @math matrices @math that project the data @math from all views @math to a common (latent) space, where the separability between the classes is the highest. A generalized framework for multi-view subspace learning, that includes many of the existing methods as special cases, was proposed in @cite_0 . Here, the optimization problem is defined as where @math and @math are the inter-view and intra-view covariance matrices. The solution is obtained by solving the generalized eigendecomposition problem ), where @math is the projection matrix of the view @math . The feature vectors in the latent space are obtained as @math , where @math is data representation in the view @math . =1pt Here, ), ), ), where @math is either @math or @math , as defined below, @math and @math are the view labels, and @math is the number of views.
@cite_0
1989529706 2156872152 1670132599 2090101874
Multiview representations reveal the fundamental attributes of the studied instances from different perspectives. Some common perspectives are reviewed by multiple views simultaneously, while some specific ones are reflected by individual views. That is, there are two kinds of properties embedded in the multiview data: 1) consistency and 2) complementarity. Different from most multiview learning approaches only focusing on either consistency or complementarity, this paper proposes a novel semisupervised multiview learning algorithm, called partially shared latent factor (PSLF) learning, which jointly exploits both consistent and complementary information among multiple views. In PSLF, a nonnegative matrix factorization (NMF)-based formulation is adopted to learn a compact and comprehensive partially shared latent representation, which is composed of common latent factors shared by multiple views and some specific latent factors to each view. With the learned representations of multiview data, we introduce a robust sparse regression model to predict the cluster labels of labeled data. By integrating the NMF-based model and the regression model, we obtain a unified formulation and propose a multiplicative-based alternative algorithm for optimization. In addition, PSLF can learn the weights of different views adaptively according to the reconstruction precisions of data matrices. Our experimental study indicates different multiview data that contains consistent and complementary information in different degrees. In addition, the encouraging results of the proposed algorithm are achieved in comparison with the state-of-the-art algorithms on real-world data sets. Recent approaches to multi-view learning have shown that factorizing the information into parts that are shared across all views and parts that are private to each view could effectively account for the dependencies and independencies between the different input modalities. Unfortunately, these approaches involve minimizing non-convex objective functions. In this paper, we propose an approach to learning such factorized representations inspired by sparse coding techniques. In particular, we show that structured sparsity allows us to address the multi-view learning problem by alternately solving two convex optimization problems. Furthermore, the resulting factorized latent spaces generalize over existing approaches in that they allow having latent dimensions shared between any subset of the views instead of between all the views only. We show that our approach outperforms state-of-the-art methods on the task of human pose estimation. In recent years, a great many methods of learning from multi-view data by considering the diversity of different views have been proposed. These views may be obtained from multiple sources or different feature subsets. In trying to organize and highlight similarities and differences between the variety of multi-view learning approaches, we review a number of representative multi-view learning algorithms in different areas and classify them into three groups: 1) co-training, 2) multiple kernel learning, and 3) subspace learning. Notably, co-training style algorithms train alternately to maximize the mutual agreement on two distinct views of the data; multiple kernel learning algorithms exploit kernels that naturally correspond to different views and combine kernels either linearly or non-linearly to improve learning performance; and subspace learning algorithms aim to obtain a latent subspace shared by multiple views by assuming that the input views are generated from this latent subspace. Though there is significant variance in the approaches to integrating multiple views to improve learning performance, they mainly exploit either the consensus principle or the complementary principle to ensure the success of multi-view learning. Since accessing multiple views is the fundament of multi-view learning, with the exception of study on learning a model from multiple views, it is also valuable to study how to construct multiple views and how to evaluate these views. Overall, by exploring the consistency and complementary properties of different views, multi-view learning is rendered more effective, more promising, and has better generalization ability than single-view learning. Multi-view data is very popular in real-world applications, as different view-points and various types of sensors help to better represent data when fused across views or modalities. Samples from different views of the same class are less similar than those with the same view but different class. We consider a more general case that prior view information of testing data is inaccessible in multi-view learning. Traditional multi-view learning algorithms were designed to obtain multiple view-specific linear projections and would fail without this prior information available. That was because they assumed the probe and gallery views were known in advance, so the correct view-specific projections were to be applied in order to better learn low-dimensional features. To address this, we propose a Low-Rank Common Subspace (LRCS) for multi-view data analysis, which seeks a common low-rank linear projection to mitigate the semantic gap among different views. The low-rank common projection is able to capture compatible intrinsic information across different views and also well-align the within-class samples from different views. Furthermore, with a low-rank constraint on the view-specific projected data and that transformed by the common subspace, the within-class samples from multiple views would concentrate together. Different from the traditional supervised multi-view algorithms, our LRCS works in a weakly supervised way, where only the view information gets observed. Such a common projection can make our model more flexible when dealing with the problem of lacking prior view information of testing data. Two scenarios of experiments, robust subspace learning and transfer learning, are conducted to evaluate our algorithm. Experimental results on several multi-view datasets reveal that our proposed method outperforms state-of-the-art, even when compared with some supervised learning methods.