In real-world applications, not all instances in multi-view data are fully represented. To deal with incomplete multi-view data, traditional multi-view algorithms usually throw away the incomplete instances, resulting in loss of available information. To overcome this loss, Incomplete Multi-view Learning (IML) has become a hot research topic. In this paper, we propose a general IML framework for unifying existing IML methods and gaining insight into IML. The proposed framework jointly performs embedding learning and low-rank approximation. Concretely, it approximates the incomplete data by a set of low-rank matrices and learns a full and common embedding by linear transformation. Several existing IML methods can be unified as special cases of the framework. More interestingly, some linear transformation based full-view methods can be adapted to IML directly with the guidance of the framework. This bridges the gap between full multi-view learning and IML. Moreover, the framework can provide guidance for developing new algorithms. For illustration, within the framework, we propose a specific method, termed as Incomplete Multi-view Learning with Block Diagonal Representation (IML-BDR). Based on the assumption that the sampled examples have approximate linear subspace structure, IML-BDR uses the block diagonal structure prior to learn the full embedding, which would lead to more correct clustering. A convergent alternating iterative algorithm with the Successive Over-Relaxation (SOR) optimization technique is devised for optimization. Experimental results on various datasets demonstrate the effectiveness of IML-BDR.
The Incomplete Multi-modality Grouping (IMG) approach can be regarded as an enhanced version of PVC. Differently, IMG gets rid of the nonnegative constraint and considers the global structure in the latent space @cite_32 . Using the same notations with PVC, the latent representation of all samples can be denoted as @math . With a Laplacian graph regularization (LGR) to capture the global structure, the objective function of IMG is where @math is the Laplacian matrix of similarity matrix @math , @math , @math and @math are positive parameters.
@cite_32
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Nowadays multi-modal visual data are much easier to access as the technology develops. Nevertheless, there is an underlying problem hidden behind the emerging multi-modality techniques: What if one more modal data fail? Motivated by this question, we propose an unsupervised method which well handles the incomplete multimodal data by transforming the original and incomplete data to a new and complete representation in a latent space. Different from the existing efforts that simply project data from each modality into a common subspace, a novel graph Laplacian term with a good probabilistic interpretation is proposed to couple the incomplete multi-modal samples. In such a way, a compact global structure over the entire heterogeneous data is well preserved, leading to a strong grouping discriminability. As a non-trivial contribution, we provide the optimization solution to the proposed model. In experiments, we extensively test our method and competitors on one synthetic data, two RGB-D video datasets and two image datasets. The superior results validate the benefits of the proposed method, especially when multimodal data suffer from large incompleteness. Localizing objects in cluttered backgrounds is a challenging task in weakly supervised localization. Due to large object variations in cluttered images, objects have large ambiguity with backgrounds. However, backgrounds contain useful latent information, e.g., the sky for aeroplanes. If we can learn this latent information, object-background ambiguity can be reduced to suppress the background. In this paper, we propose the latent category learning (LCL), which is an unsupervised learning problem given only image-level class labels. Firstly, inspired by the latent semantic discovery, we use the typical probabilistic Latent Semantic Analysis (pLSA) to learn the latent categories, which can represent objects, object parts or backgrounds. Secondly, to determine which category contains the target object, we propose a category selection method evaluating each category’s discrimination. We evaluate the method on the PASCAL VOC 2007 database and ILSVRC 2013 detection challenge. On VOC 2007, the proposed method yields the annotation accuracy of 48 , which outperforms previous results by 10 . More importantly, we achieve the detection average precision of 30.9 , which improves previous results by 8 and can be competitive with the supervised deformable part model (DPM) 5.0 baseline 33.7 . On ILSVRC 2013 detection, the method yields the precision of 6.0 , which is also competitive with the DPM 5.0. 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. We propose a multi-input multi-output fully convolutional neural network model for MRI synthesis. The model is robust to missing data, as it benefits from, but does not require, additional input modalities. The model is trained end-to-end, and learns to embed all input modalities into a shared modality-invariant latent space. These latent representations are then combined into a single fused representation, which is transformed into the target output modality with a learnt decoder. We avoid the need for curriculum learning by exploiting the fact that the various input modalities are highly correlated. We also show that by incorporating information from segmentation masks the model can both decrease its error and generate data with synthetic lesions. We evaluate our model on the ISLES and BRATS data sets and demonstrate statistically significant improvements over state-of-the-art methods for single input tasks. This improvement increases further when multiple input modalities are used, demonstrating the benefits of learning a common latent space, again resulting in a statistically significant improvement over the current best method. Finally, we demonstrate our approach on non skull-stripped brain images, producing a statistically significant improvement over the previous best method. Code is made publicly available at https: github.com agis85 multimodal_brain_synthesis .