Low-rank Assumption Research Articles

Global and local multi-view multi-label learning with incomplete views and labels

Multi-view multi-label learning is widely used in multiple fields, and it aims to process data sets represented by multiple forms (views) and labeled by multiple classes. But most real-world data sets maybe loss some labels and views due to lack of manpower and equipment failure and this causes some difficulties in processing data sets. In this paper, we develop a global and local multi-view multi-label learning with incomplete views and labels (GLMVML-IVL) to process this. In GLMVML-IVL, the usage of label-specific features indicates that class label is determined by some specific features rather than all features; global and local label correlations are taken into consideration with clustering technology; the construction of the pseudo-class label matrix offsets the defect of missing (partial) labels; the adoption of low-rank assumption matrix restores incomplete views; a consensus multi-view representation is put to use to encode the complementary information from different views; the regularizer imposed on label matrix reflects the partial pairwise constraints. Different from traditional methods, this is the first attempt to design a multi-view multi-label learning method with incomplete views and labels by the learning of label-specific features, pseudo-class label matrix, low-rank assumption matrix, global and local label correlations, complementary information, and regularizer imposed on label matrix. Experimental results validate that GLMVML-IVL improves the performance of traditional multi-view multi-label learning methods in statistical and achieves a better performance.

Robust Structural Low-Rank Tracking

Visual object tracking is an essential task for many computer vision applications. It becomes very challenging when the target appearance changes especially in the presence of occlusion, background clutter, and sudden illumination variations. Methods, that incorporate sparse representation and low-rank assumptions on the target particles have achieved promising results. However, because of the lack of structural constraints, these methods show performance degradation when facing the aforementioned challenges. To alleviate these limitations, we propose a new structural low-rank modeling algorithm for robust object tracking in complex scenarios. In the proposed algorithm, we consider spatial and temporal appearance consistency constraints, among the particles in the low-rank subspace, embedded in four different graphs. The resulting objective function encoding these constraints is novel and it is solved using linearized alternating direction method with adaptive penalty both in batch fashion as well as in online fashion. Our proposed objective function jointly learns the spatial and temporal structure of the target particles in consecutive frames and makes the proposed tracker consistent against many complex tracking scenarios. Results on four challenging datasets demonstrate excellent performance of the proposed algorithm as compared to current state-of-the-art methods.

Local low rank approximation with a parametric disparity model for light field compression.

We address the problem of light field dimensionality reduction for compression. We describe a local low rank approximation method using a parametric disparity model. The local support of the approximation is defined by super-rays. A super-ray can be seen as a set of super-pixels that are coherent across all light field views. A dedicated super-ray construction method is first described that constrains the super-pixels forming a given super-ray to be all of the same shape and size, dealing with occlusions. This constraint is needed so that the super-rays can be used as supports of angular dimensionality reduction based on low rank matrix approximation. The light field low rank assumption depends on how much the views are correlated, i.e. on how well they can be aligned by disparity compensation. We first introduce a parametric model describing the local variations of disparity within each super-ray. We then consider two methods for estimating the model parameters. The first method simply fits the model on an input disparity map. We then introduce a disparity estimation method using a low rank prior. This method alternatively searches for the best parameters of the disparity model and of the low rank approximation. We assess the proposed disparity parametric model, first assuming that the disparity is constant within a super-ray, and second by considering an affine disparity model. We show that using the proposed disparity parametric model and estimation algorithm gives an alignment of super-pixels across views that favours the low rank approximation compared with using disparity estimated with classical computer vision methods. The low rank matrix approximation is computed on the disparity compensated super-rays using a singular value decomposition (SVD). A coding algorithm is then described for the different components of the proposed disparity-compensated low rank approximation. Experimental results show performance gains, with a rate saving going up to 92.61%, compared with the JPEG Pleno anchor, for real light fields captured by a Lytro Illum camera. The rate saving goes up to 37.72% with synthetic light fields. The approach is also shown to outperform an HEVC-based light field compression scheme.

Semi-Supervised Multichannel Speech Enhancement With a Deep Speech Prior

This paper describes a semi-supervised multichannel speech enhancement method that uses clean speech data for prior training. Although multichannel nonnegative matrix factorization (MNMF) and its constrained variant called independent low-rank matrix analysis (ILRMA) have successfully been used for unsupervised speech enhancement, the low-rank assumption on the power spectral densities (PSDs) of all sources (speech and noise) does not hold in reality. To solve this problem, we replace a low-rank speech model with a deep generative speech model, i.e., formulate a probabilistic model of noisy speech by integrating a deep speech model, a low-rank noise model, and a full-rank or rank-1 model of spatial characteristics of speech and noise. The deep speech model is trained from clean speech data in an unsupervised auto-encoding variational Bayesian manner. Given multichannel noisy speech spectra, the full-rank or rank-1 spatial covariance matrices and PSDs of speech and noise are estimated in an unsupervised maximum-likelihood manner. Experimental results showed that the full-rank version of the proposed method was significantly better than MNMF, ILRMA, and the rank-1 version. We confirmed that the initialization-sensitivity and local-optimum problems of MNMF with many spatial parameters can be solved by incorporating the precise speech model.

Intelligent Missing Shots’ Reconstruction Using the Spatial Reciprocity of Green’s Function Based on Deep Learning

The trace interval in the common shot and receiver gathers is always inconsistent. The inconsistency affects the final performance of seismic data processing, and the reconstruction methods can enhance the consistency. Unfortunately, most interpolation algorithms are suitable in randomly missing cases, and the difficulty increases sharply in regularly missing cases, especially with big gaps. As deep learning (DL) has a strong self-learning ability in nonlinear characterizations to avoid linear events, sparsity, and low rank assumptions, we introduce DL into missing shots’ reconstruction. The spatial reciprocity of Green’s function is used to provide reasonable training data sets. First, the residual learning networks (ResNets) and the interpolation issue are briefly illustrated. Then, the spatial reciprocity is reviewed and illustrated qualitatively using the common shot and receiver gathers. The similar features in the common shot and receiver gathers guarantee the reasonability to regard the common shot gathers as the training sets and to regard the common receiver gathers as the test sets. The common shot gathers are divided into the training sets to train ResNets and the validation sets to verify the performance of the trained ResNets. Finally, the trained ResNets are used to reconstruct missing shots intelligently in the common receiver gather. Three different data sets are used to prove the validity of the proposed strategy. After reconstruction, the events are more continuous with less serrations and serious frequency wavenumber (FK) aliasing is attenuated effectively. The reconstructed data with a better consistency can improve the accuracy of migration and the final reservoir characterization.

Robust weighted SVD-type latent factor models for rating prediction

Recommending system is a popular tool in many commercial or social platforms which finds interesting products for users based on their preference history. Predicting the ratings of items, such as movies, plays an essential role in the recommending system. In this context, we develop a new type of latent factor models by attaching weights to the entries of the incomplete ratings matrix. The weights are computed after estimating the user/item mean errors caused by the basic SVD model under the low-rank assumption on the ratings matrix. To accelerate the optimization process of our proposed models and other existing SVD-type models, a special design of the initial guess is suggested. In the experiments on real-world datasets, the proposed weighted models outperform other SVD-type methods, and the usage of the special initial guess improves the optimization significantly, obtaining lower MRSEs within fixed number of iterations, in comparison with the random initial guess. Furthermore, artificially noised datasets are taken to evaluate the methods, where the weighted models still perform better than other SVD-type models, implying their effectiveness and robustness in noised environment.

Guaranteed recovery of quantum processes from few measurements

Quantum process tomography is the task of reconstructing unknown quantum channels from measured data. In this work, we introduce compressed sensing-based methods that facilitate the reconstruction of quantum channels of low Kraus rank. Our main contribution is the analysis of a natural measurement model for this task: We assume that data is obtained by sending pure states into the channel and measuring expectation values on the output. Neither ancillary systems nor coherent operations across multiple channel uses are required. Most previous results on compressed process reconstruction reduce the problem to quantum state tomography on the channel's Choi matrix. While this ansatz yields recovery guarantees from an essentially minimal number of measurements, physical implementations of such schemes would typically involve ancillary systems. A priori, it is unclear whether a measurement model tailored directly to quantum process tomography might require more measurements. We establish that this is not the case.Technically, we prove recovery guarantees for three different reconstruction algorithms. The reconstructions are based on a trace, diamond, and ℓ2-norm minimization, respectively. Our recovery guarantees are uniform in the sense that with one random choice of measurement settings all quantum channels can be recovered equally well. Moreover, stability against arbitrary measurement noise and robustness against violations of the low-rank assumption is guaranteed. Numerical studies demonstrate the feasibility of the approach.

Drug repositioning based on bounded nuclear norm regularization.

MotivationComputational drug repositioning is a cost-effective strategy to identify novel indications for existing drugs. Drug repositioning is often modeled as a recommendation system problem. Taking advantage of the known drug–disease associations, the objective of the recommendation system is to identify new treatments by filling out the unknown entries in the drug–disease association matrix, which is known as matrix completion. Underpinned by the fact that common molecular pathways contribute to many different diseases, the recommendation system assumes that the underlying latent factors determining drug–disease associations are highly correlated. In other words, the drug–disease matrix to be completed is low-rank. Accordingly, matrix completion algorithms efficiently constructing low-rank drug–disease matrix approximations consistent with known associations can be of immense help in discovering the novel drug–disease associations.ResultsIn this article, we propose to use a bounded nuclear norm regularization (BNNR) method to complete the drug–disease matrix under the low-rank assumption. Instead of strictly fitting the known elements, BNNR is designed to tolerate the noisy drug–drug and disease–disease similarities by incorporating a regularization term to balance the approximation error and the rank properties. Moreover, additional constraints are incorporated into BNNR to ensure that all predicted matrix entry values are within the specific interval. BNNR is carried out on an adjacency matrix of a heterogeneous drug–disease network, which integrates the drug–drug, drug–disease and disease–disease networks. It not only makes full use of available drugs, diseases and their association information, but also is capable of dealing with cold start naturally. Our computational results show that BNNR yields higher drug–disease association prediction accuracy than the current state-of-the-art methods. The most significant gain is in prediction precision measured as the fraction of the positive predictions that are truly positive, which is particularly useful in drug design practice. Cases studies also confirm the accuracy and reliability of BNNR.Availability and implementationThe code of BNNR is freely available at https://github.com/BioinformaticsCSU/BNNR.Supplementary information Supplementary data are available at Bioinformatics online.

Hyperspectral Super-Resolution via Global–Local Low-Rank Matrix Estimation

Hyperspectral super-resolution (HSR) is a problem that aims to estimate an image of high spectral and spatial resolutions from a pair of co-registered multispectral (MS) and hyperspectral (HS) images, which have coarser spectral and spatial resolutions, respectively. In this paper we pursue a low-rank matrix estimation approach for HSR. We assume that the spectral-spatial matrices associated with the whole image and the local areas of the image have low-rank structures. The local low-rank assumption, in particular, has the aim of providing a more flexible model for accounting for local variation effects due to endmember variability. We formulate the HSR problem as a global-local rank-regularized least-squares problem. By leveraging on the recent advances in non-convex large-scale optimization, namely, the smooth Schatten-p approximation and the accelerated majorization-minimization method, we develop an efficient algorithm for the global-local low-rank problem. Numerical experiments on synthetic, semi-real and real data show that the proposed algorithm outperforms a number of benchmark algorithms in terms of recovery performance.

Deep-learning-based seismic data interpolation: A preliminary result

Seismic data interpolation is a longstanding issue. Most current methods are only suitable for randomly missing cases. To deal with regularly missing cases, an antialiasing strategy should be included. However, seismic survey design using a random distribution of shots and receivers is always operationally challenging and impractical. We have used deep-learning-based approaches for seismic data antialiasing interpolation, which could extract deeper features of the training data in a nonlinear way by self-learning. It can also avoid linear events, sparsity, and low-rank assumptions of the traditional interpolation methods. Based on convolutional neural networks, eight-layers residual learning networks (ResNets) with a better back-propagation property for deep layers is designed for interpolation. Detailed training analysis is also performed. A set of simulated data is used to train the designed ResNets. The performance is assessed with several synthetic and field data. Numerical examples indicate that the trained ResNets can help to reconstruct regularly missing traces with high accuracy. The interpolated results in the time-space domain and the frequency-wavenumber ([Formula: see text]-[Formula: see text]) domain demonstrate the validity of the trained ResNets. Even though the accuracy decreases with the increase of the feature difference between the test and training data, the proposed method can still provide reasonable interpolation results. Finally, the trained ResNets is used to reconstruct dense data with halved trace intervals for synthetic and field data. The reconstructed dense data are more continuous along the spatial direction, and the spatial aliasing effects disappear in the [Formula: see text]-[Formula: see text] domain. The reconstructed dense data have the potential to improve the accuracy of subsequent seismic data processing and inversion.

General Collaborative Filtering for Web Service QoS Prediction

To avoid the expensive and time-consuming evaluation, collaborative filtering (CF) methods have been widely studied for web service QoS prediction in recent years. Among the various CF techniques, matrix factorization is the most popular one. Much effort has been devoted to improving matrix factorization collaborative filtering. The key idea of matrix factorization is that it assumes the rating matrix is low rank and projects users and services into a shared low-dimensional latent space, making a prediction by using the dot product of a user latent vector and a service latent vector. Unfortunately, unlike the recommender systems, QoS usually takes continuous values with very wide range, and the low rank assumption might incur high bias. Furthermore, when the QoS matrix is extremely sparse, the low rank assumption also incurs high variance. To reduce the bias, we must use more complex assumptions. To reduce the variance, we can adopt complex regularization techniques. In this paper, we proposed a neural network based framework, named GCF (general collaborative filtering), with the dropout regularization, to model the user-service interactions. We conduct our experiments on a large real-world dataset, the QoS values of which are obtained from 339 users on 5825 web services. The comprehensive experimental studies show that our approach offers higher prediction accuracy than the traditional collaborative filtering approaches.

Double truncated nuclear norm-based matrix decomposition with application to background modeling

Many topics in pattern recognition and machine learning, such as subspace learning, image restoration, background modeling, can be viewed as the matrix decomposing problem. Double nuclear norm-based matrix decomposition (DNMD) is a new emerging method for dealing with the image data corrupted by continuous occlusion. The method uses a unified low rank assumption to characterize the real image data and continuous occlusion. However, one major limitation of the nuclear norm is that each singular value is treated equally, since the nuclear norm is defined as the sum of all singular values. Thus the rank function may not be well approximated in practice. To overcome this drawback, this paper presents double truncated nuclear norm-based matrix decomposition (DTNMD). The truncated nuclear norm can reflect the rank function more accurate and robust. Experimental results show encouraging results of the proposed algorithm in comparison to the state-of-the-art matrix completion methods on both synthetic and real visual datasets.

Double Low-Rank and Sparse Decomposition for Surface Defect Segmentation of Steel Sheet

Surface defect segmentation supports real-time surface defect detection system of steel sheet by reducing redundant information and highlighting the critical defect regions for high-level image understanding. Existing defect segmentation methods usually lack adaptiveness to different shape, size and scale of the defect object. Based on the observation that the defective area can be regarded as the salient part of image, a saliency detection model using double low-rank and sparse decomposition (DLRSD) is proposed for surface defect segmentation. The proposed method adopts a low-rank assumption which characterizes the defective sub-regions and defect-free background sub-regions respectively. In addition, DLRSD model uses sparse constrains for background sub-regions so as to improve the robustness to noise and uneven illumination simultaneously. Then the Laplacian regularization among spatially adjacent sub-regions is incorporated into the DLRSD model in order to uniformly highlight the defect object. Our proposed DLRSD-based segmentation method consists of three steps: firstly, using DLRSD model to obtain the defect foreground image; then, enhancing the foreground image to establish the good foundation for segmentation; finally, the Otsu’s method is used to choose an optimal threshold automatically for segmentation. Experimental results demonstrate that the proposed method outperforms state-of-the-art approaches in terms of both subjective and objective tests. Meanwhile, the proposed method is applicable to industrial detection with limited computational resources.

Image and Spectrum Image Denoising under the local low Rank Assumption

Image and Spectrum Image Denoising under the local low Rank Assumption

Quantization for low-rank matrix recovery

Abstract We study Sigma–Delta $(\varSigma\!\varDelta) $ quantization methods coupled with appropriate reconstruction algorithms for digitizing randomly sampled low-rank matrices. We show that the reconstruction error associated with our methods decays polynomially with the oversampling factor, and we leverage our results to obtain root-exponential accuracy by optimizing over the choice of quantization scheme. Additionally, we show that a random encoding scheme, applied to the quantized measurements, yields a near-optimal exponential bit rate. As an added benefit, our schemes are robust both to noise and to deviations from the low-rank assumption. In short, we provide a full generalization of analogous results, obtained in the classical setup of band-limited function acquisition, and more recently, in the finite frame and compressed sensing setups to the case of low-rank matrices sampled with sub-Gaussian linear operators. Finally, we believe our techniques for generalizing results from the compressed sensing setup to the analogous low-rank matrix setup is applicable to other quantization schemes.

Manifold regularized matrix completion for multi-label learning with ADMM

Multi-label learning is a common machine learning problem arising from numerous real-world applications in diverse fields, e.g, natural language processing, bioinformatics, information retrieval and so on. Among various multi-label learning methods, the matrix completion approach has been regarded as a promising approach to transductive multi-label learning. By constructing a joint matrix comprising the feature matrix and the label matrix, the missing labels of test samples are regarded as missing values of the joint matrix. With the low-rank assumption of the constructed joint matrix, the missing labels can be recovered by minimizing its rank. Despite its success, most matrix completion based approaches ignore the smoothness assumption of unlabeled data, i.e., neighboring instances should also share a similar set of labels. Thus they may under exploit the intrinsic structures of data. In addition, the matrix completion problem can be less efficient. To this end, we propose to efficiently solve the multi-label learning problem as an enhanced matrix completion model with manifold regularization, where the graph Laplacian is used to ensure the label smoothness over it. To speed up the convergence of our model, we develop an efficient iterative algorithm, which solves the resulted nuclear norm minimization problem with the alternating direction method of multipliers (ADMM). Experiments on both synthetic and real-world data have shown the promising results of the proposed approach.

Light Field inpainting propagation via Low Rank Matrix completion.

Building up on the advances in low rank matrix completion, this article presents a novel method for propagating the inpainting of the central view of a light field to all the other views. After generating a set of warped versions of the inpainted central view with random homographies, both the original light field views and the warped ones are vectorized and concatenated into a matrix. Because of the redundancy between the views, the matrix satisfies a low rank assumption enabling us to fill the region to inpaint with low rank matrix completion. To this end, a new matrix completion algorithm, better suited to the inpainting application than existing methods, is also developed in this paper. In its simple form, our method does not require any depth prior, unlike most existing light field inpainting algorithms. The method has then been extended to better handle the case where the area to inpaint contains depth discontinuities. In this case, a segmentation map of the different depth layers of the inpainted central view is required. This information is used to warp the depth layers with different homographies. Our experiments with natural light fields captured with plenoptic cameras demonstrate the robustness of the low rank approach to noisy data as well as large color and illumination variations between the views of the light field.

Procrustean Regression: A Flexible Alignment-Based Framework for Nonrigid Structure Estimation.

Non-rigid structure from motion (NRSfM) is a fundamental problem of computer vision. Recently, it has been shown that incorporating shape alignment in NRSfM can improve the performance significantly compared with the other algorithms, which do not consider shape alignment. However, realizing this idea was at a cost of a heavy, complicated process, which limits its usefulness and possible extensions. In this paper, we propose a novel regression framework for NRSfM, of which the variables (3D shapes) are regularized based on their aligned shapes. We show that this can be casted into an unconstrained problem or a problem with simple bound constraints, which can be efficiently solved by existing solvers. This framework can be easily integrated with numerous existing models and assumptions, such as orthographic or perspective camera models, occlusion, low-rank assumption, smooth deformations, and so on, which makes it more practical for various real situations. The experimental results show that the proposed method gives competitive result to the state-of-the-art methods for orthographic projection with much less time complexity and memory requirement, and outperforms the existing methods for perspective projection.

Saliency fusion via sparse and double low rank decomposition

Video surveillance-oriented biometrics is a very challenging task and has tremendous significance to the security of public places. Saliency detection can support video surveillance systems by reducing redundant information and highlighting the critical regions, e.g., faces. Existing saliency detection models usually behave differently over an individual image, and meanwhile these methods often complement each other. This paper addresses the problem of fusing various saliency detection methods such that the fusion result outperforms each of the individual methods. A novel sparse and double low rank decomposition model (SDLRD) is proposed for such a purpose. Given an image described by multiple saliency maps, SDLRD uses a unified low rank assumption to characterize the object regions and background regions respectively. Furthermore, SDLRD depicts the noises covered on the whole image by a sparse matrix, based on the observation that the noises generally lie in a sparse subspace. After reducing the influence by noises, the correlations among object and background regions can be enhanced simultaneously. In this way, an image is represented as the combination of a sparse matrix plus two low rank matrices. As such, we cast the saliency fusion as a subspace decomposition problem and aim at inferring the low rank one that indicates the salient target. Experiments on five datasets demonstrate that our fusion method consistently outperforms each individual saliency method and other state-of-the-art saliency fusion approaches. Specifically, the proposed method is demonstrated to be effective on the applications of video-based biometrics such as face detection.

Indefinite Core Vector Machine

The recently proposed Krĕin space Support Vector Machine (KSVM) is an efficient classifier for indefinite learning problems, but with quadratic to cubic complexity and a non-sparse decision function. In this paper a Krĕin space Core Vector Machine (iCVM) solver is derived. A sparse model with linear runtime complexity can be obtained under a low rank assumption. The obtained iCVM models can be applied to indefinite kernels without additional preprocessing. Using iCVM one can solve CVM with usually troublesome kernels having large negative eigenvalues or large numbers of negative eigenvalues. Experiments show that our algorithm is similar efficient as the Krĕin space Support Vector Machine but with substantially lower costs, such that also large scale problems can be processed.